Package evaluation of ExactODEReduction on Julia 1.10.8 (92f03a4775*) started at 2025-02-25T17:42:00.592


################################################################################
# Set-up
#

Installing PkgEval dependencies (TestEnv)...

Set-up completed after 4.98s


################################################################################
# Installation
#

Installing ExactODEReduction...
   Resolving package versions...
    Updating `~/.julia/environments/v1.10/Project.toml`
  [790186a0] + ExactODEReduction v0.1.0
    Updating `~/.julia/environments/v1.10/Manifest.toml`
  [47edcb42] + ADTypes v1.13.0
⌅ [c3fe647b] + AbstractAlgebra v0.27.10
  [1520ce14] + AbstractTrees v0.4.5
  [7d9f7c33] + Accessors v0.1.41
  [79e6a3ab] + Adapt v4.2.0
  [66dad0bd] + AliasTables v1.1.3
  [ec485272] + ArnoldiMethod v0.4.0
  [4fba245c] + ArrayInterface v7.18.0
  [4c555306] + ArrayLayouts v1.11.1
  [e2ed5e7c] + Bijections v0.1.9
  [f01c122e] + BinaryWrappers v0.1.3
  [62783981] + BitTwiddlingConvenienceFunctions v0.1.6
  [2a0fbf3d] + CPUSummary v0.2.6
  [00ebfdb7] + CSTParser v3.4.3
  [d360d2e6] + ChainRulesCore v1.25.1
  [fb6a15b2] + CloseOpenIntervals v0.1.13
  [861a8166] + Combinatorics v1.0.2
  [a80b9123] + CommonMark v0.8.15
  [38540f10] + CommonSolve v0.2.4
  [bbf7d656] + CommonSubexpressions v0.3.1
  [f70d9fcc] + CommonWorldInvalidations v1.0.0
  [34da2185] + Compat v4.16.0
  [b152e2b5] + CompositeTypes v0.1.4
  [a33af91c] + CompositionsBase v0.1.2
  [2569d6c7] + ConcreteStructs v0.2.3
⌅ [187b0558] + ConstructionBase v1.5.6
  [adafc99b] + CpuId v0.3.1
  [a8cc5b0e] + Crayons v4.1.1
⌅ [1f15a43c] + CxxWrap v0.12.1
  [9a962f9c] + DataAPI v1.16.0
  [864edb3b] + DataStructures v0.18.20
  [e2d170a0] + DataValueInterfaces v1.0.0
  [55939f99] + DecFP v1.4.1
  [2b5f629d] + DiffEqBase v6.164.1
⌅ [459566f4] + DiffEqCallbacks v2.37.0
  [163ba53b] + DiffResults v1.1.0
  [b552c78f] + DiffRules v1.15.1
  [a0c0ee7d] + DifferentiationInterface v0.6.42
  [b4f34e82] + Distances v0.10.12
  [31c24e10] + Distributions v0.25.117
  [ffbed154] + DocStringExtensions v0.9.3
⌅ [5b8099bc] + DomainSets v0.6.7
⌅ [7c1d4256] + DynamicPolynomials v0.5.7
  [4e289a0a] + EnumX v1.0.4
  [f151be2c] + EnzymeCore v0.8.8
  [790186a0] + ExactODEReduction v0.1.0
  [d4d017d3] + ExponentialUtilities v1.27.0
  [e2ba6199] + ExprTools v0.1.10
  [55351af7] + ExproniconLite v0.10.14
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  [069b7b12] + FunctionWrappers v1.1.3
  [77dc65aa] + FunctionWrappersWrappers v0.1.3
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  [3e5b6fbb] + HostCPUFeatures v0.1.17
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  [2ab3a3ac] + LogExpFunctions v0.3.29
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  [e1d29d7a] + Missings v1.2.0
⌅ [961ee093] + ModelingToolkit v8.75.0
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  [2e0e35c7] + Moshi v0.3.5
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  [d8a4904e] + MutableArithmetics v1.6.4
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⌅ [2edaba10] + Nemo v0.32.7
⌃ [8913a72c] + NonlinearSolve v3.15.1
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⌅ [727e6d20] + SimpleNonlinearSolve v1.12.3
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⌃ [19f23fe9] + SymbolicLimits v0.2.1
⌅ [d1185830] + SymbolicUtils v1.7.1
⌅ [0c5d862f] + Symbolics v5.28.0
  [3783bdb8] + TableTraits v1.0.1
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⌅ [e134572f] + FLINT_jll v200.900.9+0
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⌅ [83958c19] + Perl_jll v5.34.0+2
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  [508c9074] + bliss_jll v0.77.0+1
⌅ [28df3c45] + boost_jll v1.76.0+1
  [f07e07eb] + cddlib_jll v0.94.14+0
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⌅ [3eaa8342] + libcxxwrap_julia_jll v0.9.7+3
⌅ [4d8266f6] + libpolymake_julia_jll v0.8.3+1
  [3873f7d0] + lrslib_jll v0.3.3+0
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⌅ [6690c6e9] + normaliz_jll v300.900.301+0
  [1317d2d5] + oneTBB_jll v2022.0.0+0
⌅ [7c209550] + polymake_jll v400.700.1+1
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  [b27032c2] + LibCURL v0.6.4
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  [37e2e46d] + LinearAlgebra
  [56ddb016] + Logging
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        Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

Installation completed after 12.18s


################################################################################
# Precompilation
#

Precompiling PkgEval dependencies...

Precompiling package dependencies...
ERROR: LoadError: The following 1 direct dependency failed to precompile:

Polymake 

Failed to precompile Polymake [d720cf60-89b5-51f5-aff5-213f193123e7] to "/home/pkgeval/.julia/compiled/v1.10/Polymake/jl_xG64PA".
ERROR: LoadError: InitError: could not load library "/home/pkgeval/.julia/artifacts/beeb384c8ba60497d81e26a28f74ed99aef88791/lib/libcxxwrap_julia.so"
/home/pkgeval/.julia/artifacts/beeb384c8ba60497d81e26a28f74ed99aef88791/lib/libcxxwrap_julia.so: undefined symbol: small_typeof, version JL_LIBJULIA_1.10
Stacktrace:
  [1] dlopen(s::String, flags::UInt32; throw_error::Bool)
    @ Base.Libc.Libdl ./libdl.jl:117
  [2] dlopen(s::String, flags::UInt32)
    @ Base.Libc.Libdl ./libdl.jl:116
  [3] macro expansion
    @ ~/.julia/packages/JLLWrappers/GfYNv/src/products/library_generators.jl:63 [inlined]
  [4] __init__()
    @ libcxxwrap_julia_jll ~/.julia/packages/libcxxwrap_julia_jll/zmDeI/src/wrappers/x86_64-linux-gnu-cxx11-julia_version+1.10.0.jl:9
  [5] run_module_init(mod::Module, i::Int64)
    @ Base ./loading.jl:1193
  [6] register_restored_modules(sv::Core.SimpleVector, pkg::Base.PkgId, path::String)
    @ Base ./loading.jl:1181
  [7] _include_from_serialized(pkg::Base.PkgId, path::String, ocachepath::Nothing, depmods::Vector{Any})
    @ Base ./loading.jl:1126
  [8] _require_search_from_serialized(pkg::Base.PkgId, sourcepath::String, build_id::UInt128)
    @ Base ./loading.jl:1651
  [9] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:2008
 [10] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1882
 [11] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [12] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [13] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1873
 [14] macro expansion
    @ ./loading.jl:1860 [inlined]
 [15] macro expansion
    @ ./lock.jl:267 [inlined]
 [16] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1823
 [17] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [18] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [19] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1816
 [20] include
    @ ./Base.jl:495 [inlined]
 [21] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::String)
    @ Base ./loading.jl:2292
 [22] top-level scope
    @ stdin:4
during initialization of module libcxxwrap_julia_jll
in expression starting at /home/pkgeval/.julia/packages/CxxWrap/IdOJa/src/CxxWrap.jl:1
in expression starting at stdin:4
ERROR: LoadError: Failed to precompile CxxWrap [1f15a43c-97ca-5a2a-ae31-89f07a497df4] to "/home/pkgeval/.julia/compiled/v1.10/CxxWrap/jl_ZtfQik".
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:2539
  [3] compilecache
    @ ./loading.jl:2411 [inlined]
  [4] (::Base.var"#969#970"{Base.PkgId})()
    @ Base ./loading.jl:2044
  [5] mkpidlock(f::Base.var"#969#970"{Base.PkgId}, at::String, pid::Int32; kwopts::@Kwargs{stale_age::Int64, wait::Bool})
    @ FileWatching.Pidfile /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:93
  [6] #mkpidlock#6
    @ /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:88 [inlined]
  [7] trymkpidlock(::Function, ::Vararg{Any}; kwargs::@Kwargs{stale_age::Int64})
    @ FileWatching.Pidfile /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:111
  [8] #invokelatest#2
    @ ./essentials.jl:894 [inlined]
  [9] invokelatest
    @ ./essentials.jl:889 [inlined]
 [10] maybe_cachefile_lock(f::Base.var"#969#970"{Base.PkgId}, pkg::Base.PkgId, srcpath::String; stale_age::Int64)
    @ Base ./loading.jl:3054
 [11] maybe_cachefile_lock
    @ ./loading.jl:3051 [inlined]
 [12] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:2040
 [13] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1882
 [14] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [15] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [16] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1873
 [17] macro expansion
    @ ./loading.jl:1860 [inlined]
 [18] macro expansion
    @ ./lock.jl:267 [inlined]
 [19] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1823
 [20] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [21] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [22] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1816
 [23] include
    @ ./Base.jl:495 [inlined]
 [24] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::Nothing)
    @ Base ./loading.jl:2292
 [25] top-level scope
    @ stdin:4
in expression starting at /home/pkgeval/.julia/packages/Polymake/w7g9z/src/Polymake.jl:1
in expression starting at stdin:
in expression starting at /PkgEval.jl/scripts/precompile.jl:37

Precompilation failed after 194.9s



################################################################################
# Testing
#

     Testing ExactODEReduction
      Status `/tmp/jl_C0wVk1/Project.toml`
⌅ [c3fe647b] AbstractAlgebra v0.27.10
  [790186a0] ExactODEReduction v0.1.0
  [682c06a0] JSON v0.21.4
  [1914dd2f] MacroTools v0.5.15
⌅ [961ee093] ModelingToolkit v8.75.0
⌅ [2edaba10] Nemo v0.32.7
⌅ [d720cf60] Polymake v0.8.3
  [27ebfcd6] Primes v0.5.6
  [ae029012] Requires v1.3.0
⌅ [98d24dd4] TestSetExtensions v2.0.0
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [9a3f8284] Random
  [2f01184e] SparseArrays v1.10.0
  [8dfed614] Test
      Status `/tmp/jl_C0wVk1/Manifest.toml`
  [47edcb42] ADTypes v1.13.0
⌅ [c3fe647b] AbstractAlgebra v0.27.10
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.41
  [79e6a3ab] Adapt v4.2.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.1
  [e2ed5e7c] Bijections v0.1.9
  [f01c122e] BinaryWrappers v0.1.3
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
⌅ [187b0558] ConstructionBase v1.5.6
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
⌅ [1f15a43c] CxxWrap v0.12.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [55939f99] DecFP v1.4.1
  [ab62b9b5] DeepDiffs v1.2.0
  [2b5f629d] DiffEqBase v6.164.1
⌅ [459566f4] DiffEqCallbacks v2.37.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.42
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.117
  [ffbed154] DocStringExtensions v0.9.3
⌅ [5b8099bc] DomainSets v0.6.7
⌅ [7c1d4256] DynamicPolynomials v0.5.7
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.8.8
  [790186a0] ExactODEReduction v0.1.0
  [d4d017d3] ExponentialUtilities v1.27.0
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [29a986be] FastLapackInterface v2.0.4
  [a4df4552] FastPower v1.1.1
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [d9f16b24] Functors v0.4.12
  [46192b85] GPUArraysCore v0.2.0
  [c145ed77] GenericSchur v0.5.4
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
⌅ [d5909c97] GroupsCore v0.4.2
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.27
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [98e50ef6] JuliaFormatter v1.0.62
  [ccbc3e58] JumpProcesses v9.14.2
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.10
  [b964fa9f] LaTeXStrings v1.4.0
  [2ee39098] LabelledArrays v1.16.0
⌅ [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.6
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
⌅ [7ed4a6bd] LinearSolve v2.39.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.15
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
⌅ [961ee093] ModelingToolkit v8.75.0
⌅ [4fe8b98c] Mongoc v0.7.1
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.6.4
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.1.2
⌅ [2edaba10] Nemo v0.32.7
⌃ [8913a72c] NonlinearSolve v3.15.1
  [6fe1bfb0] OffsetArrays v1.15.0
  [bac558e1] OrderedCollections v1.8.0
  [1dea7af3] OrdinaryDiffEq v6.91.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
  [6ad6398a] OrdinaryDiffEqBDF v1.2.0
  [bbf590c4] OrdinaryDiffEqCore v1.18.1
  [50262376] OrdinaryDiffEqDefault v1.3.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.4.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.3.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.4.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.7.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.2.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.5.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.2.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.6.0
  [2d112036] OrdinaryDiffEqSDIRK v1.2.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.2.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.32
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
⌅ [d720cf60] Polymake v0.8.3
  [d236fae5] PreallocationTools v0.4.25
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [27ebfcd6] Primes v0.5.6
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [fb686558] RandomExtensions v0.4.4
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.30.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.75.0
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.6.1
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
⌅ [727e6d20] SimpleNonlinearSolve v1.12.3
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.13
  [47a9eef4] SparseDiffTools v2.23.1
  [0a514795] SparseMatrixColorings v0.4.13
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.5.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.12
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.4
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [2efcf032] SymbolicIndexingInterface v0.3.38
⌃ [19f23fe9] SymbolicLimits v0.2.1
⌅ [d1185830] SymbolicUtils v1.7.1
⌅ [0c5d862f] Symbolics v5.28.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
⌅ [98d24dd4] TestSetExtensions v2.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.27
  [0796e94c] Tokenize v0.5.29
  [d5829a12] TriangularSolve v0.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.22.0
  [a7c27f48] Unityper v0.1.6
  [3d5dd08c] VectorizationBase v0.21.71
  [19fa3120] VertexSafeGraphs v0.2.0
  [e21ec000] Antic_jll v0.201.500+0
  [d9960996] Arb_jll v200.2300.0+0
  [fcfa6d1b] Calcium_jll v0.401.100+0
  [47200ebd] DecFP_jll v2.0.3+1
⌅ [e134572f] FLINT_jll v200.900.9+0
  [e8aa6df9] GLPK_jll v5.0.1+1
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [856f044c] MKL_jll v2025.0.1+1
  [90100e71] MongoC_jll v1.28.1+0
  [68e3532b] Ncurses_jll v6.5.1+0
  [76642167] Ninja_jll v1.12.1+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
  [458c3c95] OpenSSL_jll v3.0.16+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [80dd9cbb] PPL_jll v1.2.1+0
⌅ [83958c19] Perl_jll v5.34.0+2
  [05236dd9] Readline_jll v8.2.13+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [36f60fef] TOPCOM_jll v0.17.8+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [508c9074] bliss_jll v0.77.0+1
⌅ [28df3c45] boost_jll v1.76.0+1
  [f07e07eb] cddlib_jll v0.94.14+0
  [1493ae25] lib4ti2_jll v1.6.10+0
⌅ [3eaa8342] libcxxwrap_julia_jll v0.9.7+3
⌅ [4d8266f6] libpolymake_julia_jll v0.8.3+1
  [3873f7d0] lrslib_jll v0.3.3+0
⌅ [55c6dc9b] nauty_jll v2.6.13+1
⌅ [6690c6e9] normaliz_jll v300.900.301+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
⌅ [7c209550] polymake_jll v400.700.1+1
  [fe1e1685] snappy_jll v1.2.2+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [781609d7] GMP_jll v6.2.1+6
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [3a97d323] MPFR_jll v4.2.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+4
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
        Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading.
     Testing Running tests...
WARNING: Method definition random_sparse_vector(Tuple, Nemo.FlintRationalField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
WARNING: Method definition kwcall(NamedTuple{names, T} where T<:Tuple where names, typeof(ExactODEReduction.random_sparse_vector), Tuple, Nemo.FlintRationalField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
WARNING: Method definition random_sparse_vector(Tuple, Nemo.GaloisFmpzField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
WARNING: Method definition kwcall(NamedTuple{names, T} where T<:Tuple where names, typeof(ExactODEReduction.random_sparse_vector), Tuple, Nemo.GaloisFmpzField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
WARNING: Method definition random_sparse_vector(Tuple, Nemo.CalciumQQBarField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
WARNING: Method definition kwcall(NamedTuple{names, T} where T<:Tuple where names, typeof(ExactODEReduction.random_sparse_vector), Tuple, Nemo.CalciumQQBarField) in module ExactODEReduction at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/src/sparse.jl:74 overwritten on the same line (check for duplicate calls to `include`).
[ Info: Testing started

parser: [ Info: Summary of the model:
[ Info: State variables: Ap, ApB, Au, AuB, B
[ Info: Parameters: r1, r2, r3, r4
[ Info: Loaded an ODE system with 5 states and 4 parameters


modular: 
sparse: 

reconstruction: 

indices_conversion: 
gizmos: [ Info: Constructed a set of 3 matrices 4×4 from the system Jacobian
[ Info: Constructed a set of 3 matrices 3×3 from the system Jacobian

random_elements: <
sparse([1, 2], [2, 2], fmpq[1, 1], 2, 2),
sparse([1, 2], [1, 2], fmpq[1, 1], 2, 2)
>


find_basis: 
eigenspaces: 
radical: 
invariants: 
ERROR: LoadError: InitError: could not load library "/home/pkgeval/.julia/artifacts/beeb384c8ba60497d81e26a28f74ed99aef88791/lib/libcxxwrap_julia.so"
/home/pkgeval/.julia/artifacts/beeb384c8ba60497d81e26a28f74ed99aef88791/lib/libcxxwrap_julia.so: undefined symbol: small_typeof, version JL_LIBJULIA_1.10
Stacktrace:
  [1] dlopen(s::String, flags::UInt32; throw_error::Bool)
    @ Base.Libc.Libdl ./libdl.jl:117
  [2] dlopen(s::String, flags::UInt32)
    @ Base.Libc.Libdl ./libdl.jl:116
  [3] macro expansion
    @ ~/.julia/packages/JLLWrappers/GfYNv/src/products/library_generators.jl:63 [inlined]
  [4] __init__()
    @ libcxxwrap_julia_jll ~/.julia/packages/libcxxwrap_julia_jll/zmDeI/src/wrappers/x86_64-linux-gnu-cxx11-julia_version+1.10.0.jl:9
  [5] run_module_init(mod::Module, i::Int64)
    @ Base ./loading.jl:1193
  [6] register_restored_modules(sv::Core.SimpleVector, pkg::Base.PkgId, path::String)
    @ Base ./loading.jl:1181
  [7] _include_from_serialized(pkg::Base.PkgId, path::String, ocachepath::Nothing, depmods::Vector{Any})
    @ Base ./loading.jl:1126
  [8] _tryrequire_from_serialized(pkg::Base.PkgId, path::String, ocachepath::Nothing)
    @ Base ./loading.jl:1601
  [9] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:2060
 [10] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1882
 [11] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [12] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [13] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1873
 [14] macro expansion
    @ ./loading.jl:1860 [inlined]
 [15] macro expansion
    @ ./lock.jl:267 [inlined]
 [16] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1823
 [17] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [18] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [19] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1816
 [20] include
    @ ./Base.jl:495 [inlined]
 [21] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::String)
    @ Base ./loading.jl:2292
 [22] top-level scope
    @ stdin:4
during initialization of module libcxxwrap_julia_jll
in expression starting at /home/pkgeval/.julia/packages/CxxWrap/IdOJa/src/CxxWrap.jl:1
in expression starting at stdin:4
ERROR: LoadError: Failed to precompile CxxWrap [1f15a43c-97ca-5a2a-ae31-89f07a497df4] to "/home/pkgeval/.julia/compiled/v1.10/CxxWrap/jl_e6FRUM".
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:2539
  [3] compilecache
    @ ./loading.jl:2411 [inlined]
  [4] (::Base.var"#969#970"{Base.PkgId})()
    @ Base ./loading.jl:2044
  [5] mkpidlock(f::Base.var"#969#970"{Base.PkgId}, at::String, pid::Int32; kwopts::@Kwargs{stale_age::Int64, wait::Bool})
    @ FileWatching.Pidfile /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:93
  [6] #mkpidlock#6
    @ /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:88 [inlined]
  [7] trymkpidlock(::Function, ::Vararg{Any}; kwargs::@Kwargs{stale_age::Int64})
    @ FileWatching.Pidfile /opt/julia/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:111
  [8] #invokelatest#2
    @ ./essentials.jl:894 [inlined]
  [9] invokelatest
    @ ./essentials.jl:889 [inlined]
 [10] maybe_cachefile_lock(f::Base.var"#969#970"{Base.PkgId}, pkg::Base.PkgId, srcpath::String; stale_age::Int64)
    @ Base ./loading.jl:3054
 [11] maybe_cachefile_lock
    @ ./loading.jl:3051 [inlined]
 [12] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:2040
 [13] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1882
 [14] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [15] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [16] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1873
 [17] macro expansion
    @ ./loading.jl:1860 [inlined]
 [18] macro expansion
    @ ./lock.jl:267 [inlined]
 [19] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1823
 [20] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [21] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [22] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1816
 [23] include
    @ ./Base.jl:495 [inlined]
 [24] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::String)
    @ Base ./loading.jl:2292
 [25] top-level scope
    @ stdin:4
in expression starting at /home/pkgeval/.julia/packages/Polymake/w7g9z/src/Polymake.jl:1
in expression starting at stdin:4

ode: [ Info: Summary of the model:
[ Info: State variables: x, y, z
[ Info: Parameters: a, b, c
[ Info: Summary of the model:
[ Info: State variables: x, z, x3
[ Info: Parameters: a
[ Info: Summary of the model:
[ Info: State variables: x0, x1, y
[ Info: Parameters: a01, a12, a21, u
[ Info: Summary of the model:
[ Info: State variables: x0, x1, x2, y1
[ Info: Parameters: a, b, c
[ Info: Summary of the model:
[ Info: State variables: x1, x0
[ Info: Parameters: b, c, d, u
[ Info: Summary of the model:
[ Info: State variables: x, y, z
[ Info: Parameters: a, b, c
[ Info: Summary of the model:
[ Info: State variables: x1, x3, x2
[ Info: Parameters: a, b
[ Info: Summary of the model:
[ Info: State variables: x, y, z
[ Info: Parameters: 
[ Info: Preproccessing `ExactODEReduction.ODE` object
[ Info: Preproccessing `ModelingToolkit.ODESystem` object
[ Info: Summary of the model:
[ Info: State variables: x1, x3, x2
[ Info: Parameters: a, b
ODE to MTK and vice versa: Error During Test at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/test/ode.jl:97
  Got exception outside of a @test
  ArgumentError: Function x1 is not supported
  Stacktrace:
    [1] eval_at_nemo(e::SymbolicUtils.BasicSymbolic{Real}, vals::Dict{SymbolicUtils.BasicSymbolic{Real}, fmpq_mpoly})
      @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/utils.jl:83
    [2] (::Main.ExactODEReduction.var"#13#14"{Dict{SymbolicUtils.BasicSymbolic{Real}, fmpq_mpoly}})(a::SymbolicUtils.BasicSymbolic{Real})
      @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/utils.jl:71
    [3] iterate
      @ ./generator.jl:47 [inlined]
    [4] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, Main.ExactODEReduction.var"#13#14"{Dict{SymbolicUtils.BasicSymbolic{Real}, fmpq_mpoly}}}, ::Base.EltypeUnknown, isz::Base.HasShape{1})
      @ Base ./array.jl:854
    [5] collect_similar
      @ ./array.jl:763 [inlined]
    [6] map
      @ ./abstractarray.jl:3286 [inlined]
    [7] eval_at_nemo(e::SymbolicUtils.BasicSymbolic{Real}, vals::Dict{SymbolicUtils.BasicSymbolic{Real}, fmpq_mpoly})
      @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/utils.jl:71
    [8] MTKtoODE(de::ModelingToolkit.ODESystem)
      @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/ODE.jl:407
    [9] macro expansion
      @ ~/.julia/packages/ExactODEReduction/wVtYc/test/ode.jl:113 [inlined]
   [10] macro expansion
      @ /opt/julia/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
   [11] top-level scope
      @ ~/.julia/packages/ExactODEReduction/wVtYc/test/ode.jl:98
   [12] include(mod::Module, _path::String)
      @ Base ./Base.jl:495
   [13] macro expansion
      @ ~/.julia/packages/TestSetExtensions/lB7xG/src/TestSetExtensions.jl:40 [inlined]
   [14] macro expansion
      @ ~/.julia/packages/ExactODEReduction/wVtYc/test/runtests.jl:45 [inlined]
   [15] macro expansion
      @ /opt/julia/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
   [16] top-level scope
      @ ~/.julia/packages/ExactODEReduction/wVtYc/test/runtests.jl:30
   [17] include(fname::String)
      @ Base.MainInclude ./client.jl:494
   [18] top-level scope
      @ none:6
   [19] eval
      @ ./boot.jl:385 [inlined]
   [20] exec_options(opts::Base.JLOptions)
      @ Base ./client.jl:296
   [21] _start()
      @ Base ./client.jl:557

reduction: [ Info: Summary of the model:
[ Info: State variables: x, y, z
[ Info: Parameters: 
[ Info: Global random seed: 1740505840
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space


find_reductions: [ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: s1, s6, s2, s3, s8, s4, s5
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x0, x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x0, x1, x2, x3, x4, x5, x6, x7, x8
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x0, x1, x2, x3, x4, x5, x6, x7, x8, x9
[ Info: Parameters: 
┌ Info: Testing the system x1'(t) = x1(t)
└ x2'(t) = 2*x2(t)
[ Info: Global random seed: 1740505859
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505860
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505862
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505863
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Global random seed: 1740505863
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505865
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505867
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Info: Testing the system x1'(t) = x1(t)
│ x2'(t) = 2*x2(t)
└ x3'(t) = 3*x3(t)
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505868
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505869
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505870
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Info: Testing the system x1'(t) = x1(t) + 2
│ x2'(t) = x1(t)^3 + x1(t) + x2(t)
│ x3'(t) = x1(t)*x2(t) - 10*x2(t)^2 + x3(t)
└ x4'(t) = x1(t)^3 - 7*x1(t)*x3(t) + x2(t)^6 - x4(t)
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505871
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505873
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505874
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505874
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505875
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505875
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505876
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505876
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505877
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505877
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505878
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505878
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505879
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505879
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505879
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505880
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505880
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505880
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505881
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505881
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505882
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505882
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505883
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505883
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505883
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505884
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505884
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505885
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505885
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [3]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505887
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [3]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505887
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505888
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505889
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505890
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505891
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505892
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505892
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505893
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505893
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505894
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505895
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505895
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505896
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505896
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505897
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505898
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505898
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505899
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505899
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Info: Testing the system x1'(t) = 2
│ x2'(t) = x1(t)^3 + x1(t)
│ x3'(t) = x1(t)*x2(t) - 10*x2(t)^2
└ x4'(t) = x1(t)^3 - 7*x1(t)*x3(t) + x2(t)^6
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505900
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505901
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505901
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505901
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505902
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505902
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505902
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505902
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505903
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505903
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505903
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505903
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505904
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505904
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505904
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505905
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505905
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505905
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505905
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505905
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505906
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505906
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505906
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505906
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505907
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505907
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505907
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505907
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505907
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505908
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505909
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505909
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505909
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505909
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505909
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505910
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505910
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505910
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505910
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505911
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505911
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505911
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505911
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 71 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 71 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 6
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 71 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 3
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 71 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Info: Testing the system x1'(t) = x1(t)
│ x2'(t) = x2(t)
└ x3'(t) = x3(t)
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Info: Testing the system x1'(t) = 0
│ x2'(t) = 0
└ x3'(t) = 0
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found [1, 2]-dimensional subspaces in the ambient 3-dimensional space
┌ Info: Testing the system x1'(t) = -x2(t)
│ x2'(t) = x1(t)
│ x3'(t) = -x4(t)
└ x4'(t) = x3(t)
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505912
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
[ Info: Global random seed: 1740505913
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505938
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 1 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system x1'(t) = 3*x1(t)^2 + 7
│ x2'(t) = -3*x2(t)*x3(t) + x2(t) + x3(t)^3 + 7*x3(t)
└ x3'(t) = x2(t)^2*x3(t) - 5*x2(t) + x3(t)
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 7 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 7 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 7 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 7 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 7 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 7 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 7 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 7 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 7 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 7 matrices 3×3 from the system Jacobian
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505939
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505940
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 10 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 10 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 10 matrices 2×2
[ Info: Generating a basis for the algebra
┌ Info: Testing the system x1'(t) = x1(t) - x2(t) + x3(t)^3
│ x2'(t) = x1(t)
│ x3'(t) = -x4(t)
└ x4'(t) = x3(t)
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 2 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 2 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 2 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 2 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505941
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505942
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505942
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505942
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505942
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505942
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505943
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505943
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505943
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505943
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505943
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505944
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505945
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505946
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505946
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505946
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505946
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505946
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505947
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505947
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505947
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505947
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505947
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505948
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505949
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505949
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505949
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505950
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505951
[ Info: Constructed a set of 11 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 11 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system s1'(t) = -83//1000*s1(t) + 24//25*s6(t) + 1//20*s2(t)
│ s6'(t) = 0
│ s2'(t) = 1//20*s1(t) - 3//50*s2(t)
│ s3'(t) = 1//100*s2(t) - 1//100*s3(t)
│ s8'(t) = 33//1000*s1(t)
│ s4'(t) = 1//100*s3(t) - 1//200*s4(t)
└ s5'(t) = 1//200*s4(t)
[ Info: Global random seed: 1740505952
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505952
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [3]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Global random seed: 1740505952
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [3]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505952
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505953
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505953
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505954
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505954
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505955
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505955
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505956
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [5]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [4]-dimensional subspaces found
[ Info: Found [4]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505956
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505956
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505957
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505957
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505957
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505958
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505959
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505959
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505959
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505960
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505960
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505961
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505961
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505961
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505962
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505962
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505963
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505963
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505964
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505964
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505964
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505965
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505965
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505966
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505966
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505966
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505967
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505967
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505967
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505968
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505968
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505969
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505969
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505970
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505970
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505970
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505971
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505972
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505972
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505972
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505973
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505973
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [6]-dimensional subspaces in the ambient 7-dimensional space
[ Info: Search for a subspace of 1 matrices 6×6
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [5]-dimensional subspaces found
[ Info: Found [5]-dimensional subspaces in the ambient 6-dimensional space
[ Info: Search for a subspace of 1 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 1 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system x1'(t) = x1(t) + x3(t)^2 - x4(t)^2
│ x2'(t) = x2(t) + 2*x3(t)*x4(t)
│ x3'(t) = x1(t)^2 - x2(t)^2 - x3(t)
└ x4'(t) = 2*x1(t)*x2(t) - x4(t)
[ Info: Global random seed: 1740505974
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505976
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Any[]-dimensional subspaces found
┌ Warning: No reductions found
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/ExactODEReduction.jl:377
[ Info: Global random seed: 1740505976
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505976
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Global random seed: 1740505976
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505976
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505977
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505977
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505977
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505977
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505977
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505990
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505990
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505990
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505990
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505991
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505992
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505993
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505994
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: `lead(f)` is deprecated, use `leading_coefficient(f)` instead.
│   caller = evaluate(f::fmpq_poly, x₀::SparseMatrixCSC{fmpq, Int64}) at linalg_utils.jl:80
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/linalg_utils.jl:80
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505995
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505995
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505995
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system x0'(t) = 0
│ x1'(t) = x0(t)*x2(t) + x2(t)
│ x2'(t) = 2*x0(t)*x1(t) + x1(t)
│ x3'(t) = x0(t)*x4(t) + x4(t)
└ x4'(t) = 2*x0(t)*x3(t) + x3(t)
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505996
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505997
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505997
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505997
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505998
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505998
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505998
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505998
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505998
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505999
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505999
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505999
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740505999
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506000
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506000
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506000
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506000
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506000
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506001
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506001
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506001
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506013
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506013
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506014
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506014
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506014
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506014
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506014
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506015
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506015
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [3]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 3×3
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 2
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506015
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506015
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506015
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506016
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Search for a subspace of 6 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506016
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506016
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506016
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506017
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506017
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506017
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506017
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506018
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506018
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506018
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506018
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506018
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506019
[ Info: Constructed a set of 6 matrices 5×5 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system x0'(t) = 0
│ x1'(t) = x0(t)^3*x4(t) + x0(t)^2*x3(t) + x0(t)*x2(t) + x1(t)
│ x2'(t) = x0(t)^3*x3(t) - x0(t)^2*x4(t) - x0(t)*x1(t) + x2(t)
│ x3'(t) = -x0(t)^3*x2(t) - x0(t)^2*x1(t) + x0(t)*x4(t) + x3(t)
│ x4'(t) = -x0(t)^3*x1(t) + x0(t)^2*x2(t) - x0(t)*x3(t) + x4(t)
│ x5'(t) = x0(t)^3*x8(t) + x0(t)^2*x7(t) + x0(t)*x6(t) + x5(t)
│ x6'(t) = x0(t)^3*x7(t) - x0(t)^2*x8(t) - x0(t)*x5(t) + x6(t)
│ x7'(t) = -x0(t)^3*x6(t) - x0(t)^2*x5(t) + x0(t)*x8(t) + x7(t)
└ x8'(t) = -x0(t)^3*x5(t) + x0(t)^2*x6(t) - x0(t)*x7(t) + x8(t)
[ Info: Global random seed: 1740506019
[ Info: Constructed a set of 28 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 28 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506019
[ Info: Constructed a set of 28 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 28 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 28 matrices 8×8
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [4]-dimensional subspaces in the ambient 8-dimensional space
[ Info: Search for a subspace of 28 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: There are subspaces defined over Q but they come only from equal blocks.
│ If you wish to compute them, run the code over Qbar
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:136
[ Info: Any[]-dimensional subspaces found
[ Info: Search for a subspace of 28 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: There are subspaces defined over Q but they come only from equal blocks.
│ If you wish to compute them, run the code over Qbar
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:136
[ Info: Any[]-dimensional subspaces found
[ Info: Global random seed: 1740506020
[ Info: Constructed a set of 28 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 28 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 28 matrices 8×8
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [4]-dimensional subspaces in the ambient 8-dimensional space
[ Info: Search for a subspace of 28 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 28 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506020
[ Info: Constructed a set of 220 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 220 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [5]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 220 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506130
[ Info: Constructed a set of 220 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 220 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [5]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 220 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506236
[ Info: Constructed a set of 220 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 220 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [5]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 220 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
┌ Warning: Nongeneric element of the center sampled
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:152
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
[ Info: Global random seed: 1740506345
[ Info: Constructed a set of 220 matrices 9×9 from the system Jacobian
[ Info: Search for a subspace of 220 matrices 9×9
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [5]-dimensional subspaces in the ambient 9-dimensional space
[ Info: Search for a subspace of 220 matrices 5×5
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 4
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 5-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
[ Info: Search for a subspace of 220 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
[ Info: Found [2]-dimensional subspaces in the ambient 4-dimensional space
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66
┌ Info: Testing the system x0'(t) = 0
│ x1'(t) = x0(t)*x2(t) + x1(t)
│ x2'(t) = x0(t)*x4(t) + x3(t)
│ x3'(t) = x0(t)*x5(t) + x2(t)
│ x4'(t) = x0(t)*x6(t) + x5(t)
│ x5'(t) = x0(t)*x7(t) + x4(t)
│ x6'(t) = x0(t)*x1(t) + x8(t)
│ x7'(t) = x0(t)*x9(t) + x7(t)
│ x8'(t) = x0(t)*x8(t) + x6(t)
└ x9'(t) = x0(t)*x3(t) - x1(t) - x2(t) - x3(t) - x4(t) - x5(t) - x6(t) - x7(t) - x8(t) - x9(t)
[ Info: Global random seed: 1740506438
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506438
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506438
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506438
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 9
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506441
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 9
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506445
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 9
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra
[ Info: Global random seed: 1740506448
[ Info: Constructed a set of 11 matrices 10×10 from the system Jacobian
[ Info: Search for a subspace of 11 matrices 10×10
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 9
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 10-dimensional space
[ Info: Search for a subspace of 11 matrices 9×9
[ Info: Generating a basis for the algebra


find_some_reduction: [ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: s1, s6, s2, s3, s8, s4, s5
[ Info: Parameters: 
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4
[ Info: Parameters: 
[ Info: Global random seed: 1740506454
[ Info: Constructed a set of 3 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 3 matrices 4×4
[ Info: Generating a basis for the algebra
┌ Warning: No reductions found
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/ExactODEReduction.jl:193
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 3 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 3 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 1 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 6 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 6 matrices 4×4
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 0 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 3×3
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 1 matrices 7×7 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 7×7
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Global random seed: 1740506455
[ Info: Constructed a set of 5 matrices 4×4 from the system Jacobian
[ Info: Search for a subspace of 5 matrices 4×4
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 0
[ Info: Radical is trivial, going to semisimple case
┌ Warning: No invariant subspaces defined over Q
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/matrix_algebras.jl:126
[ Info: Computing eigenspaces a random element in the centralizer
[ Info: [2]-dimensional subspaces found
┌ Warning: Complex-valued reduction, skipping the initial conditions
└ @ Main.ExactODEReduction ~/.julia/packages/ExactODEReduction/wVtYc/src/Reduction.jl:66


find_reductions_params: [ Info: Summary of the model:
[ Info: State variables: x1
[ Info: Parameters: a
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: a
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: 
[ Info: Testing the system x1'(t) = x1(t)*a
[ Info: Strategy inheritance
[ Info: Global random seed: 1740506456
[ Info: Constructed a set of 2 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(0, 1)])
[ Info: Strategy constants
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 2 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(0, 1)])
[ Info: Strategy none
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 2 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(1, 0)])
┌ Info: Testing the system x1'(t) = x1(t)*a
└ x2'(t) = 0
[ Info: Strategy inheritance
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 2 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(1, 1), (0, 1)])
[ Info: Strategy constants
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 2 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(1, 1), (0, 1)])
[ Info: Strategy none
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 2 matrices 3×3 from the system Jacobian
[ Info: Search for a subspace of 2 matrices 3×3
[ Info: Found an invariant subspace by saturating the first unit vector
[ Info: Found [2]-dimensional subspaces in the ambient 3-dimensional space
[ Info: Search for a subspace of 2 matrices 2×2
[ Info: Generating a basis for the algebra
[ Info: Computing the radical
[ Info: Size of the radical is 1
[ Info: Radical is nontrivial, computing the common kernel of radical
[ Info: [1]-dimensional subspaces found
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(2, 0), (1, 0)])
┌ Info: Testing the system x1'(t) = 0
└ x2'(t) = 0
[ Info: Strategy inheritance
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 0 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(1, 0)])
[ Info: Strategy constants
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 0 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(0, 1)])
[ Info: Strategy none
[ Info: Global random seed: 1740506458
[ Info: Constructed a set of 0 matrices 2×2 from the system Jacobian
[ Info: Search for a subspace of 1 matrices 2×2
[ Info: Found [1]-dimensional subspaces in the ambient 2-dimensional space
[ Info: Set([(1, 0)])

Test Summary:                        | Pass  Error  Broken  Total      Time
All tests                            | 2882      1       2   2885  12m58.5s
  Loading from .ode                  |    2                     2      8.8s
  Modular numbers                    |   10                    10      0.5s
  Sparse instantiation               |    9                     9      4.1s
  Sparse add-on functions            |    6              2      8      2.9s
  Rational reconstruction            |   42                    42      0.0s
  Matrix linear indexing             |   15                    15      1.2s
  Unit sparse vectors                |    3                     3      0.3s
  Lazy matrix indexing               |   12                    12      0.1s
  Construct jacobians                |    2                     2      3.5s
  Randomness                         |   12                    12      0.0s
  Check invariance                   |    9                     9      6.2s
  Gram matrix                        |    3                     3      1.2s
  Random algebra element             |  104                   104      4.6s
  Find basis, just in case           |  175                   175     28.1s
  Find basis, β algorithm            |  175                   175     23.4s
  Eigenspaces                        |   48                    48     12.8s
  radical                            |    9                     9      1.7s
  Restrict tests                     |   10                    10      2.8s
  Factorize tests                    |   10                    10      2.1s
  struct ODE                         |    5                     5      1.3s
  Variable order in @ODEsystem       |    3                     3      0.0s
  ODE ad-hoc stuff                   |    2                     2      0.0s
  ODE to MTK and vice versa          |           1              1     20.7s
  struct Reduction                   |    2                     2     22.9s
  Finding reductions                 | 2198                  2198   9m54.3s
  Finding one reduction              |    6                     6      0.6s
  Finding one reduction over QQbar   |    1                     1      0.1s
  Finding reductions with parameters |    9                     9      1.8s
ERROR: LoadError: Some tests did not pass: 2882 passed, 0 failed, 1 errored, 2 broken.
in expression starting at /home/pkgeval/.julia/packages/ExactODEReduction/wVtYc/test/runtests.jl:29

Testing failed after 894.14s

ERROR: LoadError: Package ExactODEReduction errored during testing
Stacktrace:
 [1] pkgerror(msg::String)
   @ Pkg.Types /opt/julia/share/julia/stdlib/v1.10/Pkg/src/Types.jl:70
 [2] test(ctx::Pkg.Types.Context, pkgs::Vector{Pkg.Types.PackageSpec}; coverage::Bool, julia_args::Cmd, test_args::Cmd, test_fn::Nothing, force_latest_compatible_version::Bool, allow_earlier_backwards_compatible_versions::Bool, allow_reresolve::Bool)
   @ Pkg.Operations /opt/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:2034
 [3] test
   @ /opt/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1915 [inlined]
 [4] test(ctx::Pkg.Types.Context, pkgs::Vector{Pkg.Types.PackageSpec}; coverage::Bool, test_fn::Nothing, julia_args::Cmd, test_args::Cmd, force_latest_compatible_version::Bool, allow_earlier_backwards_compatible_versions::Bool, allow_reresolve::Bool, kwargs::@Kwargs{io::Base.PipeEndpoint})
   @ Pkg.API /opt/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:444
 [5] test(pkgs::Vector{Pkg.Types.PackageSpec}; io::Base.PipeEndpoint, kwargs::@Kwargs{julia_args::Cmd})
   @ Pkg.API /opt/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:159
 [6] test
   @ /opt/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:147 [inlined]
 [7] #test#74
   @ /opt/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:146 [inlined]
 [8] top-level scope
   @ /PkgEval.jl/scripts/evaluate.jl:219
in expression starting at /PkgEval.jl/scripts/evaluate.jl:210

PkgEval failed after 1145.13s: package fails to precompile