Package evaluation to test StructuralIdentifiability on Julia 1.10.10 (c8be17dcfd*) started at 2026-02-02T17:16:20.771 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Activating project at `~/.julia/environments/v1.10` Set-up completed after 5.32s ################################################################################ # Installation # Installing StructuralIdentifiability... Resolving package versions... Updating `~/.julia/environments/v1.10/Project.toml` [220ca800] + StructuralIdentifiability v0.5.18 Updating `~/.julia/environments/v1.10/Manifest.toml` ⌅ [c3fe647b] + AbstractAlgebra v0.47.6 [a9b6321e] + Atomix v1.1.2 [861a8166] + Combinatorics v1.1.0 [864edb3b] + DataStructures v0.19.3 [e2ba6199] + ExprTools v0.1.10 [0b43b601] + Groebner v0.10.2 [18e54dd8] + IntegerMathUtils v0.1.3 [c8e1da08] + IterTools v1.10.0 [692b3bcd] + JLLWrappers v1.7.1 [1914dd2f] + MacroTools v0.5.16 ⌅ [2edaba10] + Nemo v0.52.4 [bac558e1] + OrderedCollections v1.8.1 [3e851597] + ParamPunPam v0.5.7 ⌅ [aea7be01] + PrecompileTools v1.2.1 [21216c6a] + Preferences v1.5.1 [27ebfcd6] + Primes v0.5.7 [92933f4c] + ProgressMeter v1.11.0 [fb686558] + RandomExtensions v0.4.4 ⌅ [73480bc8] + RationalFunctionFields v0.2.3 [220ca800] + StructuralIdentifiability v0.5.18 [a759f4b9] + TimerOutputs v0.5.29 [013be700] + UnsafeAtomics v0.3.0 ⌅ [e134572f] + FLINT_jll v301.300.102+0 ⌅ [656ef2d0] + OpenBLAS32_jll v0.3.24+0 [56f22d72] + Artifacts [ade2ca70] + Dates [8ba89e20] + Distributed [8f399da3] + Libdl [37e2e46d] + LinearAlgebra [56ddb016] + Logging [de0858da] + Printf [9a3f8284] + Random [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization [6462fe0b] + Sockets [2f01184e] + SparseArrays v1.10.0 [fa267f1f] + TOML v1.0.3 [4ec0a83e] + Unicode [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [781609d7] + GMP_jll v6.2.1+6 [3a97d323] + MPFR_jll v4.2.0+1 [4536629a] + OpenBLAS_jll v0.3.23+5 [bea87d4a] + SuiteSparse_jll v7.2.1+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Installation completed after 9.39s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompiling packages... 91571.0 ms ✓ RationalFunctionFields 9379.6 ms ✓ StructuralIdentifiability 2 dependencies successfully precompiled in 103 seconds. 47 already precompiled. Precompilation completed after 116.07s ################################################################################ # Testing # Testing StructuralIdentifiability Status `/tmp/jl_0LvT5K/Project.toml` ⌅ [c3fe647b] AbstractAlgebra v0.47.6 [4c88cf16] Aqua v0.8.14 [2a0fbf3d] CPUSummary v0.2.7 [861a8166] Combinatorics v1.1.0 [864edb3b] DataStructures v0.19.3 [0b43b601] Groebner v0.10.2 [c8e1da08] IterTools v1.10.0 [1914dd2f] MacroTools v0.5.16 ⌅ [2edaba10] Nemo v0.52.4 [3e851597] ParamPunPam v0.5.7 ⌅ [aea7be01] PrecompileTools v1.2.1 [27ebfcd6] Primes v0.5.7 ⌅ [73480bc8] RationalFunctionFields v0.2.3 [276daf66] SpecialFunctions v2.6.1 [220ca800] StructuralIdentifiability v0.5.18 [98d24dd4] TestSetExtensions v3.0.0 [a759f4b9] TimerOutputs v0.5.29 [ade2ca70] Dates [37e2e46d] LinearAlgebra [56ddb016] Logging [44cfe95a] Pkg v1.10.0 [9a3f8284] Random [8dfed614] Test Status `/tmp/jl_0LvT5K/Manifest.toml` ⌅ [c3fe647b] AbstractAlgebra v0.47.6 [4c88cf16] Aqua v0.8.14 [a9b6321e] Atomix v1.1.2 [2a0fbf3d] CPUSummary v0.2.7 [861a8166] Combinatorics v1.1.0 [f70d9fcc] CommonWorldInvalidations v1.0.0 [34da2185] Compat v4.18.1 [adafc99b] CpuId v0.3.1 [864edb3b] DataStructures v0.19.3 [ab62b9b5] DeepDiffs v1.2.0 [ffbed154] DocStringExtensions v0.9.5 [e2ba6199] ExprTools v0.1.10 [0b43b601] Groebner v0.10.2 [615f187c] IfElse v0.1.1 [18e54dd8] IntegerMathUtils v0.1.3 [92d709cd] IrrationalConstants v0.2.6 [c8e1da08] IterTools v1.10.0 [692b3bcd] JLLWrappers v1.7.1 [2ab3a3ac] LogExpFunctions v0.3.29 [1914dd2f] MacroTools v0.5.16 ⌅ [2edaba10] Nemo v0.52.4 [bac558e1] OrderedCollections v1.8.1 [3e851597] ParamPunPam v0.5.7 ⌅ [aea7be01] PrecompileTools v1.2.1 [21216c6a] Preferences v1.5.1 [27ebfcd6] Primes v0.5.7 [92933f4c] ProgressMeter v1.11.0 [fb686558] RandomExtensions v0.4.4 ⌅ [73480bc8] RationalFunctionFields v0.2.3 [431bcebd] SciMLPublic v1.0.1 [276daf66] SpecialFunctions v2.6.1 [aedffcd0] Static v1.3.1 [220ca800] StructuralIdentifiability v0.5.18 [98d24dd4] TestSetExtensions v3.0.0 [a759f4b9] TimerOutputs v0.5.29 [013be700] UnsafeAtomics v0.3.0 ⌅ [e134572f] FLINT_jll v301.300.102+0 ⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0 [efe28fd5] OpenSpecFun_jll v0.5.6+0 [0dad84c5] ArgTools v1.1.1 [56f22d72] Artifacts [2a0f44e3] Base64 [ade2ca70] Dates [8ba89e20] Distributed [f43a241f] Downloads v1.6.0 [7b1f6079] FileWatching [b77e0a4c] InteractiveUtils [b27032c2] LibCURL v0.6.4 [76f85450] LibGit2 [8f399da3] Libdl [37e2e46d] LinearAlgebra [56ddb016] Logging [d6f4376e] Markdown [ca575930] NetworkOptions v1.2.0 [44cfe95a] Pkg v1.10.0 [de0858da] Printf [3fa0cd96] REPL [9a3f8284] Random [ea8e919c] SHA v0.7.0 [9e88b42a] Serialization [6462fe0b] Sockets [2f01184e] SparseArrays v1.10.0 [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 v2.28.1010+0 [14a3606d] MozillaCACerts_jll v2025.12.2 [4536629a] OpenBLAS_jll v0.3.23+5 [05823500] OpenLibm_jll v0.8.5+0 [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 ⌅ have new versions available but compatibility constraints restrict them from upgrading. Testing Running tests... Resolving package versions... Installed ModelingToolkitTearing ─ v1.2.5 Updating `/tmp/jl_0LvT5K/Project.toml` ⌅ [861a8166] ↓ Combinatorics v1.1.0 ⇒ v1.0.2 [961ee093] + ModelingToolkit v11.9.0 Updating `/tmp/jl_0LvT5K/Manifest.toml` [47edcb42] + ADTypes v1.21.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [1520ce14] + AbstractTrees v0.4.5 [7d9f7c33] + Accessors v0.1.43 [79e6a3ab] + Adapt v4.4.0 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.22.0 [4c555306] + ArrayLayouts v1.12.2 [e2ed5e7c] + Bijections v0.2.2 [caf10ac8] + BipartiteGraphs v0.1.6 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [8e7c35d0] + BlockArrays v1.9.3 [70df07ce] + BracketingNonlinearSolve v1.6.2 [d360d2e6] + ChainRulesCore v1.26.0 [fb6a15b2] + CloseOpenIntervals v0.1.13 ⌅ [861a8166] ↓ Combinatorics v1.1.0 ⇒ v1.0.2 [38540f10] + CommonSolve v0.2.6 [bbf7d656] + CommonSubexpressions v0.3.1 [b152e2b5] + CompositeTypes v0.1.4 [a33af91c] + CompositionsBase v0.1.2 [2569d6c7] + ConcreteStructs v0.2.3 [187b0558] + ConstructionBase v1.6.0 [2b5f629d] + DiffEqBase v6.200.0 [459566f4] + DiffEqCallbacks v4.12.0 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [a0c0ee7d] + DifferentiationInterface v0.7.16 [5b8099bc] + DomainSets v0.7.16 [7c1d4256] + DynamicPolynomials v0.6.4 [4e289a0a] + EnumX v1.0.6 [f151be2c] + EnzymeCore v0.8.18 [55351af7] + ExproniconLite v0.10.14 [7034ab61] + FastBroadcast v0.3.5 [9aa1b823] + FastClosures v0.3.2 [a4df4552] + FastPower v1.3.1 [1a297f60] + FillArrays v1.16.0 [64ca27bc] + FindFirstFunctions v1.8.0 [6a86dc24] + FiniteDiff v2.29.0 [f6369f11] + ForwardDiff v1.3.2 [069b7b12] + FunctionWrappers v1.1.3 [77dc65aa] + FunctionWrappersWrappers v0.1.3 [46192b85] + GPUArraysCore v0.2.0 [86223c79] + Graphs v1.13.4 [3263718b] + ImplicitDiscreteSolve v1.7.0 [d25df0c9] + Inflate v0.1.5 [8197267c] + IntervalSets v0.7.13 [3587e190] + InverseFunctions v0.1.17 [82899510] + IteratorInterfaceExtensions v1.0.0 [ae98c720] + Jieko v0.2.1 [ccbc3e58] + JumpProcesses v9.21.1 [ba0b0d4f] + Krylov v0.10.5 [10f19ff3] + LayoutPointers v0.1.17 [87fe0de2] + LineSearch v0.1.6 [7ed4a6bd] + LinearSolve v3.57.0 [e6f89c97] + LoggingExtras v1.2.0 [d125e4d3] + ManualMemory v0.1.8 [bb5d69b7] + MaybeInplace v0.1.4 [961ee093] + ModelingToolkit v11.9.0 [7771a370] + ModelingToolkitBase v1.9.0 [6bb917b9] + ModelingToolkitTearing v1.2.5 [2e0e35c7] + Moshi v0.3.7 [46d2c3a1] + MuladdMacro v0.2.4 [102ac46a] + MultivariatePolynomials v0.5.13 [d8a4904e] + MutableArithmetics v1.6.7 [77ba4419] + NaNMath v1.1.3 [be0214bd] + NonlinearSolveBase v2.11.2 [5959db7a] + NonlinearSolveFirstOrder v1.11.1 [6fe1bfb0] + OffsetArrays v1.17.0 [bbf590c4] + OrdinaryDiffEqCore v3.4.0 [e409e4f3] + PoissonRandom v0.4.7 [f517fe37] + Polyester v0.7.18 [1d0040c9] + PolyesterWeave v0.2.2 [d236fae5] + PreallocationTools v1.1.2 [988b38a3] + ReadOnlyArrays v0.2.0 [795d4caa] + ReadOnlyDicts v1.0.1 [3cdcf5f2] + RecipesBase v1.3.4 [731186ca] + RecursiveArrayTools v3.47.0 [189a3867] + Reexport v1.2.2 [ae029012] + Requires v1.3.1 [7e49a35a] + RuntimeGeneratedFunctions v0.5.17 [9dfe8606] + SCCNonlinearSolve v1.9.0 [94e857df] + SIMDTypes v0.1.0 [0bca4576] + SciMLBase v2.136.0 [19f34311] + SciMLJacobianOperators v0.1.12 [a6db7da4] + SciMLLogging v1.8.0 [c0aeaf25] + SciMLOperators v1.15.1 [53ae85a6] + SciMLStructures v1.10.0 [efcf1570] + Setfield v1.1.2 [727e6d20] + SimpleNonlinearSolve v2.10.0 [699a6c99] + SimpleTraits v0.9.5 [64909d44] + StateSelection v1.3.0 [0d7ed370] + StaticArrayInterface v1.8.0 [90137ffa] + StaticArrays v1.9.16 [1e83bf80] + StaticArraysCore v1.4.4 [7792a7ef] + StrideArraysCore v0.5.8 [3384d301] + SymbolicCompilerPasses v0.1.1 [2efcf032] + SymbolicIndexingInterface v0.3.46 [19f23fe9] + SymbolicLimits v1.1.0 [d1185830] + SymbolicUtils v4.16.0 [0c5d862f] + Symbolics v7.11.0 [ed4db957] + TaskLocalValues v0.1.3 [8ea1fca8] + TermInterface v2.0.0 [8290d209] + ThreadingUtilities v0.5.5 [781d530d] + TruncatedStacktraces v1.4.0 [3a884ed6] + UnPack v1.0.2 [d30d5f5c] + WeakCacheSets v0.1.0 [1d5cc7b8] + IntelOpenMP_jll v2025.2.0+0 [856f044c] + MKL_jll v2025.2.0+0 [1317d2d5] + oneTBB_jll v2022.0.0+1 [9fa8497b] + Future [4af54fe1] + LazyArtifacts [10745b16] + Statistics v1.10.0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Resolving package versions... Updating `/tmp/jl_0LvT5K/Project.toml` [0c5d862f] + Symbolics v7.11.0 No Changes to `/tmp/jl_0LvT5K/Manifest.toml` ┌ Warning: Module OrdinaryDiffEqCoreEnzymeCoreExt with build ID ffffffff-ffff-ffff-593f-cbdf66955f2c is missing from the cache. │ This may mean OrdinaryDiffEqCoreEnzymeCoreExt [ca1c724a-f4aa-55ef-b8e4-2f05449449ac] does not support precompilation but is imported by a module that does. └ @ Base loading.jl:2021 ┌ Error: Error during loading of extension OrdinaryDiffEqCoreEnzymeCoreExt of OrdinaryDiffEqCore, use `Base.retry_load_extensions()` to retry. │ exception = │ 1-element ExceptionStack: │ Declaring __precompile__(false) is not allowed in files that are being precompiled. │ Stacktrace: │ [1] _require(pkg::Base.PkgId, env::Nothing) │ @ Base ./loading.jl:2025 │ [2] __require_prelocked(uuidkey::Base.PkgId, env::Nothing) │ @ Base ./loading.jl:1885 │ [3] #invoke_in_world#3 │ @ ./essentials.jl:926 [inlined] │ [4] invoke_in_world │ @ ./essentials.jl:923 [inlined] │ [5] _require_prelocked │ @ ./loading.jl:1876 [inlined] │ [6] _require_prelocked │ @ ./loading.jl:1875 [inlined] │ [7] run_extension_callbacks(extid::Base.ExtensionId) │ @ Base ./loading.jl:1368 │ [8] run_extension_callbacks(pkgid::Base.PkgId) │ @ Base ./loading.jl:1403 │ [9] run_package_callbacks(modkey::Base.PkgId) │ @ Base ./loading.jl:1227 │ [10] __require_prelocked(uuidkey::Base.PkgId, env::String) │ @ Base ./loading.jl:1892 │ [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:1876 │ [14] macro expansion │ @ ./loading.jl:1863 [inlined] │ [15] macro expansion │ @ ./lock.jl:270 [inlined] │ [16] __require(into::Module, mod::Symbol) │ @ Base ./loading.jl:1826 │ [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:1819 │ [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:2295 │ [22] top-level scope │ @ stdin:4 │ [23] eval │ @ ./boot.jl:385 [inlined] │ [24] include_string(mapexpr::typeof(identity), mod::Module, code::String, filename::String) │ @ Base ./loading.jl:2149 │ [25] include_string │ @ ./loading.jl:2159 [inlined] │ [26] exec_options(opts::Base.JLOptions) │ @ Base ./client.jl:314 │ [27] _start() │ @ Base ./client.jl:550 └ @ Base loading.jl:1374 [ Info: Testing started [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y ┌ Warning: New variable c, treating as a scalar parameter └ @ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/MQy2n/src/pb_representation.jl:94 [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: a [ Info: Inputs: u [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: a [ Info: Parameters: b [ Info: Inputs: c [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: a, b [ Info: Parameters: k1, k2 [ Info: Inputs: c [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x, y [ Info: Parameters: a, b [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x, y [ Info: Parameters: a, b [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x, y [ Info: Parameters: a, b [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x, y [ Info: Parameters: a, b [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: u [ Info: Outputs: y 1.600886 seconds (686.41 k allocations: 45.545 MiB, 99.54% compilation time) 0.001065 seconds (5.93 k allocations: 310.117 KiB) 0.001654 seconds (10.46 k allocations: 601.742 KiB) 0.001477 seconds (10.42 k allocations: 598.406 KiB) 0.049768 seconds (14.09 k allocations: 769.555 KiB, 78.55% gc time) 0.001256 seconds (7.68 k allocations: 464.445 KiB) 0.000706 seconds (6.57 k allocations: 321.234 KiB) 9.784008 seconds (3.71 M allocations: 252.506 MiB, 1.12% gc time, 99.77% compilation time) [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: [ Info: Inputs: u [ Info: Outputs: y 0.305625 seconds (73.21 k allocations: 5.236 MiB, 98.65% compilation time) [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: [ Info: Inputs: u [ Info: Outputs: y 0.010282 seconds (3.63 k allocations: 220.531 KiB, 89.80% compilation time) [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a, b [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: a [ Info: Inputs: u [ Info: Outputs: y1, y2 IOEQS: Dict{QQMPolyRingElem, QQMPolyRingElem}(y1(t)_2 => -y1(t)_0 + y1(t)_2, y2(t)_1 => -a*y2(t)_0 + a*u(t)_0 + y2(t)_1 - u(t)_1) [ Info: Summary of the model: [ Info: State variables: x0, x1 [ Info: Parameters: a01, a12, a21 [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x0, x1 [ Info: Parameters: a, b, c, d [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: S, I, W, R [ Info: Parameters: a, bi, bw, gam, k, mu, xi [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: alpha, b, beta, c, delta, gama, sigma [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: b [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a1, a2, a21 [ Info: Inputs: [ Info: Outputs: y1 [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a1, a2, a21 [ Info: Inputs: u [ Info: Outputs: y1 [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: a01, a12, a13, a21, a31 [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: S, E, In [ Info: Parameters: N, a, b, nu [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003145 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 3.987323627 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 0.044397236 seconds [ Info: Global identifiability assessed in 24.80210731 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001881973 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Global identifiability assessed in 0.530812437 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Global identifiability assessed in 5.147e-5 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.023115579 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.254442168 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.353e-5 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:08 ✓ # Computing specializations.. Time: 0:00:09 [ Info: Search for polynomial generators concluded in 6.781665 [ Info: Selecting generators in 0.014758159 [ Info: Inclusion checked with probability 0.9955 in 0.049209569 seconds [ Info: Global identifiability assessed in 61.542561612 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 1.665733469 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 1.63949883 seconds [ Info: Dimensions of the Wronskians [676] [ Info: Ranks of the Wronskians computed in 0.096094322 seconds [ Info: Global identifiability assessed in 26.635130281 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014570421 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.030160562 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000310397 seconds [ Info: Global identifiability assessed in 0.073064622 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Note: the input model has nontrivial submodels. If the computation for the full model will be too heavy, you may want to try to first analyze one of the submodels. They can be produced using function `find_submodels` [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 5.848411941 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00320733 seconds [ Info: Dimensions of the Wronskians [2, 3, 2] [ Info: Ranks of the Wronskians computed in 2.0699e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.558113486 [ Info: Selecting generators in 0.000404686 [ Info: Inclusion checked with probability 0.9955 in 0.002748984 seconds [ Info: Global identifiability assessed in 7.487394506 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002337788 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001670364 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.745e-5 seconds [ Info: Global identifiability assessed in 0.006388738 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002442587 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001806613 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.138e-5 seconds [ Info: Global identifiability assessed in 0.007146591 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004766075 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003991681 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.952e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.775486378 [ Info: Selecting generators in 0.012458101 [ Info: Inclusion checked with probability 0.9955 in 0.004519597 seconds [ Info: Global identifiability assessed in 1.58510317 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007528648 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003665275 seconds [ Info: Dimensions of the Wronskians [5, 2] [ Info: Ranks of the Wronskians computed in 2.4879e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004797124 [ Info: Selecting generators in 0.002932852 [ Info: Inclusion checked with probability 0.9955 in 0.00309541 seconds [ Info: Global identifiability assessed in 0.043355896 seconds [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: Θ [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: V_m, c, k01, k_m [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a, b, c [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x0, x1 [ Info: Parameters: a01, a12, a21 [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: k1, k2, k3, k4 [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: β1, β2, β3, λ1, λ2, λ3 [ Info: Inputs: u1, u2, u3 [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: a1, a2, b1, b2 [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: a1, a2, b1, b2 [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: p1, p2, p3, p4 [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: alpha, b, beta, c, delta, gama, sigma [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: s, i, r, x1, x2 [ Info: Parameters: M, b0, b1, g, mu, nu [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: S, E, I, R, Q [ Info: Parameters: beta, gamma, psi, v [ Info: Inputs: [ Info: Outputs: y1 [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: k01, k12, k13, k14, k21, k31, k41 [ Info: Inputs: u [ Info: Outputs: y1 [ Info: Summary of the model: [ Info: State variables: x5, x7, x4, x6 [ Info: Parameters: k10, k5, k6, k7, k8, k9 [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: S, In, L, Q [ Info: Parameters: Ninv, a, b, e, g, s [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: S, R, W [ Info: Parameters: Dd, T, a, d, dr, e, g, r, rR [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: P3, P0, P5, P4, P1, P2 [ Info: Parameters: Ks, M, Mar, alpa, beta, beta_SA, beta_SI, phi, siga1, siga2 [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a, b, c, d [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: a, b, c, d [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: β1, β2, β3, λ1, λ2, λ3 [ Info: Inputs: u1, u2, u3 [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: Θ [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: C, α [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: α [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a, b, c [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: p1, p2, p3, p4 [ Info: Inputs: u [ Info: Outputs: y1 [ Info: Summary of the model: [ Info: State variables: EGFR, pEGFR, pEGFR_Akt, Akt, pAkt, S6, pAkt_S6, pS6, EGF_EGFR [ Info: Parameters: EGFR_turnover, a1, a2, a3, reaction_1_k1, reaction_1_k2, reaction_2_k1, reaction_2_k2, reaction_3_k1, reaction_4_k1, reaction_5_k1, reaction_5_k2, reaction_6_k1, reaction_7_k1, reaction_8_k1, reaction_9_k1 [ Info: Inputs: pro_EGFR [ Info: Outputs: y1, y2, y3 [ Info: Summary of the model: [ Info: State variables: beta, cry, zea, beta10, OHbeta10, betaio, OHbetaio [ Info: Parameters: kOHbeta10, kbeta, kbeta10, kcryOH, kcrybeta, kzea [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: EpoR_A, k1, k2, k3, k5, k6, k7 [ Info: Inputs: [ Info: Outputs: y1, y2, y3 [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: S, E, U, I [ Info: Parameters: N, a, b, d, g [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: alpha [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: k01, k02, k12, k21, v [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: K_M, V_M, b1, c, k02, k12, k21 [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3 [ Info: Parameters: k02, k03, k12, k13, k21, k31, v [ Info: Inputs: u [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: a03, a04, a13, a24, a31, a42, a43 [ Info: Inputs: u [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: S, I [ Info: Parameters: N, beta, k, mu, nu [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: p1, p2, p3, p4, p5 [ Info: Inputs: [ Info: Outputs: y [ Info: Summary of the model: [ Info: State variables: x1, x2, x3, x4 [ Info: Parameters: beta, c, d, k1, k2, mu1, mu2, q1, q2, s [ Info: Inputs: [ Info: Outputs: y1, y2 [ Info: Summary of the model: [ Info: State variables: A, I, H, R, D, E [ Info: Parameters: N, a, c1, c2, d, h, r1, r2, r3, s [ Info: Inputs: [ Info: Outputs: y [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001438586 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001262117 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.073e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.8819e-5 [ Info: Selecting generators in 0.670545851 [ Info: Inclusion checked with probability 0.995 in 0.002656634 seconds [ Info: The search for identifiable functions concluded in 1.858356328 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001617585 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001432547 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.983e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.1539e-5 [ Info: Selecting generators in 0.000814962 [ Info: Inclusion checked with probability 0.995 in 0.001952222 seconds [ Info: The search for identifiable functions concluded in 0.0104348 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001408146 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001249308 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.029e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.0919e-5 [ Info: Selecting generators in 0.000882612 [ Info: Inclusion checked with probability 0.995 in 0.00208337 seconds [ Info: The search for identifiable functions concluded in 0.010612148 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001356167 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001238188 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.972e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000480446 [ Info: Selecting generators in 0.000839282 [ Info: Inclusion checked with probability 0.995 in 0.001800123 seconds [ Info: The search for identifiable functions concluded in 0.01044557 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001240378 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00102325 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.8399e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000407716 [ Info: Selecting generators in 0.000715843 [ Info: Inclusion checked with probability 0.995 in 0.001695694 seconds [ Info: The search for identifiable functions concluded in 0.00938776 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001095349 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000971851 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.136e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000352937 [ Info: Selecting generators in 0.000635594 [ Info: Inclusion checked with probability 0.995 in 0.001650294 seconds [ Info: The search for identifiable functions concluded in 0.008799836 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001579425 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001085649 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.699e-5 seconds [ Info: The search for identifiable functions concluded in 0.028896243 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001609644 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00107415 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.606e-5 seconds [ Info: The search for identifiable functions concluded in 0.003310219 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001378406 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.0010293 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.679e-5 seconds [ Info: The search for identifiable functions concluded in 0.002996971 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001187929 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000955631 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.668e-5 seconds [ Info: The search for identifiable functions concluded in 0.002707844 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001256948 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000966161 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.491e-5 seconds [ Info: The search for identifiable functions concluded in 0.002769394 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001239088 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00101337 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.8059e-5 seconds [ Info: The search for identifiable functions concluded in 0.002882813 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001793202 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001156459 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.502e-5 seconds [ Info: The search for identifiable functions concluded in 0.003814184 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001441416 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001114689 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 4.1509e-5 seconds [ Info: The search for identifiable functions concluded in 0.00320468 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001421216 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001066889 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.6e-5 seconds [ Info: The search for identifiable functions concluded in 0.00312257 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001395287 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00103085 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.732e-5 seconds [ Info: The search for identifiable functions concluded in 0.003038321 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001333497 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00105584 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.536e-5 seconds [ Info: The search for identifiable functions concluded in 0.003041511 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001445547 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001155749 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.4779e-5 seconds [ Info: The search for identifiable functions concluded in 0.003280369 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.275965153 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001703813 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.787e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.1959e-5 [ Info: Selecting generators in 0.000579934 [ Info: Inclusion checked with probability 0.995 in 0.001639324 seconds [ Info: The search for identifiable functions concluded in 0.284195994 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002371768 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001465396 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.68e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 6.8009e-5 [ Info: Selecting generators in 0.000540875 [ Info: Inclusion checked with probability 0.995 in 0.001635465 seconds [ Info: The search for identifiable functions concluded in 0.01041535 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002209129 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001479576 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.714e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.6529e-5 [ Info: Selecting generators in 0.000677814 [ Info: Inclusion checked with probability 0.995 in 0.001700423 seconds [ Info: The search for identifiable functions concluded in 0.010664838 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002283528 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001507105 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.621e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000382496 [ Info: Selecting generators in 0.000551715 [ Info: Inclusion checked with probability 0.995 in 0.001645345 seconds [ Info: The search for identifiable functions concluded in 0.01047624 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002185869 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001422857 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.634e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000339357 [ Info: Selecting generators in 0.000572395 [ Info: Inclusion checked with probability 0.995 in 0.001572905 seconds [ Info: The search for identifiable functions concluded in 0.009948535 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002257098 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001396547 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.543e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000346997 [ Info: Selecting generators in 0.000543795 [ Info: Inclusion checked with probability 0.995 in 0.001562636 seconds [ Info: The search for identifiable functions concluded in 0.009928495 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[Θ] │ case = │ (ode = x1'(t) = x2(t)^2*Θ │ x2'(t) = u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 5 variables x1(t), x2(t), y(t), u(t), Θ │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001144189 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001111339 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.2459e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.213e-5 [ Info: Selecting generators in 0.001870222 [ Info: Inclusion checked with probability 0.995 in 0.003184359 seconds [ Info: The search for identifiable functions concluded in 0.015156455 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m//k_m] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001172509 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.0010643 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.854e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.5139e-5 [ Info: Selecting generators in 0.001758394 [ Info: Inclusion checked with probability 0.995 in 0.002856142 seconds [ Info: The search for identifiable functions concluded in 0.014500181 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m//k_m] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001168179 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001086129 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.182e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.031e-5 [ Info: Selecting generators in 0.001876012 [ Info: Inclusion checked with probability 0.995 in 0.003028411 seconds [ Info: The search for identifiable functions concluded in 0.015080626 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m//k_m] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001180989 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001128969 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.186e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.142659337 [ Info: Selecting generators in 0.003203879 [ Info: Inclusion checked with probability 0.995 in 0.00318066 seconds [ Info: The search for identifiable functions concluded in 0.159287927 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m*c] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), V_m, c, k01, k_m] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001223898 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001185079 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.2769e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.175638392 [ Info: Selecting generators in 0.004063891 [ Info: Inclusion checked with probability 0.995 in 0.003626605 seconds [ Info: The search for identifiable functions concluded in 0.19460689 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m*c] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), V_m, c, k01, k_m] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001420376 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001451546 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.26e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.012819667 [ Info: Selecting generators in 0.00319189 [ Info: Inclusion checked with probability 0.995 in 0.002852242 seconds [ Info: The search for identifiable functions concluded in 0.031960525 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, c*k_m, V_m*c] │ case = │ (ode = x'(t) = (x(t)^2*k01 - x(t)*V_m + x(t)*k01*k_m)//(x(t) + k_m) │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[k01, c*k_m, V_m*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), V_m, c, ..., k_m │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), V_m, c, k01, k_m] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00115215 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00103397 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.905e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.0929e-5 [ Info: Selecting generators in 0.001758403 [ Info: Inclusion checked with probability 0.995 in 0.002148009 seconds [ Info: The search for identifiable functions concluded in 0.670486712 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00113215 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000835983 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.697e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 6.3829e-5 [ Info: Selecting generators in 0.001562615 [ Info: Inclusion checked with probability 0.995 in 0.001968081 seconds [ Info: The search for identifiable functions concluded in 0.010596559 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001227118 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000950441 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.6959e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 6.677e-5 [ Info: Selecting generators in 0.001690834 [ Info: Inclusion checked with probability 0.995 in 0.002419867 seconds [ Info: The search for identifiable functions concluded in 0.011743178 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001255748 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00105563 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.0289e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.148344822 [ Info: Selecting generators in 0.002233959 [ Info: Inclusion checked with probability 0.995 in 0.002383807 seconds [ Info: The search for identifiable functions concluded in 0.161822433 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001248338 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000989841 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.791e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004933383 [ Info: Selecting generators in 0.002018231 [ Info: Inclusion checked with probability 0.995 in 0.002266928 seconds [ Info: The search for identifiable functions concluded in 0.017311994 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.0011193 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00096915 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.808e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004894223 [ Info: Selecting generators in 0.001987601 [ Info: Inclusion checked with probability 0.995 in 0.002260868 seconds [ Info: The search for identifiable functions concluded in 0.016902558 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , ident_funcs = QQMPolyRingElem[b*c, a]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001968961 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001510766 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.717e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.0149e-5 [ Info: Selecting generators in 0.000471756 [ Info: Inclusion checked with probability 0.995 in 0.002452417 seconds [ Info: The search for identifiable functions concluded in 0.015081246 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001882972 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001449096 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.586e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.4049e-5 [ Info: Selecting generators in 0.000504785 [ Info: Inclusion checked with probability 0.995 in 0.002396477 seconds [ Info: The search for identifiable functions concluded in 0.015083076 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001903362 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001415076 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.636e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.1949e-5 [ Info: Selecting generators in 0.000463045 [ Info: Inclusion checked with probability 0.995 in 0.002494676 seconds [ Info: The search for identifiable functions concluded in 0.015024687 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001740383 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001260878 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.382e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005829874 [ Info: Selecting generators in 0.000622624 [ Info: Inclusion checked with probability 0.995 in 0.002322367 seconds [ Info: The search for identifiable functions concluded in 0.020071939 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x0(t), x1(t), y(t), a01, a12, a21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001924032 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001345768 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.487e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005821744 [ Info: Selecting generators in 0.000643174 [ Info: Inclusion checked with probability 0.995 in 0.002470136 seconds [ Info: The search for identifiable functions concluded in 0.020720842 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x0(t), x1(t), y(t), a01, a12, a21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001881702 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001474926 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.719e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006422779 [ Info: Selecting generators in 0.000676044 [ Info: Inclusion checked with probability 0.995 in 0.002931622 seconds [ Info: The search for identifiable functions concluded in 0.022519385 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a01 + a12 + a21, a01*a12] │ case = │ (ode = x0'(t) = -x0(t)*a01 - x0(t)*a21 + x1(t)*a12 │ x1'(t) = x0(t)*a21 - x1(t)*a12 │ y(t) = x0(t) │ , ident_funcs = QQMPolyRingElem[a01*a12, a01 + a12 + a21]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x0(t), x1(t), y(t), a01, ..., a21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x0(t), x1(t), y(t), a01, a12, a21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002864723 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001867263 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.5189e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000101829 [ Info: Selecting generators in 0.002447456 [ Info: Inclusion checked with probability 0.995 in 0.002793094 seconds [ Info: The search for identifiable functions concluded in 0.020406295 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002655945 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001962231 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.2409e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.2739e-5 [ Info: Selecting generators in 0.002922672 [ Info: Inclusion checked with probability 0.995 in 0.00315192 seconds [ Info: The search for identifiable functions concluded in 0.021044578 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002528646 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001887902 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.319e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.6249e-5 [ Info: Selecting generators in 0.003302868 [ Info: Inclusion checked with probability 0.995 in 0.003640325 seconds [ Info: The search for identifiable functions concluded in 0.021733433 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002673875 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002004651 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.2139e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.010089124 [ Info: Selecting generators in 0.003010311 [ Info: Inclusion checked with probability 0.995 in 0.003439007 seconds [ Info: The search for identifiable functions concluded in 0.031463629 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k1, k2, k3, k4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002772613 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002040001 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.366e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01251552 [ Info: Selecting generators in 0.002670755 [ Info: Inclusion checked with probability 0.995 in 0.002781083 seconds [ Info: The search for identifiable functions concluded in 0.033199303 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k1, k2, k3, k4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002580805 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001976251 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.132e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.012139274 [ Info: Selecting generators in 0.002814993 [ Info: Inclusion checked with probability 0.995 in 0.002909702 seconds [ Info: The search for identifiable functions concluded in 0.031581138 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3 + k4, k1 + k2, k2*k3] │ case = │ (ode = x1'(t) = -x1(t)*k1 - x1(t)*k2 + x2(t)*k3 + u(t) │ x2'(t) = x1(t)*k2 - x2(t)*k3 - x2(t)*k4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[k1 + k2, k3 + k4, k2*k3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), u(t), ..., k4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k1, k2, k3, k4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014891047 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.211042703 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 4.699e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000123649 [ Info: Selecting generators in 0.009784556 [ Info: Inclusion checked with probability 0.995 in 0.006002672 seconds [ Info: The search for identifiable functions concluded in 0.411766805 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006863705 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004883614 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.9e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000113759 [ Info: Selecting generators in 0.009954315 [ Info: Inclusion checked with probability 0.995 in 0.005899083 seconds [ Info: The search for identifiable functions concluded in 0.046137109 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006902654 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004878134 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.315e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000131789 [ Info: Selecting generators in 0.008679847 [ Info: Inclusion checked with probability 0.995 in 0.004547677 seconds [ Info: The search for identifiable functions concluded in 0.042946039 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006856555 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004645606 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.691e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001658474 [ Info: Selecting generators in 0.007795545 [ Info: Inclusion checked with probability 0.995 in 0.004767665 seconds [ Info: The search for identifiable functions concluded in 0.041959049 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006484418 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004640565 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.001e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00207276 [ Info: Selecting generators in 0.00937663 [ Info: Inclusion checked with probability 0.995 in 0.00524612 seconds [ Info: The search for identifiable functions concluded in 0.045882171 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00625124 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004807764 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.9369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002027791 [ Info: Selecting generators in 0.009724697 [ Info: Inclusion checked with probability 0.995 in 0.005705315 seconds [ Info: The search for identifiable functions concluded in 0.046867553 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004841863 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002851713 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.132e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000101229 [ Info: Selecting generators in 0.001905371 [ Info: Inclusion checked with probability 0.995 in 0.003445817 seconds [ Info: The search for identifiable functions concluded in 0.023586315 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004814644 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003019851 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.835e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.6599e-5 [ Info: Selecting generators in 0.001842102 [ Info: Inclusion checked with probability 0.995 in 0.003470937 seconds [ Info: The search for identifiable functions concluded in 0.023459486 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004674645 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002945032 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.975e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.3679e-5 [ Info: Selecting generators in 0.001872892 [ Info: Inclusion checked with probability 0.995 in 0.003494107 seconds [ Info: The search for identifiable functions concluded in 0.023240258 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004596316 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002969601 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.945e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001115059 [ Info: Selecting generators in 0.001909512 [ Info: Inclusion checked with probability 0.995 in 0.003262719 seconds [ Info: The search for identifiable functions concluded in 0.023721844 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004487987 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002941552 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 7.6829e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00112607 [ Info: Selecting generators in 0.001919982 [ Info: Inclusion checked with probability 0.995 in 0.003784274 seconds [ Info: The search for identifiable functions concluded in 35.424900569 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004574547 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002916352 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.808e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00108693 [ Info: Selecting generators in 0.001901172 [ Info: Inclusion checked with probability 0.995 in 0.003327029 seconds [ Info: The search for identifiable functions concluded in 0.023593794 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[b2, b1, a2, a1] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 + u(t) │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[a1, a2, b1, b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004542297 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002909472 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.162e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.3789e-5 [ Info: Selecting generators in 0.002078581 [ Info: Inclusion checked with probability 0.995 in 0.003293358 seconds [ Info: The search for identifiable functions concluded in 0.02614544 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2 + b1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004455147 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002876893 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.323e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.4369e-5 [ Info: Selecting generators in 0.00212354 [ Info: Inclusion checked with probability 0.995 in 0.003379187 seconds [ Info: The search for identifiable functions concluded in 0.026422117 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2 + b1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005465438 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008921025 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.3319e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000114058 [ Info: Selecting generators in 0.002980841 [ Info: Inclusion checked with probability 0.995 in 0.003957432 seconds [ Info: The search for identifiable functions concluded in 0.303163902 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2 + b1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004680125 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003006582 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.131e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014959357 [ Info: Selecting generators in 0.003407607 [ Info: Inclusion checked with probability 0.995 in 0.003205419 seconds [ Info: The search for identifiable functions concluded in 0.042740982 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004439508 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003043001 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.32e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015230985 [ Info: Selecting generators in 0.003831744 [ Info: Inclusion checked with probability 0.995 in 0.003446247 seconds [ Info: The search for identifiable functions concluded in 0.043503145 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005005562 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002868302 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.58e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015136765 [ Info: Selecting generators in 0.003501627 [ Info: Inclusion checked with probability 0.995 in 0.00318249 seconds [ Info: The search for identifiable functions concluded in 0.043854921 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a1 + a2 + b1 + b2, b1*b2, a1*a2 + a1*b2] │ case = │ (ode = x1'(t) = -x1(t)*a1 + x2(t)*b1 │ x2'(t) = x1(t)*a1 - x2(t)*a2 - x2(t)*b1 + x3(t)*b2 │ x3'(t) = x2(t)*a2 - x3(t)*b2 + u(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[b1*b2, a1 + a2 + b1 + b2, a1*a2 + a1*b2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y(t), ..., b2 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), a1, a2, b1, b2] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002367807 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001801133 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.689e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.0839e-5 [ Info: Selecting generators in 0.001725683 [ Info: Inclusion checked with probability 0.995 in 0.002863632 seconds [ Info: The search for identifiable functions concluded in 0.017046647 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002335878 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001697494 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.762e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.3929e-5 [ Info: Selecting generators in 0.001769023 [ Info: Inclusion checked with probability 0.995 in 0.002992061 seconds [ Info: The search for identifiable functions concluded in 0.016917309 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002280838 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001694704 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.6409e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.9739e-5 [ Info: Selecting generators in 0.001837413 [ Info: Inclusion checked with probability 0.995 in 0.002616405 seconds [ Info: The search for identifiable functions concluded in 0.016861989 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001927992 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001476616 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.395e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01046391 [ Info: Selecting generators in 0.001952292 [ Info: Inclusion checked with probability 0.995 in 0.002849072 seconds [ Info: The search for identifiable functions concluded in 0.026058401 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002310528 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001843743 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.033e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01048792 [ Info: Selecting generators in 0.001976891 [ Info: Inclusion checked with probability 0.995 in 0.003084241 seconds [ Info: The search for identifiable functions concluded in 0.028099411 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002451577 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001746213 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.937e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01044743 [ Info: Selecting generators in 0.001881502 [ Info: Inclusion checked with probability 0.995 in 0.003012421 seconds [ Info: The search for identifiable functions concluded in 0.027975713 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p1 + p4, p1*p4 - p2*p3] │ case = │ (ode = x1'(t) = x1(t)^2*p1 + x1(t)*x2(t)*p2 │ x2'(t) = x1(t)^2*p3 + x1(t)*x2(t)*p4 │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[p1 + p4, p1*p4 - p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), p1, ..., p4 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013768668 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.030563638 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000286287 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:02 ✓ # Computing specializations.. Time: 0:00:02 [ Info: Search for polynomial generators concluded in 0.000153909 [ Info: Selecting generators in 0.016456492 [ Info: Inclusion checked with probability 0.995 in 0.024371667 seconds [ Info: The search for identifiable functions concluded in 6.423861043 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013737719 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.029227061 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000299267 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000106099 [ Info: Selecting generators in 0.014872848 [ Info: Inclusion checked with probability 0.995 in 0.023850772 seconds [ Info: The search for identifiable functions concluded in 0.150356013 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014518191 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.029438608 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000279427 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000103309 [ Info: Selecting generators in 0.014609951 [ Info: Inclusion checked with probability 0.995 in 0.023960142 seconds [ Info: The search for identifiable functions concluded in 0.152299565 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012444641 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.02826356 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000267038 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.135666945 [ Info: Selecting generators in 0.020095808 [ Info: Inclusion checked with probability 0.995 in 0.024788743 seconds [ Info: The search for identifiable functions concluded in 1.29113754 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y(t), alpha, b, beta, c, delta, gama, sigma] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012702359 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.026535406 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000270748 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.033190722 [ Info: Selecting generators in 0.0146297 [ Info: Inclusion checked with probability 0.995 in 0.021844191 seconds [ Info: The search for identifiable functions concluded in 0.173857188 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y(t), alpha, b, beta, c, delta, gama, sigma] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012818147 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.027954723 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000247388 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.035251563 [ Info: Selecting generators in 0.014758469 [ Info: Inclusion checked with probability 0.995 in 0.022753552 seconds [ Info: The search for identifiable functions concluded in 0.182537756 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[sigma, c, b, beta + delta, beta*delta] │ case = │ (ode = x1'(t) = (-x1(t)*x4(t)*b - x1(t)*b*c + 1)//(x4(t) + c) │ x2'(t) = x1(t)*alpha - x2(t)*beta │ x3'(t) = x2(t)*gama - x3(t)*delta │ x4'(t) = (x2(t)*x4(t)*gama*sigma - x3(t)*x4(t)*delta*sigma)//x3(t) │ y(t) = x1(t) │ , ident_funcs = QQMPolyRingElem[sigma, beta + delta, c, b, beta*delta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), x4(t), ..., sigma │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y(t), alpha, b, beta, c, delta, gama, sigma] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.633160338 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 6.903971244 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.180311817 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:01 ⌝ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000117549 [ Info: Selecting generators in 1.023501857 [ Info: Inclusion checked with probability 0.995 in 2.272695768 seconds [ Info: The search for identifiable functions concluded in 17.261534971 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.435056992 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 7.356203602 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.193327513 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000144699 [ Info: Selecting generators in 2.213756382 [ Info: Inclusion checked with probability 0.995 in 2.852044661 seconds [ Info: The search for identifiable functions concluded in 17.53065384 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.82653031 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 7.913669936 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.203341907 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 5   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000184059 [ Info: Selecting generators in 0.628381165 [ Info: Inclusion checked with probability 0.995 in 2.757450875 seconds [ Info: The search for identifiable functions concluded in 17.160066223 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.457020142 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.240514472 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.184288688 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 5   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.02511572 [ Info: Selecting generators in 1.246262699 [ Info: Inclusion checked with probability 0.995 in 2.494101073 seconds [ Info: The search for identifiable functions concluded in 17.115495701 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[s(t), i(t), r(t), x1(t), x2(t), y1(t), y2(t), M, b0, b1, g, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.423070987 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 10.08645471 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.191753237 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.03554501 [ Info: Selecting generators in 1.138476459 [ Info: Inclusion checked with probability 0.995 in 2.215278958 seconds [ Info: The search for identifiable functions concluded in 18.616246029 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[s(t), i(t), r(t), x1(t), x2(t), y1(t), y2(t), M, b0, b1, g, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.42899875 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.413330412 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.200535444 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.035719699 [ Info: Selecting generators in 1.270401759 [ Info: Inclusion checked with probability 0.995 in 2.235558834 seconds [ Info: The search for identifiable functions concluded in 17.125034002 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, g, b0, M^2] │ case = │ (ode = s'(t) = -s(t)*i(t)*x1(t)*b0*b1 - s(t)*i(t)*b0 - s(t)*mu + r(t)*g + mu │ i'(t) = s(t)*i(t)*x1(t)*b0*b1 + s(t)*i(t)*b0 - i(t)*mu - i(t)*nu │ r'(t) = i(t)*nu - r(t)*g - r(t)*mu │ x1'(t) = -x2(t)*M │ x2'(t) = x1(t)*M │ y1(t) = i(t) │ y2(t) = r(t) │ , ident_funcs = QQMPolyRingElem[g, mu, b0, nu, M^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables s(t), i(t), r(t), x1(t), ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[s(t), i(t), r(t), x1(t), x2(t), y1(t), y2(t), M, b0, b1, g, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013919057 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012043455 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.536e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000119929 [ Info: Selecting generators in 0.008277481 [ Info: Inclusion checked with probability 0.995 in 0.008147552 seconds [ Info: The search for identifiable functions concluded in 0.08059604 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, gamma*psi - gamma - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.016625381 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012222563 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.284e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000107549 [ Info: Selecting generators in 0.008062263 [ Info: Inclusion checked with probability 0.995 in 0.007976684 seconds [ Info: The search for identifiable functions concluded in 0.083296184 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, gamma*psi - gamma - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.011221673 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011253063 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.428e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000116679 [ Info: Selecting generators in 0.007847145 [ Info: Inclusion checked with probability 0.995 in 0.007200361 seconds [ Info: The search for identifiable functions concluded in 0.074855355 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, gamma*psi - gamma - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.011853727 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011174533 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.532e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.026902383 [ Info: Selecting generators in 0.01154693 [ Info: Inclusion checked with probability 0.995 in 0.007748866 seconds [ Info: The search for identifiable functions concluded in 0.10466532 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, psi*v - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), E(t), I(t), R(t), Q(t), y1(t), beta, gamma, psi, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.010762437 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010628698 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.408e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.027667325 [ Info: Selecting generators in 0.012882227 [ Info: Inclusion checked with probability 0.995 in 0.008662247 seconds [ Info: The search for identifiable functions concluded in 0.107230505 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, psi*v - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), E(t), I(t), R(t), Q(t), y1(t), beta, gamma, psi, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013910627 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012263053 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.9169e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.028845845 [ Info: Selecting generators in 0.01353602 [ Info: Inclusion checked with probability 0.995 in 0.008742507 seconds [ Info: The search for identifiable functions concluded in 0.119340629 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[gamma, beta//psi, gamma*psi - psi*v, psi*v - psi - v] │ case = │ (ode = S'(t) = -S(t)*I(t)*beta │ E'(t) = S(t)*I(t)*beta - E(t)*v │ I'(t) = E(t)*v + I(t)*gamma*psi - I(t)*gamma - I(t)*psi │ R'(t) = -I(t)*gamma*psi + I(t)*gamma + Q(t)*gamma │ Q'(t) = I(t)*psi - Q(t)*gamma │ y1(t) = Q(t) │ , ident_funcs = RingElem[gamma*psi - psi*v, beta//psi, gamma, psi*v - psi - v]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), I(t), R(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), E(t), I(t), R(t), Q(t), y1(t), beta, gamma, psi, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013450851 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00840373 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.305e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000250947 [ Info: Selecting generators in 0.051116362 [ Info: Inclusion checked with probability 0.995 in 0.014412742 seconds [ Info: The search for identifiable functions concluded in 1.417107807 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k12*k13 + k12*k14 + k13*k14, k01*k12 + k01*k13 + k01*k14 + k12*k13 + k12*k14 + k12*k31 + k12*k41 + k13*k14 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k12*k13*k14, k01*k12*k13 + k01*k12*k14 + k01*k13*k14 + k12*k13*k14 + k12*k13*k41 + k12*k14*k31 + k13*k14*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01460527 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010013834 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.348e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000223498 [ Info: Selecting generators in 0.033360522 [ Info: Inclusion checked with probability 0.995 in 0.011795977 seconds [ Info: The search for identifiable functions concluded in 0.458656946 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k12*k13 + k12*k14 + k13*k14, k01*k12 + k01*k13 + k01*k14 + k12*k13 + k12*k14 + k12*k31 + k12*k41 + k13*k14 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k12*k13*k14, k01*k12*k13 + k01*k12*k14 + k01*k13*k14 + k12*k13*k14 + k12*k13*k41 + k12*k14*k31 + k13*k14*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.011167953 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007474588 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.636e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000256727 [ Info: Selecting generators in 0.036113695 [ Info: Inclusion checked with probability 0.995 in 0.013194934 seconds [ Info: The search for identifiable functions concluded in 0.445379273 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k12*k13 + k12*k14 + k13*k14, k01*k12 + k01*k13 + k01*k14 + k12*k13 + k12*k14 + k12*k31 + k12*k41 + k13*k14 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k12*k13*k14, k01*k12*k13 + k01*k12*k14 + k01*k13*k14 + k12*k13*k14 + k12*k13*k41 + k12*k14*k31 + k13*k14*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012451931 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008265381 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.213e-5 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 1.557887371 [ Info: Selecting generators in 0.052867255 [ Info: Inclusion checked with probability 0.995 in 0.010844477 seconds [ Info: The search for identifiable functions concluded in 2.67761025 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31 + k21*k41 + k31*k41, k12*k13 + k12*k14 + k13*k14, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31*k41, k12*k13*k14] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), u(t), k01, k12, k13, k14, k21, k31, k41] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.010714478 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006703706 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.287e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.25529314 [ Info: Selecting generators in 0.062831959 [ Info: Inclusion checked with probability 0.995 in 0.01150709 seconds [ Info: The search for identifiable functions concluded in 1.242199899 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31 + k21*k41 + k31*k41, k12*k13 + k12*k14 + k13*k14, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31*k41, k12*k13*k14] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), u(t), k01, k12, k13, k14, k21, k31, k41] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.010407051 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006830155 seconds [ Info: Dimensions of the Wronskians [8] [ Info: Ranks of the Wronskians computed in 2.439e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.746821203 [ Info: Selecting generators in 0.089984321 [ Info: Inclusion checked with probability 0.995 in 0.014463882 seconds [ Info: The search for identifiable functions concluded in 1.25359684 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31 + k21*k41 + k31*k41, k12*k13 + k12*k14 + k13*k14, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31*k41, k12*k13*k14] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 - x1(t)*k31 - x1(t)*k41 + x2(t)*k12 + x3(t)*k13 + x4(t)*k14 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k13 │ x4'(t) = x1(t)*k41 - x4(t)*k14 │ y1(t) = x1(t) │ , ident_funcs = AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k12*k13 + k12*k14 + k13*k14, k01, k21 + k31 + k41, k12 + k13 + k14, k21*k31*k41, k12*k31 + k12*k41 + k13*k21 + k13*k41 + k14*k21 + k14*k31, k21*k31 + k21*k41 + k31*k41, k12*k13*k14]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), x4(t), ..., k41 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), u(t), k01, k12, k13, k14, k21, k31, k41] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.036380572 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.018713121 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 9.5849e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000148839 [ Info: Selecting generators in 0.010339041 [ Info: Inclusion checked with probability 0.995 in 0.013802578 seconds [ Info: The search for identifiable functions concluded in 0.129620891 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10//k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.026495926 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.016298654 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 7.753e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000129759 [ Info: Selecting generators in 0.009491699 [ Info: Inclusion checked with probability 0.995 in 0.012911307 seconds [ Info: The search for identifiable functions concluded in 0.111277396 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10//k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.025906583 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.016036997 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.7089e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000121329 [ Info: Selecting generators in 0.00939248 [ Info: Inclusion checked with probability 0.995 in 0.011964806 seconds [ Info: The search for identifiable functions concluded in 0.107551712 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10//k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.026054491 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01881347 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.446e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.03661905 [ Info: Selecting generators in 0.013207274 [ Info: Inclusion checked with probability 0.995 in 0.01256591 seconds [ Info: The search for identifiable functions concluded in 0.148766408 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10*k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x5(t), x7(t), x4(t), x6(t), y1(t), y2(t), k10, k5, k6, k7, k8, k9] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.026558296 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.0146579 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.52e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.053036283 [ Info: Selecting generators in 0.016339764 [ Info: Inclusion checked with probability 0.995 in 0.014179735 seconds [ Info: The search for identifiable functions concluded in 0.174018077 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10*k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x5(t), x7(t), x4(t), x6(t), y1(t), y2(t), k10, k5, k6, k7, k8, k9] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.027977963 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01892346 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 9.225e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.042683132 [ Info: Selecting generators in 0.016875648 [ Info: Inclusion checked with probability 0.995 in 0.014136514 seconds [ Info: The search for identifiable functions concluded in 0.170225383 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k7, k6, k5, k10 + 2*k8, k9^2, k10*k9] │ case = │ (ode = x5'(t) = (x5(t)*x4(t)*k5 - x5(t)*x4(t)*k7 - x5(t)*k6*k7 + x4(t)*x6(t)*k5 + x4(t)*k5*k8)//(x5(t)*x4(t) + x5(t)*k6 + x4(t)*x6(t) + x4(t)*k8 + x6(t)*k6 + k6*k8) │ x7'(t) = (-x6(t)^2*k9 + x6(t)*k10*k9)//k10 │ x4'(t) = (-x4(t)*k5)//(x4(t) + k6) │ x6'(t) = (x5(t)*x6(t)^2*k9 - x5(t)*x6(t)*k10*k9 + x5(t)*k10*k7 + x6(t)^3*k9 - x6(t)^2*k10*k9 + x6(t)^2*k8*k9 - x6(t)*k10*k8*k9)//(x5(t)*k10 + x6(t)*k10 + k10*k8) │ y1(t) = x4(t) │ y2(t) = x5(t) │ , ident_funcs = QQMPolyRingElem[k7, k5, k6, k10*k9, k9^2, k10 + 2*k8]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x5(t), x7(t), x4(t), x6(t), ..., k9 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x5(t), x7(t), x4(t), x6(t), y1(t), y2(t), k10, k5, k6, k7, k8, k9] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012332632 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017506153 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.407e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000176998 [ Info: Selecting generators in 0.084173516 [ Info: Inclusion checked with probability 0.995 in 0.015125825 seconds [ Info: The search for identifiable functions concluded in 1.286620234 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*b*g + a*b*s + b*e*g*s, (a*e)//(a + e*s - s)] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.011178153 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01572203 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 7.0239e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000175978 [ Info: Selecting generators in 0.085568623 [ Info: Inclusion checked with probability 0.995 in 0.016153245 seconds [ Info: The search for identifiable functions concluded in 0.582898219 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*b*g + a*b*s + b*e*g*s, (a*e)//(a + e*s - s)] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.011893127 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017453783 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 9.0639e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000261288 [ Info: Selecting generators in 0.10884571 [ Info: Inclusion checked with probability 0.995 in 0.017448153 seconds [ Info: The search for identifiable functions concluded in 1.251483899 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*b*g + a*b*s + b*e*g*s, (a*e)//(a + e*s - s)] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012041925 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.015335064 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.9949e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.067370576 [ Info: Selecting generators in 0.089359016 [ Info: Inclusion checked with probability 0.995 in 0.016464343 seconds [ Info: The search for identifiable functions concluded in 0.592458228 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*e*g, a*g + e*g*s - g*s] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), In(t), L(t), Q(t), y(t), u(t), Ninv, a, b, e, g, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014158475 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017252255 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 8.5189e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.096244851 [ Info: Selecting generators in 0.101199363 [ Info: Inclusion checked with probability 0.995 in 0.016511812 seconds [ Info: The search for identifiable functions concluded in 1.36858457 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*e*g, a*g + e*g*s - g*s] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), In(t), L(t), Q(t), y(t), u(t), Ninv, a, b, e, g, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01145761 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.015880728 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.7619e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.081014078 [ Info: Selecting generators in 0.097699406 [ Info: Inclusion checked with probability 0.995 in 0.018127487 seconds [ Info: The search for identifiable functions concluded in 1.644394454 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, b, Ninv, a + g, a*e*g, a*g + e*g*s - g*s] │ case = │ (ode = S'(t) = -S(t)*In(t)*Ninv*b - S(t)*u(t)*Ninv │ In'(t) = -In(t)*g + L(t)*a + Q(t)*s │ L'(t) = S(t)*In(t)*Ninv*b - L(t)*a │ Q'(t) = -In(t)*e*g + In(t)*g - Q(t)*s │ y(t) = In(t)*Ninv │ , ident_funcs = QQMPolyRingElem[a*g + e*g*s - g*s, b, a + g, a*e*g, s, Ninv]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables S(t), In(t), L(t), Q(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), In(t), L(t), Q(t), y(t), u(t), Ninv, a, b, e, g, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 3.216368851 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.085988989 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 7.8799e-5 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:01 Points: 18   ⌞ # Computing specializations.. Time: 0:00:01 Points: 25   ⌜ # Computing specializations.. Time: 0:00:01 Points: 31   ⌝ # Computing specializations.. Time: 0:00:02 Points: 37   ⌟ # Computing specializations.. Time: 0:00:02 Points: 44   ⌞ # Computing specializations.. Time: 0:00:02 Points: 50   ⌜ # Computing specializations.. Time: 0:00:03 Points: 56   ⌝ # Computing specializations.. Time: 0:00:03 Points: 62   ⌟ # Computing specializations.. Time: 0:00:04 Points: 68   ⌞ # Computing specializations.. Time: 0:00:04 Points: 74   ⌜ # Computing specializations.. Time: 0:00:04 Points: 80   ⌝ # Computing specializations.. Time: 0:00:05 Points: 87   ⌟ # Computing specializations.. Time: 0:00:05 Points: 93   ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ⌟ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 15   ⌟ # Computing specializations.. Time: 0:00:01 Points: 24   ⌞ # Computing specializations.. Time: 0:00:01 Points: 33   ⌜ # Computing specializations.. Time: 0:00:01 Points: 40   ⌝ # Computing specializations.. Time: 0:00:02 Points: 49   ⌟ # Computing specializations.. Time: 0:00:02 Points: 56   ⌞ # Computing specializations.. Time: 0:00:02 Points: 65   ⌜ # Computing specializations.. Time: 0:00:03 Points: 74   ⌝ # Computing specializations.. Time: 0:00:03 Points: 81   ⌟ # Computing specializations.. Time: 0:00:04 Points: 89   ⌞ # Computing specializations.. Time: 0:00:04 Points: 98   ⌜ # Computing specializations.. Time: 0:00:04 Points: 107   ⌝ # Computing specializations.. Time: 0:00:05 Points: 116   ⌟ # Computing specializations.. Time: 0:00:05 Points: 123   ⌞ # Computing specializations.. Time: 0:00:05 Points: 129   ⌜ # Computing specializations.. Time: 0:00:06 Points: 135   ⌝ # Computing specializations.. Time: 0:00:06 Points: 141   ⌟ # Computing specializations.. Time: 0:00:07 Points: 148   ⌞ # Computing specializations.. Time: 0:00:07 Points: 154   ⌜ # Computing specializations.. Time: 0:00:07 Points: 160   ⌝ # Computing specializations.. Time: 0:00:08 Points: 166   ⌟ # Computing specializations.. Time: 0:00:08 Points: 172   ⌞ # Computing specializations.. Time: 0:00:08 Points: 179   ⌜ # Computing specializations.. Time: 0:00:09 Points: 184   ⌝ # Computing specializations.. Time: 0:00:09 Points: 191   ⌟ # Computing specializations.. Time: 0:00:10 Points: 197   ⌞ # Computing specializations.. Time: 0:00:10 Points: 203   ⌜ # Computing specializations.. Time: 0:00:10 Points: 209   ⌝ # Computing specializations.. Time: 0:00:11 Points: 215   ⌟ # Computing specializations.. Time: 0:00:11 Points: 221   ⌞ # Computing specializations.. Time: 0:00:12 Points: 227   ⌜ # Computing specializations.. Time: 0:00:12 Points: 233   ⌝ # Computing specializations.. Time: 0:00:12 Points: 239   ⌟ # Computing specializations.. Time: 0:00:13 Points: 246   ⌞ # Computing specializations.. Time: 0:00:13 Points: 253   ⌜ # Computing specializations.. Time: 0:00:13 Points: 260   ⌝ # Computing specializations.. Time: 0:00:14 Points: 266   ⌟ # Computing specializations.. Time: 0:00:14 Points: 272   ⌞ # Computing specializations.. Time: 0:00:15 Points: 278   ⌜ # Computing specializations.. Time: 0:00:15 Points: 284   ⌝ # Computing specializations.. Time: 0:00:15 Points: 290   ⌟ # Computing specializations.. Time: 0:00:16 Points: 297   ⌞ # Computing specializations.. Time: 0:00:16 Points: 303   ⌜ # Computing specializations.. Time: 0:00:16 Points: 309   ⌝ # Computing specializations.. Time: 0:00:17 Points: 315   ⌟ # Computing specializations.. Time: 0:00:17 Points: 321   ⌞ # Computing specializations.. Time: 0:00:18 Points: 327   ⌜ # Computing specializations.. Time: 0:00:18 Points: 333   ⌝ # Computing specializations.. Time: 0:00:18 Points: 340   ⌟ # Computing specializations.. Time: 0:00:19 Points: 346   ⌞ # Computing specializations.. Time: 0:00:19 Points: 352   ⌜ # Computing specializations.. Time: 0:00:20 Points: 358   ⌝ # Computing specializations.. Time: 0:00:20 Points: 364   ⌟ # Computing specializations.. Time: 0:00:20 Points: 370   ⌞ # Computing specializations.. Time: 0:00:21 Points: 376   ⌜ # Computing specializations.. Time: 0:00:21 Points: 383   ⌝ # Computing specializations.. Time: 0:00:21 Points: 389   ⌟ # Computing specializations.. Time: 0:00:22 Points: 395   ⌞ # Computing specializations.. Time: 0:00:22 Points: 402   ⌜ # Computing specializations.. Time: 0:00:23 Points: 408   ⌝ # Computing specializations.. Time: 0:00:23 Points: 414   ⌟ # Computing specializations.. Time: 0:00:23 Points: 420   ⌞ # Computing specializations.. Time: 0:00:24 Points: 426   ⌜ # Computing specializations.. Time: 0:00:24 Points: 432   ⌝ # Computing specializations.. Time: 0:00:25 Points: 438   ⌟ # Computing specializations.. Time: 0:00:25 Points: 445   ⌞ # Computing specializations.. Time: 0:00:25 Points: 451   ⌜ # Computing specializations.. Time: 0:00:26 Points: 457   ⌝ # Computing specializations.. Time: 0:00:26 Points: 463   ⌟ # Computing specializations.. Time: 0:00:26 Points: 469   ⌞ # Computing specializations.. Time: 0:00:27 Points: 475   ⌜ # Computing specializations.. Time: 0:00:27 Points: 481   ⌝ # Computing specializations.. Time: 0:00:28 Points: 488   ⌟ # Computing specializations.. Time: 0:00:28 Points: 494   ⌞ # Computing specializations.. Time: 0:00:28 Points: 501   ⌜ # Computing specializations.. Time: 0:00:29 Points: 506   ⌝ # Computing specializations.. Time: 0:00:29 Points: 512   ⌟ # Computing specializations.. Time: 0:00:29 Points: 518   ⌞ # Computing specializations.. Time: 0:00:30 Points: 524   ⌜ # Computing specializations.. Time: 0:00:30 Points: 531   ⌝ # Computing specializations.. Time: 0:00:30 Points: 537   ⌟ # Computing specializations.. Time: 0:00:31 Points: 544   ⌞ # Computing specializations.. Time: 0:00:31 Points: 549   ⌜ # Computing specializations.. Time: 0:00:32 Points: 555   ⌝ # Computing specializations.. Time: 0:00:32 Points: 562   ⌟ # Computing specializations.. Time: 0:00:32 Points: 567   ⌞ # Computing specializations.. Time: 0:00:33 Points: 574   ⌜ # Computing specializations.. Time: 0:00:33 Points: 580   ⌝ # Computing specializations.. Time: 0:00:33 Points: 587   ⌟ # Computing specializations.. Time: 0:00:34 Points: 592   ⌞ # Computing specializations.. Time: 0:00:34 Points: 598   ⌜ # Computing specializations.. Time: 0:00:34 Points: 604   ⌝ # Computing specializations.. Time: 0:00:35 Points: 610   ⌟ # Computing specializations.. Time: 0:00:35 Points: 617   ⌞ # Computing specializations.. Time: 0:00:36 Points: 623   ⌜ # Computing specializations.. Time: 0:00:36 Points: 629   ⌝ # Computing specializations.. Time: 0:00:36 Points: 635   ✓ # Computing specializations.. Time: 0:00:37 [ Info: Search for polynomial generators concluded in 0.000349256 [ Info: Selecting generators in 0.033089304 [ Info: Inclusion checked with probability 0.995 in 7.624345865 seconds [ Info: The search for identifiable functions concluded in 70.659991953 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (T*a + T*d + T*dr + e + g - r - rR)//T, (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 2.535651357 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.068498175 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 8.0089e-5 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 3   ⌝ # Computing specializations.. Time: 0:00:00 Points: 11   ⌟ # Computing specializations.. Time: 0:00:01 Points: 18   ⌞ # Computing specializations.. Time: 0:00:01 Points: 25   ⌜ # Computing specializations.. Time: 0:00:01 Points: 32   ⌝ # Computing specializations.. Time: 0:00:02 Points: 39   ⌟ # Computing specializations.. Time: 0:00:02 Points: 45   ⌞ # Computing specializations.. Time: 0:00:03 Points: 51   ⌜ # Computing specializations.. Time: 0:00:03 Points: 57   ⌝ # Computing specializations.. Time: 0:00:03 Points: 64   ⌟ # Computing specializations.. Time: 0:00:04 Points: 71   ⌞ # Computing specializations.. Time: 0:00:04 Points: 79   ⌜ # Computing specializations.. Time: 0:00:04 Points: 86   ⌝ # Computing specializations.. Time: 0:00:05 Points: 93   ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 7   ⌝ # Computing specializations.. Time: 0:00:00 Points: 14   ⌟ # Computing specializations.. Time: 0:00:01 Points: 19   ⌞ # Computing specializations.. Time: 0:00:01 Points: 27   ⌜ # Computing specializations.. Time: 0:00:01 Points: 34   ⌝ # Computing specializations.. Time: 0:00:02 Points: 41   ⌟ # Computing specializations.. Time: 0:00:02 Points: 46   ⌞ # Computing specializations.. Time: 0:00:02 Points: 53   ⌜ # Computing specializations.. Time: 0:00:03 Points: 60   ⌝ # Computing specializations.. Time: 0:00:03 Points: 67   ⌟ # Computing specializations.. Time: 0:00:04 Points: 74   ⌞ # Computing specializations.. Time: 0:00:04 Points: 81   ⌜ # Computing specializations.. Time: 0:00:04 Points: 88   ⌝ # Computing specializations.. Time: 0:00:05 Points: 93   ⌟ # Computing specializations.. Time: 0:00:05 Points: 100   ⌞ # Computing specializations.. Time: 0:00:05 Points: 107   ⌜ # Computing specializations.. Time: 0:00:06 Points: 113   ⌝ # Computing specializations.. Time: 0:00:06 Points: 120   ⌟ # Computing specializations.. Time: 0:00:07 Points: 127   ⌞ # Computing specializations.. Time: 0:00:07 Points: 134   ⌜ # Computing specializations.. Time: 0:00:07 Points: 140   ⌝ # Computing specializations.. Time: 0:00:08 Points: 147   ⌟ # Computing specializations.. Time: 0:00:08 Points: 155   ⌞ # Computing specializations.. Time: 0:00:09 Points: 161   ⌜ # Computing specializations.. Time: 0:00:09 Points: 168   ⌝ # Computing specializations.. Time: 0:00:09 Points: 175   ⌟ # Computing specializations.. Time: 0:00:10 Points: 182   ⌞ # Computing specializations.. Time: 0:00:10 Points: 188   ⌜ # Computing specializations.. Time: 0:00:10 Points: 195   ⌝ # Computing specializations.. Time: 0:00:11 Points: 202   ⌟ # Computing specializations.. Time: 0:00:11 Points: 207   ⌞ # Computing specializations.. Time: 0:00:12 Points: 215   ⌜ # Computing specializations.. Time: 0:00:12 Points: 222   ⌝ # Computing specializations.. Time: 0:00:12 Points: 229   ⌟ # Computing specializations.. Time: 0:00:13 Points: 234   ⌞ # Computing specializations.. Time: 0:00:13 Points: 241   ⌜ # Computing specializations.. Time: 0:00:13 Points: 248   ⌝ # Computing specializations.. Time: 0:00:14 Points: 255   ⌟ # Computing specializations.. Time: 0:00:14 Points: 264   ⌞ # Computing specializations.. Time: 0:00:15 Points: 271   ⌜ # Computing specializations.. Time: 0:00:15 Points: 278   ⌝ # Computing specializations.. Time: 0:00:15 Points: 286   ⌟ # Computing specializations.. Time: 0:00:16 Points: 293   ⌞ # Computing specializations.. Time: 0:00:16 Points: 300   ⌜ # Computing specializations.. Time: 0:00:17 Points: 306   ⌝ # Computing specializations.. Time: 0:00:17 Points: 314   ⌟ # Computing specializations.. Time: 0:00:17 Points: 321   ⌞ # Computing specializations.. Time: 0:00:18 Points: 326   ⌜ # Computing specializations.. Time: 0:00:18 Points: 334   ⌝ # Computing specializations.. Time: 0:00:18 Points: 341   ⌟ # Computing specializations.. Time: 0:00:19 Points: 348   ⌞ # Computing specializations.. Time: 0:00:19 Points: 353   ⌜ # Computing specializations.. Time: 0:00:20 Points: 360   ⌝ # Computing specializations.. Time: 0:00:20 Points: 367   ⌟ # Computing specializations.. Time: 0:00:20 Points: 373   ⌞ # Computing specializations.. Time: 0:00:21 Points: 381   ⌜ # Computing specializations.. Time: 0:00:21 Points: 388   ⌝ # Computing specializations.. Time: 0:00:21 Points: 395   ⌟ # Computing specializations.. Time: 0:00:22 Points: 402   ⌞ # Computing specializations.. Time: 0:00:22 Points: 409   ⌜ # Computing specializations.. Time: 0:00:23 Points: 416   ⌝ # Computing specializations.. Time: 0:00:23 Points: 422   ⌟ # Computing specializations.. Time: 0:00:23 Points: 428   ⌞ # Computing specializations.. Time: 0:00:24 Points: 435   ⌜ # Computing specializations.. Time: 0:00:24 Points: 442   ⌝ # Computing specializations.. Time: 0:00:25 Points: 448   ⌟ # Computing specializations.. Time: 0:00:25 Points: 455   ⌞ # Computing specializations.. Time: 0:00:25 Points: 462   ⌜ # Computing specializations.. Time: 0:00:26 Points: 468   ⌝ # Computing specializations.. Time: 0:00:26 Points: 476   ⌟ # Computing specializations.. Time: 0:00:26 Points: 483   ⌞ # Computing specializations.. Time: 0:00:27 Points: 490   ⌜ # Computing specializations.. Time: 0:00:27 Points: 497   ⌝ # Computing specializations.. Time: 0:00:28 Points: 504   ⌟ # Computing specializations.. Time: 0:00:28 Points: 511   ⌞ # Computing specializations.. Time: 0:00:29 Points: 518   ⌜ # Computing specializations.. Time: 0:00:29 Points: 525   ⌝ # Computing specializations.. Time: 0:00:29 Points: 531   ⌟ # Computing specializations.. Time: 0:00:30 Points: 538   ⌞ # Computing specializations.. Time: 0:00:30 Points: 543   ⌜ # Computing specializations.. Time: 0:00:30 Points: 549   ⌝ # Computing specializations.. Time: 0:00:31 Points: 556   ⌟ # Computing specializations.. Time: 0:00:31 Points: 563   ⌞ # Computing specializations.. Time: 0:00:31 Points: 568   ⌜ # Computing specializations.. Time: 0:00:32 Points: 577   ⌝ # Computing specializations.. Time: 0:00:32 Points: 586   ⌟ # Computing specializations.. Time: 0:00:33 Points: 594   ⌞ # Computing specializations.. Time: 0:00:33 Points: 601   ⌜ # Computing specializations.. Time: 0:00:33 Points: 608   ⌝ # Computing specializations.. Time: 0:00:34 Points: 614   ⌟ # Computing specializations.. Time: 0:00:34 Points: 621   ⌞ # Computing specializations.. Time: 0:00:34 Points: 628   ⌜ # Computing specializations.. Time: 0:00:35 Points: 636   ✓ # Computing specializations.. Time: 0:00:36 [ Info: Search for polynomial generators concluded in 0.000425436 [ Info: Selecting generators in 0.041265156 [ Info: Inclusion checked with probability 0.995 in 7.597004598 seconds [ Info: The search for identifiable functions concluded in 66.365260426 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (T*a + T*d + T*dr + e + g - r - rR)//T, (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 2.625264281 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.072487077 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000110918 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:01 Points: 17   ⌞ # Computing specializations.. Time: 0:00:01 Points: 23   ⌜ # Computing specializations.. Time: 0:00:01 Points: 29   ⌝ # Computing specializations.. Time: 0:00:02 Points: 35   ⌟ # Computing specializations.. Time: 0:00:02 Points: 41   ⌞ # Computing specializations.. Time: 0:00:03 Points: 47   ⌜ # Computing specializations.. Time: 0:00:03 Points: 53   ⌝ # Computing specializations.. Time: 0:00:03 Points: 58   ⌟ # Computing specializations.. Time: 0:00:04 Points: 65   ⌞ # Computing specializations.. Time: 0:00:04 Points: 71   ⌜ # Computing specializations.. Time: 0:00:04 Points: 77   ⌝ # Computing specializations.. Time: 0:00:05 Points: 83   ⌟ # Computing specializations.. Time: 0:00:05 Points: 89   ⌞ # Computing specializations.. Time: 0:00:06 Points: 95   ✓ # Computing specializations.. Time: 0:00:06 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ⌟ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 10   ⌟ # Computing specializations.. Time: 0:00:01 Points: 16   ⌞ # Computing specializations.. Time: 0:00:01 Points: 22   ⌜ # Computing specializations.. Time: 0:00:01 Points: 28   ⌝ # Computing specializations.. Time: 0:00:02 Points: 34   ⌟ # Computing specializations.. Time: 0:00:02 Points: 40   ⌞ # Computing specializations.. Time: 0:00:02 Points: 46   ⌜ # Computing specializations.. Time: 0:00:03 Points: 52   ⌝ # Computing specializations.. Time: 0:00:03 Points: 58   ⌟ # Computing specializations.. Time: 0:00:04 Points: 64   ⌞ # Computing specializations.. Time: 0:00:04 Points: 70   ⌜ # Computing specializations.. Time: 0:00:04 Points: 76   ⌝ # Computing specializations.. Time: 0:00:05 Points: 82   ⌟ # Computing specializations.. Time: 0:00:05 Points: 88   ⌞ # Computing specializations.. Time: 0:00:05 Points: 94   ⌜ # Computing specializations.. Time: 0:00:06 Points: 100   ⌝ # Computing specializations.. Time: 0:00:06 Points: 106   ⌟ # Computing specializations.. Time: 0:00:07 Points: 112   ⌞ # Computing specializations.. Time: 0:00:07 Points: 118   ⌜ # Computing specializations.. Time: 0:00:08 Points: 124   ⌝ # Computing specializations.. Time: 0:00:08 Points: 131   ⌟ # Computing specializations.. Time: 0:00:08 Points: 137   ⌞ # Computing specializations.. Time: 0:00:09 Points: 143   ⌜ # Computing specializations.. Time: 0:00:09 Points: 149   ⌝ # Computing specializations.. Time: 0:00:09 Points: 155   ⌟ # Computing specializations.. Time: 0:00:10 Points: 161   ⌞ # Computing specializations.. Time: 0:00:10 Points: 170   ⌜ # Computing specializations.. Time: 0:00:11 Points: 177   ⌝ # Computing specializations.. Time: 0:00:11 Points: 183   ⌟ # Computing specializations.. Time: 0:00:11 Points: 189   ⌞ # Computing specializations.. Time: 0:00:12 Points: 195   ⌜ # Computing specializations.. Time: 0:00:12 Points: 201   ⌝ # Computing specializations.. Time: 0:00:12 Points: 207   ⌟ # Computing specializations.. Time: 0:00:13 Points: 213   ⌞ # Computing specializations.. Time: 0:00:13 Points: 219   ⌜ # Computing specializations.. Time: 0:00:14 Points: 226   ⌝ # Computing specializations.. Time: 0:00:14 Points: 232   ⌟ # Computing specializations.. Time: 0:00:14 Points: 238   ⌞ # Computing specializations.. Time: 0:00:15 Points: 244   ⌜ # Computing specializations.. Time: 0:00:15 Points: 250   ⌝ # Computing specializations.. Time: 0:00:15 Points: 256   ⌟ # Computing specializations.. Time: 0:00:16 Points: 262   ⌞ # Computing specializations.. Time: 0:00:16 Points: 268   ⌜ # Computing specializations.. Time: 0:00:17 Points: 274   ⌝ # Computing specializations.. Time: 0:00:17 Points: 280   ⌟ # Computing specializations.. Time: 0:00:17 Points: 286   ⌞ # Computing specializations.. Time: 0:00:18 Points: 292   ⌜ # Computing specializations.. Time: 0:00:18 Points: 298   ⌝ # Computing specializations.. Time: 0:00:18 Points: 304   ⌟ # Computing specializations.. Time: 0:00:19 Points: 310   ⌞ # Computing specializations.. Time: 0:00:19 Points: 317   ⌜ # Computing specializations.. Time: 0:00:20 Points: 323   ⌝ # Computing specializations.. Time: 0:00:20 Points: 329   ⌟ # Computing specializations.. Time: 0:00:21 Points: 335   ⌞ # Computing specializations.. Time: 0:00:21 Points: 341   ⌜ # Computing specializations.. Time: 0:00:21 Points: 347   ⌝ # Computing specializations.. Time: 0:00:22 Points: 353   ⌟ # Computing specializations.. Time: 0:00:22 Points: 359   ⌞ # Computing specializations.. Time: 0:00:22 Points: 364   ⌜ # Computing specializations.. Time: 0:00:23 Points: 370   ⌝ # Computing specializations.. Time: 0:00:23 Points: 376   ⌟ # Computing specializations.. Time: 0:00:24 Points: 380   ⌞ # Computing specializations.. Time: 0:00:24 Points: 387   ⌜ # Computing specializations.. Time: 0:00:24 Points: 393   ⌝ # Computing specializations.. Time: 0:00:25 Points: 399   ⌟ # Computing specializations.. Time: 0:00:25 Points: 405   ⌞ # Computing specializations.. Time: 0:00:26 Points: 411   ⌜ # Computing specializations.. Time: 0:00:26 Points: 417   ⌝ # Computing specializations.. Time: 0:00:26 Points: 423   ⌟ # Computing specializations.. Time: 0:00:27 Points: 429   ⌞ # Computing specializations.. Time: 0:00:27 Points: 435   ⌜ # Computing specializations.. Time: 0:00:27 Points: 441   ⌝ # Computing specializations.. Time: 0:00:28 Points: 447   ⌟ # Computing specializations.. Time: 0:00:28 Points: 453   ⌞ # Computing specializations.. Time: 0:00:29 Points: 459   ⌜ # Computing specializations.. Time: 0:00:29 Points: 465   ⌝ # Computing specializations.. Time: 0:00:29 Points: 471   ⌟ # Computing specializations.. Time: 0:00:30 Points: 476   ⌞ # Computing specializations.. Time: 0:00:30 Points: 482   ⌜ # Computing specializations.. Time: 0:00:30 Points: 488   ⌝ # Computing specializations.. Time: 0:00:31 Points: 494   ⌟ # Computing specializations.. Time: 0:00:31 Points: 500   ⌞ # Computing specializations.. Time: 0:00:32 Points: 506   ⌜ # Computing specializations.. Time: 0:00:32 Points: 512   ⌝ # Computing specializations.. Time: 0:00:32 Points: 518   ⌟ # Computing specializations.. Time: 0:00:33 Points: 524   ⌞ # Computing specializations.. Time: 0:00:33 Points: 530   ⌜ # Computing specializations.. Time: 0:00:34 Points: 536   ⌝ # Computing specializations.. Time: 0:00:34 Points: 542   ⌟ # Computing specializations.. Time: 0:00:34 Points: 548   ⌞ # Computing specializations.. Time: 0:00:35 Points: 554   ⌜ # Computing specializations.. Time: 0:00:35 Points: 560   ⌝ # Computing specializations.. Time: 0:00:35 Points: 567   ⌟ # Computing specializations.. Time: 0:00:36 Points: 573   ⌞ # Computing specializations.. Time: 0:00:36 Points: 579   ⌜ # Computing specializations.. Time: 0:00:37 Points: 585   ⌝ # Computing specializations.. Time: 0:00:37 Points: 591   ⌟ # Computing specializations.. Time: 0:00:38 Points: 598   ⌞ # Computing specializations.. Time: 0:00:38 Points: 604   ⌜ # Computing specializations.. Time: 0:00:38 Points: 610   ⌝ # Computing specializations.. Time: 0:00:39 Points: 616   ⌟ # Computing specializations.. Time: 0:00:39 Points: 622   ⌞ # Computing specializations.. Time: 0:00:39 Points: 628   ⌜ # Computing specializations.. Time: 0:00:40 Points: 634   ⌝ # Computing specializations.. Time: 0:00:40 Points: 640   ✓ # Computing specializations.. Time: 0:00:41 [ Info: Search for polynomial generators concluded in 0.000411326 [ Info: Selecting generators in 0.037048516 [ Info: Inclusion checked with probability 0.995 in 8.131002348 seconds [ Info: The search for identifiable functions concluded in 77.35339877 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 2.665306509 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.069763813 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 8.568e-5 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 3   ⌝ # Computing specializations.. Time: 0:00:00 Points: 10   ⌟ # Computing specializations.. Time: 0:00:00 Points: 16   ⌞ # Computing specializations.. Time: 0:00:01 Points: 22   ⌜ # Computing specializations.. Time: 0:00:01 Points: 28   ⌝ # Computing specializations.. Time: 0:00:02 Points: 35   ⌟ # Computing specializations.. Time: 0:00:02 Points: 41   ⌞ # Computing specializations.. Time: 0:00:02 Points: 48   ⌜ # Computing specializations.. Time: 0:00:03 Points: 54   ⌝ # Computing specializations.. Time: 0:00:03 Points: 61   ⌟ # Computing specializations.. Time: 0:00:04 Points: 67   ⌞ # Computing specializations.. Time: 0:00:04 Points: 73   ⌜ # Computing specializations.. Time: 0:00:04 Points: 80   ⌝ # Computing specializations.. Time: 0:00:05 Points: 85   ⌟ # Computing specializations.. Time: 0:00:05 Points: 91   ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ⌟ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:00 Points: 19   ⌞ # Computing specializations.. Time: 0:00:01 Points: 24   ⌜ # Computing specializations.. Time: 0:00:01 Points: 30   ⌝ # Computing specializations.. Time: 0:00:02 Points: 36   ⌟ # Computing specializations.. Time: 0:00:02 Points: 42   ⌞ # Computing specializations.. Time: 0:00:03 Points: 48   ⌜ # Computing specializations.. Time: 0:00:03 Points: 55   ⌝ # Computing specializations.. Time: 0:00:03 Points: 61   ⌟ # Computing specializations.. Time: 0:00:04 Points: 67   ⌞ # Computing specializations.. Time: 0:00:04 Points: 73   ⌜ # Computing specializations.. Time: 0:00:04 Points: 79   ⌝ # Computing specializations.. Time: 0:00:05 Points: 85   ⌟ # Computing specializations.. Time: 0:00:05 Points: 92   ⌞ # Computing specializations.. Time: 0:00:05 Points: 99   ⌜ # Computing specializations.. Time: 0:00:06 Points: 104   ⌝ # Computing specializations.. Time: 0:00:06 Points: 111   ⌟ # Computing specializations.. Time: 0:00:07 Points: 118   ⌞ # Computing specializations.. Time: 0:00:07 Points: 125   ⌜ # Computing specializations.. Time: 0:00:07 Points: 131   ⌝ # Computing specializations.. Time: 0:00:08 Points: 139   ⌟ # Computing specializations.. Time: 0:00:08 Points: 146   ⌞ # Computing specializations.. Time: 0:00:08 Points: 152   ⌜ # Computing specializations.. Time: 0:00:09 Points: 158   ⌝ # Computing specializations.. Time: 0:00:09 Points: 165   ⌟ # Computing specializations.. Time: 0:00:10 Points: 171   ⌞ # Computing specializations.. Time: 0:00:10 Points: 178   ⌜ # Computing specializations.. Time: 0:00:10 Points: 184   ⌝ # Computing specializations.. Time: 0:00:11 Points: 190   ⌟ # Computing specializations.. Time: 0:00:11 Points: 196   ⌞ # Computing specializations.. Time: 0:00:12 Points: 203   ⌜ # Computing specializations.. Time: 0:00:12 Points: 210   ⌝ # Computing specializations.. Time: 0:00:12 Points: 215   ⌟ # Computing specializations.. Time: 0:00:13 Points: 222   ⌞ # Computing specializations.. Time: 0:00:13 Points: 228   ⌜ # Computing specializations.. Time: 0:00:13 Points: 235   ⌝ # Computing specializations.. Time: 0:00:14 Points: 240   ⌟ # Computing specializations.. Time: 0:00:14 Points: 247   ⌞ # Computing specializations.. Time: 0:00:15 Points: 253   ⌜ # Computing specializations.. Time: 0:00:15 Points: 259   ⌝ # Computing specializations.. Time: 0:00:15 Points: 266   ⌟ # Computing specializations.. Time: 0:00:16 Points: 271   ⌞ # Computing specializations.. Time: 0:00:16 Points: 277   ⌜ # Computing specializations.. Time: 0:00:16 Points: 283   ⌝ # Computing specializations.. Time: 0:00:17 Points: 289   ⌟ # Computing specializations.. Time: 0:00:17 Points: 295   ⌞ # Computing specializations.. Time: 0:00:18 Points: 302   ⌜ # Computing specializations.. Time: 0:00:18 Points: 309   ⌝ # Computing specializations.. Time: 0:00:18 Points: 316   ⌟ # Computing specializations.. Time: 0:00:19 Points: 322   ⌞ # Computing specializations.. Time: 0:00:19 Points: 327   ⌜ # Computing specializations.. Time: 0:00:19 Points: 333   ⌝ # Computing specializations.. Time: 0:00:20 Points: 340   ⌟ # Computing specializations.. Time: 0:00:20 Points: 347   ⌞ # Computing specializations.. Time: 0:00:21 Points: 353   ⌜ # Computing specializations.. Time: 0:00:21 Points: 358   ⌝ # Computing specializations.. Time: 0:00:21 Points: 364   ⌟ # Computing specializations.. Time: 0:00:22 Points: 371   ⌞ # Computing specializations.. Time: 0:00:22 Points: 378   ⌜ # Computing specializations.. Time: 0:00:23 Points: 385   ⌝ # Computing specializations.. Time: 0:00:23 Points: 391   ⌟ # Computing specializations.. Time: 0:00:23 Points: 397   ⌞ # Computing specializations.. Time: 0:00:24 Points: 403   ⌜ # Computing specializations.. Time: 0:00:24 Points: 409   ⌝ # Computing specializations.. Time: 0:00:24 Points: 415   ⌟ # Computing specializations.. Time: 0:00:25 Points: 422   ⌞ # Computing specializations.. Time: 0:00:25 Points: 429   ⌜ # Computing specializations.. Time: 0:00:26 Points: 434   ⌝ # Computing specializations.. Time: 0:00:26 Points: 441   ⌟ # Computing specializations.. Time: 0:00:26 Points: 447   ⌞ # Computing specializations.. Time: 0:00:27 Points: 454   ⌜ # Computing specializations.. Time: 0:00:27 Points: 461   ⌝ # Computing specializations.. Time: 0:00:28 Points: 467   ⌟ # Computing specializations.. Time: 0:00:28 Points: 473   ⌞ # Computing specializations.. Time: 0:00:28 Points: 479   ⌜ # Computing specializations.. Time: 0:00:29 Points: 486   ⌝ # Computing specializations.. Time: 0:00:29 Points: 491   ⌟ # Computing specializations.. Time: 0:00:29 Points: 497   ⌞ # Computing specializations.. Time: 0:00:30 Points: 503   ⌜ # Computing specializations.. Time: 0:00:30 Points: 510   ⌝ # Computing specializations.. Time: 0:00:31 Points: 516   ⌟ # Computing specializations.. Time: 0:00:31 Points: 523   ⌞ # Computing specializations.. Time: 0:00:31 Points: 530   ⌜ # Computing specializations.. Time: 0:00:32 Points: 536   ⌝ # Computing specializations.. Time: 0:00:32 Points: 542   ⌟ # Computing specializations.. Time: 0:00:32 Points: 548   ⌞ # Computing specializations.. Time: 0:00:33 Points: 555   ⌜ # Computing specializations.. Time: 0:00:33 Points: 562   ⌝ # Computing specializations.. Time: 0:00:33 Points: 569   ⌟ # Computing specializations.. Time: 0:00:34 Points: 575   ⌞ # Computing specializations.. Time: 0:00:34 Points: 581   ⌜ # Computing specializations.. Time: 0:00:35 Points: 587   ⌝ # Computing specializations.. Time: 0:00:35 Points: 593   ⌟ # Computing specializations.. Time: 0:00:36 Points: 599   ⌞ # Computing specializations.. Time: 0:00:36 Points: 606   ⌜ # Computing specializations.. Time: 0:00:36 Points: 612   ⌝ # Computing specializations.. Time: 0:00:37 Points: 619   ⌟ # Computing specializations.. Time: 0:00:37 Points: 626   ⌞ # Computing specializations.. Time: 0:00:37 Points: 631   ⌜ # Computing specializations.. Time: 0:00:38 Points: 637   ✓ # Computing specializations.. Time: 0:00:38 [ Info: Search for polynomial generators concluded in 1.973981307 [ Info: Selecting generators in 0.051659956 [ Info: Inclusion checked with probability 0.995 in 7.899458292 seconds [ Info: The search for identifiable functions concluded in 72.769435527 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), R(t), W(t), y1(t), y2(t), Dd, T, a, d, dr, e, g, r, rR] [ Info: Computing IO-equations [ Info: Computed IO-equations in 3.030441561 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.106771889 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000100119 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:01 Points: 18   ⌞ # Computing specializations.. Time: 0:00:01 Points: 24   ⌜ # Computing specializations.. Time: 0:00:01 Points: 30   ⌝ # Computing specializations.. Time: 0:00:02 Points: 36   ⌟ # Computing specializations.. Time: 0:00:02 Points: 42   ⌞ # Computing specializations.. Time: 0:00:03 Points: 48   ⌜ # Computing specializations.. Time: 0:00:03 Points: 54   ⌝ # Computing specializations.. Time: 0:00:03 Points: 60   ⌟ # Computing specializations.. Time: 0:00:04 Points: 67   ⌞ # Computing specializations.. Time: 0:00:04 Points: 73   ⌜ # Computing specializations.. Time: 0:00:05 Points: 80   ⌝ # Computing specializations.. Time: 0:00:05 Points: 86   ⌟ # Computing specializations.. Time: 0:00:05 Points: 92   ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 13   ⌟ # Computing specializations.. Time: 0:00:00 Points: 20   ⌞ # Computing specializations.. Time: 0:00:01 Points: 25   ⌜ # Computing specializations.. Time: 0:00:01 Points: 31   ⌝ # Computing specializations.. Time: 0:00:02 Points: 38   ⌟ # Computing specializations.. Time: 0:00:02 Points: 45   ⌞ # Computing specializations.. Time: 0:00:03 Points: 50   ⌜ # Computing specializations.. Time: 0:00:03 Points: 57   ⌝ # Computing specializations.. Time: 0:00:03 Points: 63   ⌟ # Computing specializations.. Time: 0:00:04 Points: 69   ⌞ # Computing specializations.. Time: 0:00:04 Points: 75   ⌜ # Computing specializations.. Time: 0:00:04 Points: 81   ⌝ # Computing specializations.. Time: 0:00:05 Points: 87   ⌟ # Computing specializations.. Time: 0:00:05 Points: 93   ⌞ # Computing specializations.. Time: 0:00:05 Points: 99   ⌜ # Computing specializations.. Time: 0:00:06 Points: 106   ⌝ # Computing specializations.. Time: 0:00:06 Points: 111   ⌟ # Computing specializations.. Time: 0:00:07 Points: 118   ⌞ # Computing specializations.. Time: 0:00:07 Points: 125   ⌜ # Computing specializations.. Time: 0:00:07 Points: 132   ⌝ # Computing specializations.. Time: 0:00:08 Points: 138   ⌟ # Computing specializations.. Time: 0:00:08 Points: 145   ⌞ # Computing specializations.. Time: 0:00:09 Points: 152   ⌜ # Computing specializations.. Time: 0:00:09 Points: 159   ⌝ # Computing specializations.. Time: 0:00:09 Points: 166   ⌟ # Computing specializations.. Time: 0:00:10 Points: 171   ⌞ # Computing specializations.. Time: 0:00:10 Points: 178   ⌜ # Computing specializations.. Time: 0:00:10 Points: 185   ⌝ # Computing specializations.. Time: 0:00:11 Points: 192   ⌟ # Computing specializations.. Time: 0:00:11 Points: 197   ⌞ # Computing specializations.. Time: 0:00:12 Points: 205   ⌜ # Computing specializations.. Time: 0:00:12 Points: 212   ⌝ # Computing specializations.. Time: 0:00:12 Points: 219   ⌟ # Computing specializations.. Time: 0:00:13 Points: 226   ⌞ # Computing specializations.. Time: 0:00:13 Points: 233   ⌜ # Computing specializations.. Time: 0:00:14 Points: 240   ⌝ # Computing specializations.. Time: 0:00:14 Points: 246   ⌟ # Computing specializations.. Time: 0:00:14 Points: 253   ⌞ # Computing specializations.. Time: 0:00:15 Points: 258   ⌜ # Computing specializations.. Time: 0:00:15 Points: 265   ⌝ # Computing specializations.. Time: 0:00:15 Points: 272   ⌟ # Computing specializations.. Time: 0:00:16 Points: 279   ⌞ # Computing specializations.. Time: 0:00:16 Points: 285   ⌜ # Computing specializations.. Time: 0:00:17 Points: 292   ⌝ # Computing specializations.. Time: 0:00:17 Points: 299   ⌟ # Computing specializations.. Time: 0:00:17 Points: 306   ⌞ # Computing specializations.. Time: 0:00:18 Points: 313   ⌜ # Computing specializations.. Time: 0:00:18 Points: 318   ⌝ # Computing specializations.. Time: 0:00:19 Points: 324   ⌟ # Computing specializations.. Time: 0:00:19 Points: 331   ⌞ # Computing specializations.. Time: 0:00:19 Points: 338   ⌜ # Computing specializations.. Time: 0:00:20 Points: 344   ⌝ # Computing specializations.. Time: 0:00:20 Points: 351   ⌟ # Computing specializations.. Time: 0:00:21 Points: 358   ⌞ # Computing specializations.. Time: 0:00:21 Points: 365   ⌜ # Computing specializations.. Time: 0:00:21 Points: 372   ⌝ # Computing specializations.. Time: 0:00:22 Points: 377   ⌟ # Computing specializations.. Time: 0:00:22 Points: 383   ⌞ # Computing specializations.. Time: 0:00:22 Points: 389   ⌜ # Computing specializations.. Time: 0:00:23 Points: 395   ⌝ # Computing specializations.. Time: 0:00:23 Points: 401   ⌟ # Computing specializations.. Time: 0:00:24 Points: 407   ⌞ # Computing specializations.. Time: 0:00:24 Points: 414   ⌜ # Computing specializations.. Time: 0:00:24 Points: 420   ⌝ # Computing specializations.. Time: 0:00:25 Points: 427   ⌟ # Computing specializations.. Time: 0:00:25 Points: 432   ⌞ # Computing specializations.. Time: 0:00:25 Points: 439   ⌜ # Computing specializations.. Time: 0:00:26 Points: 445   ⌝ # Computing specializations.. Time: 0:00:26 Points: 452   ⌟ # Computing specializations.. Time: 0:00:26 Points: 459   ⌞ # Computing specializations.. Time: 0:00:27 Points: 466   ⌜ # Computing specializations.. Time: 0:00:27 Points: 472   ⌝ # Computing specializations.. Time: 0:00:28 Points: 478   ⌟ # Computing specializations.. Time: 0:00:28 Points: 484   ⌞ # Computing specializations.. Time: 0:00:29 Points: 491   ⌜ # Computing specializations.. Time: 0:00:29 Points: 498   ⌝ # Computing specializations.. Time: 0:00:29 Points: 504   ⌟ # Computing specializations.. Time: 0:00:30 Points: 510   ⌞ # Computing specializations.. Time: 0:00:30 Points: 517   ⌜ # Computing specializations.. Time: 0:00:30 Points: 522   ⌝ # Computing specializations.. Time: 0:00:31 Points: 529   ⌟ # Computing specializations.. Time: 0:00:31 Points: 536   ⌞ # Computing specializations.. Time: 0:00:31 Points: 543   ⌜ # Computing specializations.. Time: 0:00:32 Points: 550   ⌝ # Computing specializations.. Time: 0:00:32 Points: 557   ⌟ # Computing specializations.. Time: 0:00:33 Points: 564   ⌞ # Computing specializations.. Time: 0:00:33 Points: 571   ⌜ # Computing specializations.. Time: 0:00:33 Points: 577   ⌝ # Computing specializations.. Time: 0:00:34 Points: 583   ⌟ # Computing specializations.. Time: 0:00:34 Points: 589   ⌞ # Computing specializations.. Time: 0:00:35 Points: 595   ⌜ # Computing specializations.. Time: 0:00:35 Points: 602   ⌝ # Computing specializations.. Time: 0:00:36 Points: 609   ⌟ # Computing specializations.. Time: 0:00:36 Points: 616   ⌞ # Computing specializations.. Time: 0:00:36 Points: 622   ⌜ # Computing specializations.. Time: 0:00:37 Points: 628   ⌝ # Computing specializations.. Time: 0:00:37 Points: 635   ⌟ # Computing specializations.. Time: 0:00:38 Points: 640   ✓ # Computing specializations.. Time: 0:00:38 [ Info: Search for polynomial generators concluded in 2.518403605 [ Info: Selecting generators in 0.049586546 [ Info: Inclusion checked with probability 0.995 in 7.585725172 seconds [ Info: The search for identifiable functions concluded in 72.11809691 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), R(t), W(t), y1(t), y2(t), Dd, T, a, d, dr, e, g, r, rR] [ Info: Computing IO-equations [ Info: Computed IO-equations in 2.88417836 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.070845173 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 9.7159e-5 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:00 Points: 18   ⌞ # Computing specializations.. Time: 0:00:01 Points: 24   ⌜ # Computing specializations.. Time: 0:00:01 Points: 30   ⌝ # Computing specializations.. Time: 0:00:02 Points: 36   ⌟ # Computing specializations.. Time: 0:00:02 Points: 43   ⌞ # Computing specializations.. Time: 0:00:02 Points: 48   ⌜ # Computing specializations.. Time: 0:00:03 Points: 55   ⌝ # Computing specializations.. Time: 0:00:03 Points: 61   ⌟ # Computing specializations.. Time: 0:00:04 Points: 68   ⌞ # Computing specializations.. Time: 0:00:04 Points: 75   ⌜ # Computing specializations.. Time: 0:00:04 Points: 82   ⌝ # Computing specializations.. Time: 0:00:05 Points: 88   ⌟ # Computing specializations.. Time: 0:00:05 Points: 94   ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:00 ⌟ # Computing specializations.. Time: 0:00:01 ✓ # Computing specializations.. Time: 0:00:01 ⌜ # Computing specializations.. Time: 0:00:00 Points: 6   ⌝ # Computing specializations.. Time: 0:00:00 Points: 12   ⌟ # Computing specializations.. Time: 0:00:00 Points: 18   ⌞ # Computing specializations.. Time: 0:00:01 Points: 24   ⌜ # Computing specializations.. Time: 0:00:01 Points: 30   ⌝ # Computing specializations.. Time: 0:00:02 Points: 36   ⌟ # Computing specializations.. Time: 0:00:02 Points: 43   ⌞ # Computing specializations.. Time: 0:00:03 Points: 50   ⌜ # Computing specializations.. Time: 0:00:03 Points: 57   ⌝ # Computing specializations.. Time: 0:00:03 Points: 63   ⌟ # Computing specializations.. Time: 0:00:04 Points: 69   ⌞ # Computing specializations.. Time: 0:00:04 Points: 75   ⌜ # Computing specializations.. Time: 0:00:04 Points: 81   ⌝ # Computing specializations.. Time: 0:00:05 Points: 87   ⌟ # Computing specializations.. Time: 0:00:05 Points: 95   ⌞ # Computing specializations.. Time: 0:00:05 Points: 103   ⌜ # Computing specializations.. Time: 0:00:06 Points: 110   ⌝ # Computing specializations.. Time: 0:00:06 Points: 119   ⌟ # Computing specializations.. Time: 0:00:07 Points: 127   ⌞ # Computing specializations.. Time: 0:00:07 Points: 135   ⌜ # Computing specializations.. Time: 0:00:07 Points: 141   ⌝ # Computing specializations.. Time: 0:00:08 Points: 148   ⌟ # Computing specializations.. Time: 0:00:08 Points: 155   ⌞ # Computing specializations.. Time: 0:00:09 Points: 162   ⌜ # Computing specializations.. Time: 0:00:09 Points: 169   ⌝ # Computing specializations.. Time: 0:00:09 Points: 176   ⌟ # Computing specializations.. Time: 0:00:10 Points: 182   ⌞ # Computing specializations.. Time: 0:00:10 Points: 188   ⌜ # Computing specializations.. Time: 0:00:11 Points: 194   ⌝ # Computing specializations.. Time: 0:00:11 Points: 200   ⌟ # Computing specializations.. Time: 0:00:11 Points: 206   ⌞ # Computing specializations.. Time: 0:00:11 Points: 212   ⌜ # Computing specializations.. Time: 0:00:12 Points: 218   ⌝ # Computing specializations.. Time: 0:00:12 Points: 225   ⌟ # Computing specializations.. Time: 0:00:13 Points: 231   ⌞ # Computing specializations.. Time: 0:00:13 Points: 237   ⌜ # Computing specializations.. Time: 0:00:13 Points: 243   ⌝ # Computing specializations.. Time: 0:00:14 Points: 249   ⌟ # Computing specializations.. Time: 0:00:14 Points: 255   ⌞ # Computing specializations.. Time: 0:00:15 Points: 261   ⌜ # Computing specializations.. Time: 0:00:15 Points: 267   ⌝ # Computing specializations.. Time: 0:00:15 Points: 273   ⌟ # Computing specializations.. Time: 0:00:16 Points: 279   ⌞ # Computing specializations.. Time: 0:00:16 Points: 285   ⌜ # Computing specializations.. Time: 0:00:16 Points: 291   ⌝ # Computing specializations.. Time: 0:00:17 Points: 297   ⌟ # Computing specializations.. Time: 0:00:17 Points: 303   ⌞ # Computing specializations.. Time: 0:00:18 Points: 309   ⌜ # Computing specializations.. Time: 0:00:18 Points: 315   ⌝ # Computing specializations.. Time: 0:00:18 Points: 321   ⌟ # Computing specializations.. Time: 0:00:19 Points: 327   ⌞ # Computing specializations.. Time: 0:00:19 Points: 331   ⌜ # Computing specializations.. Time: 0:00:19 Points: 337   ⌝ # Computing specializations.. Time: 0:00:20 Points: 343   ⌟ # Computing specializations.. Time: 0:00:20 Points: 349   ⌞ # Computing specializations.. Time: 0:00:20 Points: 355   ⌜ # Computing specializations.. Time: 0:00:21 Points: 361   ⌝ # Computing specializations.. Time: 0:00:21 Points: 367   ⌟ # Computing specializations.. Time: 0:00:22 Points: 373   ⌞ # Computing specializations.. Time: 0:00:22 Points: 379   ⌜ # Computing specializations.. Time: 0:00:22 Points: 385   ⌝ # Computing specializations.. Time: 0:00:23 Points: 391   ⌟ # Computing specializations.. Time: 0:00:23 Points: 397   ⌞ # Computing specializations.. Time: 0:00:24 Points: 403   ⌜ # Computing specializations.. Time: 0:00:24 Points: 409   ⌝ # Computing specializations.. Time: 0:00:25 Points: 414   ⌟ # Computing specializations.. Time: 0:00:25 Points: 421   ⌞ # Computing specializations.. Time: 0:00:25 Points: 427   ⌜ # Computing specializations.. Time: 0:00:26 Points: 433   ⌝ # Computing specializations.. Time: 0:00:26 Points: 439   ⌟ # Computing specializations.. Time: 0:00:27 Points: 444   ⌞ # Computing specializations.. Time: 0:00:27 Points: 450   ⌜ # Computing specializations.. Time: 0:00:27 Points: 456   ⌝ # Computing specializations.. Time: 0:00:27 Points: 462   ⌟ # Computing specializations.. Time: 0:00:28 Points: 468   ⌞ # Computing specializations.. Time: 0:00:28 Points: 474   ⌜ # Computing specializations.. Time: 0:00:29 Points: 480   ⌝ # Computing specializations.. Time: 0:00:29 Points: 486   ⌟ # Computing specializations.. Time: 0:00:29 Points: 492   ⌞ # Computing specializations.. Time: 0:00:30 Points: 498   ⌜ # Computing specializations.. Time: 0:00:30 Points: 504   ⌝ # Computing specializations.. Time: 0:00:31 Points: 510   ⌟ # Computing specializations.. Time: 0:00:31 Points: 516   ⌞ # Computing specializations.. Time: 0:00:31 Points: 522   ⌜ # Computing specializations.. Time: 0:00:32 Points: 527   ⌝ # Computing specializations.. Time: 0:00:32 Points: 534   ⌟ # Computing specializations.. Time: 0:00:33 Points: 540   ⌞ # Computing specializations.. Time: 0:00:33 Points: 546   ⌜ # Computing specializations.. Time: 0:00:33 Points: 552   ⌝ # Computing specializations.. Time: 0:00:34 Points: 557   ⌟ # Computing specializations.. Time: 0:00:34 Points: 563   ⌞ # Computing specializations.. Time: 0:00:35 Points: 569   ⌜ # Computing specializations.. Time: 0:00:35 Points: 575   ⌝ # Computing specializations.. Time: 0:00:35 Points: 581   ⌟ # Computing specializations.. Time: 0:00:36 Points: 587   ⌞ # Computing specializations.. Time: 0:00:36 Points: 593   ⌜ # Computing specializations.. Time: 0:00:36 Points: 599   ⌝ # Computing specializations.. Time: 0:00:37 Points: 605   ⌟ # Computing specializations.. Time: 0:00:37 Points: 611   ⌞ # Computing specializations.. Time: 0:00:38 Points: 617   ⌜ # Computing specializations.. Time: 0:00:38 Points: 623   ⌝ # Computing specializations.. Time: 0:00:38 Points: 629   ⌟ # Computing specializations.. Time: 0:00:39 Points: 635   ✓ # Computing specializations.. Time: 0:00:40 [ Info: Search for polynomial generators concluded in 1.436743871 [ Info: Selecting generators in 0.054735747 [ Info: Inclusion checked with probability 0.995 in 7.768017553 seconds [ Info: The search for identifiable functions concluded in 72.84625759 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)] │ case = │ (ode = S'(t) = -S(t)*W(t)*a - S(t)*W(t)*d - S(t)*e + S(t)*r + R(t)*g │ R'(t) = S(t)*W(t)*a + S(t)*e - R(t)*W(t)*dr - R(t)*g + R(t)*rR │ W'(t) = -W(t)*Dd + Dd*T │ y1(t) = S(t) + R(t) │ y2(t) = T │ , ident_funcs = RingElem[T, Dd, T*a + T*d + T*dr + e + g - r - rR, (d*rR - dr*r)//(d - dr), (a^2 + 2*a*d + d^2 + dr^2)//(a*dr + d*dr), (a*r - a*rR + d*e + d*g - dr*e - dr*g)//(d - dr), (a*dr*r - a*dr*rR + d^2*g + d*dr*e - d*dr*g - dr^2*e)//(a*d - a*dr + d^2 - dr^2)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables S(t), R(t), W(t), y1(t), ..., rR │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), R(t), W(t), y1(t), y2(t), Dd, T, a, d, dr, e, g, r, rR] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002204449 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000114659 [ Info: Selecting generators in 0.000198358 [ Info: Inclusion checked with probability 0.995 in 0.002430086 seconds [ Info: The search for identifiable functions concluded in 0.027953032 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00105425 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.4869e-5 [ Info: Selecting generators in 0.000195178 [ Info: Inclusion checked with probability 0.995 in 0.002197779 seconds [ Info: The search for identifiable functions concluded in 0.009454859 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.000937271 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.058e-5 [ Info: Selecting generators in 0.000172798 [ Info: Inclusion checked with probability 0.995 in 0.002178359 seconds [ Info: The search for identifiable functions concluded in 0.009272861 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00100988 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000587065 [ Info: Selecting generators in 0.000227318 [ Info: Inclusion checked with probability 0.995 in 0.002299458 seconds [ Info: The search for identifiable functions concluded in 0.009894235 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001103409 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000451296 [ Info: Selecting generators in 0.000208278 [ Info: Inclusion checked with probability 0.995 in 0.002237539 seconds [ Info: The search for identifiable functions concluded in 0.009982195 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00104523 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000487385 [ Info: Selecting generators in 0.000194828 [ Info: Inclusion checked with probability 0.995 in 0.002264438 seconds [ Info: The search for identifiable functions concluded in 0.009858016 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x(t)] │ case = │ (ode = x'(t) = x(t) │ y(t) = x(t) │ , ident_funcs = QQMPolyRingElem[x(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 2 variables x(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001542565 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00201335 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 3.36e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000448336 [ Info: Selecting generators in 0.000785772 [ Info: Inclusion checked with probability 0.995 in 0.001918812 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.4009e-5 [ Info: Selecting generators in 0.000540885 [ Info: Inclusion checked with probability 0.995 in 0.002468386 seconds [ Info: The search for identifiable functions concluded in 0.022621014 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001385567 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001204599 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 3.2369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000453965 [ Info: Selecting generators in 0.001142819 [ Info: Inclusion checked with probability 0.995 in 0.002277488 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.7569e-5 [ Info: Selecting generators in 0.000608884 [ Info: Inclusion checked with probability 0.995 in 0.002722324 seconds [ Info: The search for identifiable functions concluded in 0.023405876 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001366327 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001204319 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.3129e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000452965 [ Info: Selecting generators in 0.000904531 [ Info: Inclusion checked with probability 0.995 in 0.00214714 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000100679 [ Info: Selecting generators in 0.000613104 [ Info: Inclusion checked with probability 0.995 in 0.002799624 seconds [ Info: The search for identifiable functions concluded in 0.022494565 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001416266 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001255818 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.29e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000416956 [ Info: Selecting generators in 0.000947401 [ Info: Inclusion checked with probability 0.995 in 0.002200509 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.165736576 [ Info: Selecting generators in 0.000810112 [ Info: Inclusion checked with probability 0.995 in 0.003071921 seconds [ Info: The search for identifiable functions concluded in 0.188944815 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001412146 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001212649 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.6239e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000434686 [ Info: Selecting generators in 0.000864792 [ Info: Inclusion checked with probability 0.995 in 0.002032181 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000677443 [ Info: Selecting generators in 0.000599364 [ Info: Inclusion checked with probability 0.995 in 0.002544885 seconds [ Info: The search for identifiable functions concluded in 0.02204136 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001318278 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00108743 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.1159e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000424215 [ Info: Selecting generators in 0.000809182 [ Info: Inclusion checked with probability 0.995 in 0.002219288 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000652634 [ Info: Selecting generators in 0.000603604 [ Info: Inclusion checked with probability 0.995 in 0.002699164 seconds [ Info: The search for identifiable functions concluded in 0.022185408 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, x(t)] │ case = │ (ode = x'(t) = x(t)*a + u(t) │ y(t) = x(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[a, x(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x(t), y(t), u(t), a │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002925232 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002676315 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.4249e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008643867 [ Info: Selecting generators in 0.002834712 [ Info: Inclusion checked with probability 0.995 in 0.003805574 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000118349 [ Info: Selecting generators in 0.00423606 [ Info: Inclusion checked with probability 0.995 in 0.006710715 seconds [ Info: The search for identifiable functions concluded in 0.060604321 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002959112 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002367328 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.517e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008563668 [ Info: Selecting generators in 0.003009581 [ Info: Inclusion checked with probability 0.995 in 0.003942603 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000138139 [ Info: Selecting generators in 0.00424198 [ Info: Inclusion checked with probability 0.995 in 0.006418409 seconds [ Info: The search for identifiable functions concluded in 0.061448253 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00311984 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002424216 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.4909e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008567188 [ Info: Selecting generators in 0.003032981 [ Info: Inclusion checked with probability 0.995 in 0.004011722 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000126909 [ Info: Selecting generators in 0.004304019 [ Info: Inclusion checked with probability 0.995 in 0.006134521 seconds [ Info: The search for identifiable functions concluded in 0.060405513 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003047031 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002404547 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.446e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.009256492 [ Info: Selecting generators in 0.002979642 [ Info: Inclusion checked with probability 0.995 in 0.003724745 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.026569966 [ Info: Selecting generators in 0.00416821 [ Info: Inclusion checked with probability 0.995 in 0.005629856 seconds [ Info: The search for identifiable functions concluded in 0.086494184 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002876772 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002393168 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.156e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008133142 [ Info: Selecting generators in 0.002720944 [ Info: Inclusion checked with probability 0.995 in 0.003736344 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.024908342 [ Info: Selecting generators in 0.005043482 [ Info: Inclusion checked with probability 0.995 in 0.005773905 seconds [ Info: The search for identifiable functions concluded in 0.082643711 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002653315 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002308278 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.09e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.007950934 [ Info: Selecting generators in 0.002590635 [ Info: Inclusion checked with probability 0.995 in 0.003449877 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.02506293 [ Info: Selecting generators in 0.004461508 [ Info: Inclusion checked with probability 0.995 in 0.006776155 seconds [ Info: The search for identifiable functions concluded in 0.08265062 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002803864 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002486666 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.6569e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.009026033 [ Info: Selecting generators in 0.002870242 [ Info: Inclusion checked with probability 0.995 in 0.003916872 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000125429 [ Info: Selecting generators in 0.00416818 [ Info: Inclusion checked with probability 0.995 in 0.006140091 seconds [ Info: The search for identifiable functions concluded in 0.059990487 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002686924 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002373287 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.5999e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008577258 [ Info: Selecting generators in 0.002961672 [ Info: Inclusion checked with probability 0.995 in 0.003760084 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000127599 [ Info: Selecting generators in 0.004304729 [ Info: Inclusion checked with probability 0.995 in 0.00632416 seconds [ Info: The search for identifiable functions concluded in 0.05959636 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002899452 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002431007 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.4559e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008673317 [ Info: Selecting generators in 0.002893513 [ Info: Inclusion checked with probability 0.995 in 0.004015762 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000159639 [ Info: Selecting generators in 0.00419748 [ Info: Inclusion checked with probability 0.995 in 0.006208881 seconds [ Info: The search for identifiable functions concluded in 0.061012597 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002888993 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002360848 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.319e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008844035 [ Info: Selecting generators in 0.002896052 [ Info: Inclusion checked with probability 0.995 in 0.004062811 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.026676025 [ Info: Selecting generators in 0.004492587 [ Info: Inclusion checked with probability 0.995 in 0.006172561 seconds [ Info: The search for identifiable functions concluded in 0.087002249 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002808243 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002382897 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.133e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008664597 [ Info: Selecting generators in 0.002932472 [ Info: Inclusion checked with probability 0.995 in 0.004040311 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.026948572 [ Info: Selecting generators in 0.004396778 [ Info: Inclusion checked with probability 0.995 in 0.006365549 seconds [ Info: The search for identifiable functions concluded in 0.0878467 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002960032 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002459727 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.472e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008426729 [ Info: Selecting generators in 0.00315835 [ Info: Inclusion checked with probability 0.995 in 0.004332758 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.164931438 [ Info: Selecting generators in 0.005284459 [ Info: Inclusion checked with probability 0.995 in 0.006611737 seconds [ Info: The search for identifiable functions concluded in 1.228404862 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[d, c, a, x1(t), x2(t)*b] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*b + x1(t)*a │ x2'(t) = x1(t)*x2(t)*d - x2(t)*c │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), c, d, a, x2(t)*b]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 7 variables x1(t), x2(t), y(t), a, ..., d │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), a, b, c, d] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01046069 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00843086 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.176e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003039741 [ Info: Selecting generators in 0.013387622 [ Info: Inclusion checked with probability 0.995 in 0.007154732 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000190518 [ Info: Selecting generators in 0.016546022 [ Info: Inclusion checked with probability 0.995 in 0.01152256 seconds [ Info: The search for identifiable functions concluded in 0.333178096 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.008262051 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006945704 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 6.007e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002443047 [ Info: Selecting generators in 0.010795547 [ Info: Inclusion checked with probability 0.995 in 0.006178041 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000158928 [ Info: Selecting generators in 0.014108645 [ Info: Inclusion checked with probability 0.995 in 0.01050265 seconds [ Info: The search for identifiable functions concluded in 0.122307741 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.008091793 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005581417 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 4.507e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002390177 [ Info: Selecting generators in 0.010684078 [ Info: Inclusion checked with probability 0.995 in 0.006420318 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000182858 [ Info: Selecting generators in 0.01472604 [ Info: Inclusion checked with probability 0.995 in 0.010635008 seconds [ Info: The search for identifiable functions concluded in 0.124334622 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007711957 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005872874 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.393e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004970313 [ Info: Selecting generators in 0.019748171 [ Info: Inclusion checked with probability 0.995 in 0.012314252 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004882923 [ Info: Selecting generators in 0.013905977 [ Info: Inclusion checked with probability 0.995 in 0.010365391 seconds [ Info: The search for identifiable functions concluded in 0.157577814 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007600177 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005906034 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.514e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002216779 [ Info: Selecting generators in 0.010116773 [ Info: Inclusion checked with probability 0.995 in 0.006221851 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005087451 [ Info: Selecting generators in 0.014016056 [ Info: Inclusion checked with probability 0.995 in 0.010506809 seconds [ Info: The search for identifiable functions concluded in 0.124969016 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007677047 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007279161 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.045e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002328308 [ Info: Selecting generators in 0.010118743 [ Info: Inclusion checked with probability 0.995 in 0.005969543 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004887423 [ Info: Selecting generators in 0.014303164 [ Info: Inclusion checked with probability 0.995 in 0.010546349 seconds [ Info: The search for identifiable functions concluded in 0.124204943 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[λ3, λ2, λ1, β3, β2, β1, x3(t), x2(t), x1(t)] │ case = │ (ode = x1'(t) = x1(t)*λ1 + u1(t)*β1 │ x2'(t) = x2(t)*λ2 + u2(t)*β2 │ x3'(t) = x3(t)*λ3 + u3(t)*β3 │ y(t) = x1(t) + x2(t) + x3(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[λ1, λ2, λ3, β1, β2, β3, x1(t), x2(t), x3(t)]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 13 variables x1(t), x2(t), x3(t), y(t), ..., λ3 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u1(t), u2(t), u3(t), β1, β2, β3, λ1, λ2, λ3] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00205762 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001206028 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.6309e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.5959e-5 [ Info: Selecting generators in 0.000562785 [ Info: Inclusion checked with probability 0.995 in 0.002719514 seconds [ Info: The search for identifiable functions concluded in 0.014749799 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001874952 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001222659 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.78e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.6019e-5 [ Info: Selecting generators in 0.000552105 [ Info: Inclusion checked with probability 0.995 in 0.002747103 seconds [ Info: The search for identifiable functions concluded in 0.014263424 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001911441 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001228928 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 2.129e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.2089e-5 [ Info: Selecting generators in 0.000538704 [ Info: Inclusion checked with probability 0.995 in 0.002681985 seconds [ Info: The search for identifiable functions concluded in 0.014448162 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001872172 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001209549 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 2.1e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005560567 [ Info: Selecting generators in 0.000668174 [ Info: Inclusion checked with probability 0.995 in 0.002707144 seconds [ Info: The search for identifiable functions concluded in 0.020075208 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001892412 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001216999 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 2.127e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005582107 [ Info: Selecting generators in 0.000667963 [ Info: Inclusion checked with probability 0.995 in 0.002934922 seconds [ Info: The search for identifiable functions concluded in 0.020152318 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001912711 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001199189 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.89e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005788335 [ Info: Selecting generators in 0.000694094 [ Info: Inclusion checked with probability 0.995 in 0.002785864 seconds [ Info: The search for identifiable functions concluded in 0.020210116 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), x2(t)*Θ] │ case = │ (ode = x1'(t) = x1(t) + x2(t)*Θ │ x2'(t) = 0 │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*Θ]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), Θ │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), Θ] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003686944 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002491496 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.404e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00319252 [ Info: Selecting generators in 0.00108575 [ Info: Inclusion checked with probability 0.995 in 0.002520306 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000127888 [ Info: Selecting generators in 0.005414368 [ Info: Inclusion checked with probability 0.995 in 0.004276449 seconds [ Info: The search for identifiable functions concluded in 0.042151867 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003334549 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002328728 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.119e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002935772 [ Info: Selecting generators in 0.000931281 [ Info: Inclusion checked with probability 0.995 in 0.00202216 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000119789 [ Info: Selecting generators in 0.004996992 [ Info: Inclusion checked with probability 0.995 in 0.004034992 seconds [ Info: The search for identifiable functions concluded in 0.039011658 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003333208 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002328338 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.0099e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00317242 [ Info: Selecting generators in 0.00103394 [ Info: Inclusion checked with probability 0.995 in 0.002626925 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000110388 [ Info: Selecting generators in 0.005054052 [ Info: Inclusion checked with probability 0.995 in 0.004047081 seconds [ Info: The search for identifiable functions concluded in 0.040566562 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003333248 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002310828 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.724e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002902542 [ Info: Selecting generators in 0.001027331 [ Info: Inclusion checked with probability 0.995 in 0.002390597 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.029127762 [ Info: Selecting generators in 0.005927323 [ Info: Inclusion checked with probability 0.995 in 0.004628736 seconds [ Info: The search for identifiable functions concluded in 0.071549116 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), C, α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003537626 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002513266 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.073e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003126121 [ Info: Selecting generators in 0.001006701 [ Info: Inclusion checked with probability 0.995 in 0.002326768 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.02819044 [ Info: Selecting generators in 0.005785745 [ Info: Inclusion checked with probability 0.995 in 0.004543926 seconds [ Info: The search for identifiable functions concluded in 0.070677695 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), C, α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003610805 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002386898 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.159e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003013111 [ Info: Selecting generators in 0.00105251 [ Info: Inclusion checked with probability 0.995 in 0.002250779 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.029560508 [ Info: Selecting generators in 0.005856144 [ Info: Inclusion checked with probability 0.995 in 0.004662685 seconds [ Info: The search for identifiable functions concluded in 0.07221306 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t), C*α, x3(t)*α, x2(t)*α] │ case = │ (ode = x1'(t) = x2(t)*α │ x2'(t) = x3(t) │ x3'(t) = C │ y(t) = x1(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[x1(t), x2(t)*α, x3(t)*α, C*α]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x1(t), x2(t), x3(t), y(t), ..., α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), C, α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00210461 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001404797 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.103e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000430276 [ Info: Selecting generators in 0.000724223 [ Info: Inclusion checked with probability 0.995 in 0.002010931 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000106049 [ Info: Selecting generators in 0.001567315 [ Info: Inclusion checked with probability 0.995 in 0.003071281 seconds [ Info: The search for identifiable functions concluded in 0.025723144 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002113049 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001471066 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.385e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000459456 [ Info: Selecting generators in 0.000713914 [ Info: Inclusion checked with probability 0.995 in 0.001954512 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000102479 [ Info: Selecting generators in 0.001626754 [ Info: Inclusion checked with probability 0.995 in 0.003006932 seconds [ Info: The search for identifiable functions concluded in 0.026031652 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00205571 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001482026 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.019e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000416346 [ Info: Selecting generators in 0.000664573 [ Info: Inclusion checked with probability 0.995 in 0.001850212 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.1119e-5 [ Info: Selecting generators in 0.001564225 [ Info: Inclusion checked with probability 0.995 in 0.003236059 seconds [ Info: The search for identifiable functions concluded in 0.025380987 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00202858 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001360647 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.184e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000480815 [ Info: Selecting generators in 0.000708063 [ Info: Inclusion checked with probability 0.995 in 0.001885132 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006491258 [ Info: Selecting generators in 0.001671064 [ Info: Inclusion checked with probability 0.995 in 0.002914763 seconds [ Info: The search for identifiable functions concluded in 0.030756147 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00209 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001363657 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 3.415e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000459466 [ Info: Selecting generators in 0.000714904 [ Info: Inclusion checked with probability 0.995 in 0.001903962 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006811625 [ Info: Selecting generators in 0.001765463 [ Info: Inclusion checked with probability 0.995 in 0.002923962 seconds [ Info: The search for identifiable functions concluded in 0.032740737 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001928801 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001321647 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.98e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000435976 [ Info: Selecting generators in 0.000852252 [ Info: Inclusion checked with probability 0.995 in 0.00204065 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006906574 [ Info: Selecting generators in 0.001887072 [ Info: Inclusion checked with probability 0.995 in 0.003010511 seconds [ Info: The search for identifiable functions concluded in 0.032787237 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[α, x1(t)^2 + x2(t)^2] │ case = │ (ode = x1'(t) = x1(t)*α - x2(t)*α │ x2'(t) = x1(t)*α + x2(t)*α │ y(t) = 1//2*x1(t)^2 + 1//2*x2(t)^2 │ , with_states = true, ident_funcs = QQMPolyRingElem[α, x1(t)^2 + x2(t)^2]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 4 variables x1(t), x2(t), y(t), α │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), α] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001334547 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001156599 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.967e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005731805 [ Info: Selecting generators in 0.002608205 [ Info: Inclusion checked with probability 0.995 in 0.002997222 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000102669 [ Info: Selecting generators in 0.002504986 [ Info: Inclusion checked with probability 0.995 in 0.003887142 seconds [ Info: The search for identifiable functions concluded in 0.037430233 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001381167 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001181249 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.442e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006140861 [ Info: Selecting generators in 0.002167139 [ Info: Inclusion checked with probability 0.995 in 0.002699534 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000121799 [ Info: Selecting generators in 0.002441787 [ Info: Inclusion checked with probability 0.995 in 0.003703595 seconds [ Info: The search for identifiable functions concluded in 0.037386313 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001368847 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001246338 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.606e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006503688 [ Info: Selecting generators in 0.002382347 [ Info: Inclusion checked with probability 0.995 in 0.002717814 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000123508 [ Info: Selecting generators in 0.002572466 [ Info: Inclusion checked with probability 0.995 in 0.003722955 seconds [ Info: The search for identifiable functions concluded in 0.039337964 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001298688 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001160639 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.355e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005860674 [ Info: Selecting generators in 0.002210539 [ Info: Inclusion checked with probability 0.995 in 0.002592345 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014710549 [ Info: Selecting generators in 0.002727934 [ Info: Inclusion checked with probability 0.995 in 0.003708885 seconds [ Info: The search for identifiable functions concluded in 0.051707036 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001206099 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001092269 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.0719e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005948643 [ Info: Selecting generators in 0.002381227 [ Info: Inclusion checked with probability 0.995 in 0.002809273 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01574035 [ Info: Selecting generators in 0.002834893 [ Info: Inclusion checked with probability 0.995 in 0.003762874 seconds [ Info: The search for identifiable functions concluded in 0.053509919 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001332887 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001142979 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006398309 [ Info: Selecting generators in 0.002448056 [ Info: Inclusion checked with probability 0.995 in 0.002712404 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01567 [ Info: Selecting generators in 0.003044931 [ Info: Inclusion checked with probability 0.995 in 0.003872863 seconds [ Info: The search for identifiable functions concluded in 0.055332961 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a, b*c, x(t)*c] │ case = │ (ode = x'(t) = x(t)*a + u(t)*b │ y(t) = x(t)*c │ , with_states = true, ident_funcs = QQMPolyRingElem[a, b*c, x(t)*c]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 6 variables x(t), y(t), u(t), a, ..., c │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), u(t), a, b, c] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006116702 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005498898 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.6409e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.011930646 [ Info: Selecting generators in 0.004073171 [ Info: Inclusion checked with probability 0.995 in 0.004412228 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000142049 [ Info: Selecting generators in 0.029598457 [ Info: Inclusion checked with probability 0.995 in 0.011002315 seconds [ Info: The search for identifiable functions concluded in 0.1360132 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007672827 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006938964 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.419e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016237184 [ Info: Selecting generators in 0.005436288 [ Info: Inclusion checked with probability 0.995 in 0.005414988 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000213298 [ Info: Selecting generators in 0.039273215 [ Info: Inclusion checked with probability 0.995 in 0.011797837 seconds [ Info: The search for identifiable functions concluded in 0.169282383 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007204431 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00622597 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.5369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015011467 [ Info: Selecting generators in 0.004958593 [ Info: Inclusion checked with probability 0.995 in 0.004851544 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000206059 [ Info: Selecting generators in 0.032848226 [ Info: Inclusion checked with probability 0.995 in 0.011298742 seconds [ Info: The search for identifiable functions concluded in 0.154699452 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005765395 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005499858 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.0149e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.013918557 [ Info: Selecting generators in 0.004555877 [ Info: Inclusion checked with probability 0.995 in 0.004830044 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.097855685 [ Info: Selecting generators in 0.032193742 [ Info: Inclusion checked with probability 0.995 in 0.010874996 seconds [ Info: The search for identifiable functions concluded in 0.242524443 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y1(t), u(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006533318 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005759794 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.427e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01354827 [ Info: Selecting generators in 0.004448377 [ Info: Inclusion checked with probability 0.995 in 0.004682025 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.091455266 [ Info: Selecting generators in 0.046580325 [ Info: Inclusion checked with probability 0.995 in 0.011173604 seconds [ Info: The search for identifiable functions concluded in 0.248988901 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y1(t), u(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006774925 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006011432 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 3.052e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.013346622 [ Info: Selecting generators in 0.004403758 [ Info: Inclusion checked with probability 0.995 in 0.004661925 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.1005031 [ Info: Selecting generators in 0.033148653 [ Info: Inclusion checked with probability 0.995 in 0.011084384 seconds [ Info: The search for identifiable functions concluded in 0.247668323 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x3(t), p1 + p3, p2*p4, p1*p3, x1(t)*x2(t), x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3] │ case = │ (ode = x1'(t) = -x1(t)*p1 + u(t)*p2 │ x2'(t) = -x2(t)*p3 + u(t)*p4 │ x3'(t) = x1(t)*u(t)*p4 + x2(t)*u(t)*p2 - x3(t)*p1 - x3(t)*p3 │ y1(t) = x3(t) │ , with_states = true, ident_funcs = RingElem[x3(t), x1(t)*x2(t), p1*p3, p2*p4, p1 + p3, x1(t)*p4 + x2(t)*p2, x1(t)*p1*p4 + x2(t)*p2*p3]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), x3(t), y1(t), ..., p4 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y1(t), u(t), p1, p2, p3, p4] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.224084309 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.417880407 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.00208484 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:04 ✓ # Computing specializations.. Time: 0:00:04 [ Info: Search for polynomial generators concluded in 9.028150142 [ Info: Selecting generators in 0.084349353 [ Info: Inclusion checked with probability 0.995 in 0.182156229 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:08 ✓ # Computing specializations.. Time: 0:00:08 [ Info: Search for polynomial generators concluded in 0.000570374 [ Info: Selecting generators in 0.278549168 [ Info: Inclusion checked with probability 0.995 in 8.770956051 seconds [ Info: The search for identifiable functions concluded in 38.216285309 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, pAkt_S6(t)//pS6(t), S6(t)//pS6(t), pAkt(t)//pS6(t), Akt(t)//pS6(t), pEGFR_Akt(t)//pS6(t), pEGFR(t)//pS6(t), (EGF_EGFR(t)*reaction_9_k1)//pS6(t)] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.235167043 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.410315519 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.001852072 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 7.351539433 [ Info: Selecting generators in 0.4280176 [ Info: Inclusion checked with probability 0.995 in 0.160933802 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000483935 [ Info: Selecting generators in 0.255766746 [ Info: Inclusion checked with probability 0.995 in 0.066516944 seconds [ Info: The search for identifiable functions concluded in 11.182229951 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, pAkt_S6(t)//pS6(t), S6(t)//pS6(t), pAkt(t)//pS6(t), Akt(t)//pS6(t), pEGFR_Akt(t)//pS6(t), pEGFR(t)//pS6(t), (EGF_EGFR(t)*reaction_9_k1)//pS6(t)] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.203932941 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.398940708 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.001945222 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 6.895503192 [ Info: Selecting generators in 0.080725008 [ Info: Inclusion checked with probability 0.995 in 0.135381736 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000573774 [ Info: Selecting generators in 0.27627969 [ Info: Inclusion checked with probability 0.995 in 0.067849511 seconds [ Info: The search for identifiable functions concluded in 11.124481463 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, pAkt_S6(t)//pS6(t), S6(t)//pS6(t), pAkt(t)//pS6(t), Akt(t)//pS6(t), pEGFR_Akt(t)//pS6(t), pEGFR(t)//pS6(t), (EGF_EGFR(t)*reaction_9_k1)//pS6(t)] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.200752092 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.442163955 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.002187039 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 7.670231259 [ Info: Selecting generators in 0.094767294 [ Info: Inclusion checked with probability 0.995 in 0.163433639 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 95.03961033 [ Info: Selecting generators in 1.028702501 [ Info: Inclusion checked with probability 0.995 in 0.068137099 seconds [ Info: The search for identifiable functions concluded in 105.487741976 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, pAkt_S6(t)*reaction_5_k1, S6(t)*reaction_5_k1, pAkt(t)*reaction_5_k1, Akt(t)*reaction_5_k1, pEGFR_Akt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), pAkt(t), S6(t), pAkt_S6(t), pS6(t), EGF_EGFR(t), y1(t), y2(t), y3(t), pro_EGFR(t), EGFR_turnover, a1, a2, a3, reaction_1_k1, reaction_1_k2, reaction_2_k1, reaction_2_k2, reaction_3_k1, reaction_4_k1, reaction_5_k1, reaction_5_k2, reaction_6_k1, reaction_7_k1, reaction_8_k1, reaction_9_k1] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.208210951 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.392186383 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.001541066 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:01 Points: 11   ✓ # Computing specializations.. Time: 0:00:01 [ Info: Search for polynomial generators concluded in 6.46676071 [ Info: Selecting generators in 0.058331113 [ Info: Inclusion checked with probability 0.995 in 0.092205849 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 89.242921665 [ Info: Selecting generators in 1.076452204 [ Info: Inclusion checked with probability 0.995 in 0.075465309 seconds [ Info: The search for identifiable functions concluded in 99.326405418 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, pAkt_S6(t)*reaction_5_k1, S6(t)*reaction_5_k1, pAkt(t)*reaction_5_k1, Akt(t)*reaction_5_k1, pEGFR_Akt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), pAkt(t), S6(t), pAkt_S6(t), pS6(t), EGF_EGFR(t), y1(t), y2(t), y3(t), pro_EGFR(t), EGFR_turnover, a1, a2, a3, reaction_1_k1, reaction_1_k2, reaction_2_k1, reaction_2_k2, reaction_3_k1, reaction_4_k1, reaction_5_k1, reaction_5_k2, reaction_6_k1, reaction_7_k1, reaction_8_k1, reaction_9_k1] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.233822356 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.429020511 seconds [ Info: Dimensions of the Wronskians [18, 9, 145] [ Info: Ranks of the Wronskians computed in 0.001648554 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 6.962163199 [ Info: Selecting generators in 0.093432867 [ Info: Inclusion checked with probability 0.995 in 0.146949456 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 90.888081092 [ Info: Selecting generators in 1.453589992 [ Info: Inclusion checked with probability 0.995 in 0.074418849 seconds [ Info: The search for identifiable functions concluded in 102.287276407 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[reaction_8_k1, reaction_7_k1, reaction_6_k1, reaction_5_k2, reaction_4_k1, reaction_3_k1, reaction_2_k2, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pS6(t)*reaction_5_k1, pAkt_S6(t)*reaction_5_k1, S6(t)*reaction_5_k1, pAkt(t)*reaction_5_k1, Akt(t)*reaction_5_k1, pEGFR_Akt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a3//reaction_5_k1, a2//reaction_5_k1, a1//reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1] │ case = │ (ode = EGFR'(t) = -EGFR(t)*EGFR_turnover - EGF_EGFR(t)*reaction_1_k1 + EGF_EGFR(t)*reaction_1_k2 + pro_EGFR(t)*EGFR_turnover │ pEGFR'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR(t)*reaction_4_k1 + pEGFR_Akt(t)*reaction_2_k2 + pEGFR_Akt(t)*reaction_3_k1 + EGF_EGFR(t)*reaction_9_k1 │ pEGFR_Akt'(t) = pEGFR(t)*Akt(t)*reaction_2_k1 - pEGFR_Akt(t)*reaction_2_k2 - pEGFR_Akt(t)*reaction_3_k1 │ Akt'(t) = -pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2 + pAkt(t)*reaction_7_k1 │ pAkt'(t) = pEGFR_Akt(t)*reaction_3_k1 - pAkt(t)*S6(t)*reaction_5_k1 - pAkt(t)*reaction_7_k1 + pAkt_S6(t)*reaction_5_k2 + pAkt_S6(t)*reaction_6_k1 │ S6'(t) = -pAkt(t)*S6(t)*reaction_5_k1 + pAkt_S6(t)*reaction_5_k2 + pS6(t)*reaction_8_k1 │ pAkt_S6'(t) = pAkt(t)*S6(t)*reaction_5_k1 - pAkt_S6(t)*reaction_5_k2 - pAkt_S6(t)*reaction_6_k1 │ pS6'(t) = pAkt_S6(t)*reaction_6_k1 - pS6(t)*reaction_8_k1 │ EGF_EGFR'(t) = EGF_EGFR(t)*reaction_1_k1 - EGF_EGFR(t)*reaction_1_k2 - EGF_EGFR(t)*reaction_9_k1 │ y1(t) = pEGFR(t)*a1 + pEGFR_Akt(t)*a1 │ y2(t) = pAkt(t)*a2 + pAkt_S6(t)*a2 │ y3(t) = pS6(t)*a3 │ , with_states = true, ident_funcs = RingElem[reaction_8_k1, a3//reaction_5_k1, reaction_3_k1, reaction_2_k2, pAkt(t)*reaction_5_k1, pEGFR(t)*reaction_5_k1, reaction_2_k1//reaction_5_k1, a1//reaction_5_k1, pS6(t)*reaction_5_k1, reaction_5_k2, reaction_6_k1, a2//reaction_5_k1, reaction_7_k1, reaction_4_k1, pAkt_S6(t)*reaction_5_k1, reaction_1_k1 - reaction_1_k2 - reaction_9_k1, pEGFR_Akt(t)*reaction_5_k1, S6(t)*reaction_5_k1, EGF_EGFR(t)*reaction_5_k1*reaction_9_k1, Akt(t)*reaction_5_k1]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 29 variables EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), ..., reaction_9_k1 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[EGFR(t), pEGFR(t), pEGFR_Akt(t), Akt(t), pAkt(t), S6(t), pAkt_S6(t), pS6(t), EGF_EGFR(t), y1(t), y2(t), y3(t), pro_EGFR(t), EGFR_turnover, a1, a2, a3, reaction_1_k1, reaction_1_k2, reaction_2_k1, reaction_2_k2, reaction_3_k1, reaction_4_k1, reaction_5_k1, reaction_5_k2, reaction_6_k1, reaction_7_k1, reaction_8_k1, reaction_9_k1] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.032328821 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.020135688 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 4.1019e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.02719509 [ Info: Selecting generators in 0.002038191 [ Info: Inclusion checked with probability 0.995 in 0.004638446 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000158089 [ Info: Selecting generators in 0.011477491 [ Info: Inclusion checked with probability 0.995 in 0.010371051 seconds [ Info: The search for identifiable functions concluded in 0.377589913 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.029998534 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.020890811 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 2.836e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.028073892 [ Info: Selecting generators in 0.001992411 [ Info: Inclusion checked with probability 0.995 in 0.004741045 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000199588 [ Info: Selecting generators in 0.011978276 [ Info: Inclusion checked with probability 0.995 in 0.010930686 seconds [ Info: The search for identifiable functions concluded in 0.160263689 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.034332572 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01991278 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 2.883e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.029643367 [ Info: Selecting generators in 0.00212227 [ Info: Inclusion checked with probability 0.995 in 0.004736204 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000211208 [ Info: Selecting generators in 0.01151488 [ Info: Inclusion checked with probability 0.995 in 0.010125124 seconds [ Info: The search for identifiable functions concluded in 0.165683957 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.032386911 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.022139068 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 2.903e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.028005512 [ Info: Selecting generators in 0.002034481 [ Info: Inclusion checked with probability 0.995 in 0.004458578 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.450693064 [ Info: Selecting generators in 0.012044225 [ Info: Inclusion checked with probability 0.995 in 0.010836467 seconds [ Info: The search for identifiable functions concluded in 0.614743916 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: QQMPolyRingElem[beta(t), cry(t), zea(t), beta10(t), OHbeta10(t), betaio(t), OHbetaio(t), y1(t), y2(t), kOHbeta10, kbeta, kbeta10, kcryOH, kcrybeta, kzea] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.077322041 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.025284159 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 2.8609e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.040691441 [ Info: Selecting generators in 0.002849113 [ Info: Inclusion checked with probability 0.995 in 0.006018102 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.472190319 [ Info: Selecting generators in 0.010635309 [ Info: Inclusion checked with probability 0.995 in 0.009741377 seconds [ Info: The search for identifiable functions concluded in 0.710818509 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: QQMPolyRingElem[beta(t), cry(t), zea(t), beta10(t), OHbeta10(t), betaio(t), OHbetaio(t), y1(t), y2(t), kOHbeta10, kbeta, kbeta10, kcryOH, kcrybeta, kzea] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.027398299 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.016885589 seconds [ Info: Dimensions of the Wronskians [4, 2] [ Info: Ranks of the Wronskians computed in 2.987e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.025069721 [ Info: Selecting generators in 0.001913662 [ Info: Inclusion checked with probability 0.995 in 0.004501637 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.444756761 [ Info: Selecting generators in 0.011613479 [ Info: Inclusion checked with probability 0.995 in 0.010711268 seconds [ Info: The search for identifiable functions concluded in 0.589524208 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[kbeta10, kbeta, beta10(t), beta(t), kcryOH + kcrybeta, cry(t)*kcryOH] │ case = │ (ode = beta'(t) = -beta(t)*kbeta │ cry'(t) = -cry(t)*kcryOH - cry(t)*kcrybeta │ zea'(t) = -zea(t)*kzea │ beta10'(t) = beta(t)*kbeta + cry(t)*kcryOH - beta10(t)*kbeta10 │ OHbeta10'(t) = cry(t)*kcrybeta + zea(t)*kzea - OHbeta10(t)*kOHbeta10 │ betaio'(t) = beta(t)*kbeta + cry(t)*kcrybeta + beta10(t)*kbeta10 │ OHbetaio'(t) = cry(t)*kcryOH + zea(t)*kzea + OHbeta10(t)*kOHbeta10 │ y1(t) = beta(t) │ y2(t) = beta10(t) │ , with_states = true, ident_funcs = QQMPolyRingElem[beta10(t), beta(t), kbeta, kbeta10, cry(t)*kcryOH, kcryOH + kcrybeta]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 15 variables beta(t), cry(t), zea(t), beta10(t), ..., kzea │ over rational field └ with_states = true [ Info: QQMPolyRingElem[beta(t), cry(t), zea(t), beta10(t), OHbeta10(t), betaio(t), OHbetaio(t), y1(t), y2(t), kOHbeta10, kbeta, kbeta10, kcryOH, kcrybeta, kzea] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.018478954 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010770217 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 3.3829e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000154578 [ Info: Selecting generators in 0.010680178 [ Info: Inclusion checked with probability 0.995 in 0.009461849 seconds [ Info: The search for identifiable functions concluded in 0.076548518 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.02095392 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01149794 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 4.027e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000172768 [ Info: Selecting generators in 0.01052131 [ Info: Inclusion checked with probability 0.995 in 0.008513579 seconds [ Info: The search for identifiable functions concluded in 0.083390363 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01882271 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.0115428 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 3.3799e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000159719 [ Info: Selecting generators in 0.010204293 [ Info: Inclusion checked with probability 0.995 in 0.008617218 seconds [ Info: The search for identifiable functions concluded in 0.078279842 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.019716961 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010527959 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 2.932e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.059755689 [ Info: Selecting generators in 0.010819476 [ Info: Inclusion checked with probability 0.995 in 0.008936044 seconds [ Info: The search for identifiable functions concluded in 0.135818663 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), y3(t), EpoR_A, k1, k2, k3, k5, k6, k7] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.019360155 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010763597 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 3.394e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.066070669 [ Info: Selecting generators in 0.01149765 [ Info: Inclusion checked with probability 0.995 in 0.009865736 seconds [ Info: The search for identifiable functions concluded in 0.149404673 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), y3(t), EpoR_A, k1, k2, k3, k5, k6, k7] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.019807591 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011086744 seconds [ Info: Dimensions of the Wronskians [4, 2, 10] [ Info: Ranks of the Wronskians computed in 3.328e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.062429504 [ Info: Selecting generators in 0.01039164 [ Info: Inclusion checked with probability 0.995 in 0.009271452 seconds [ Info: The search for identifiable functions concluded in 0.141639697 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k3, EpoR_A*k7, EpoR_A*k1, k5//k6, k2//k6] │ case = │ (ode = x1'(t) = -x1(t)*EpoR_A*k1 │ x2'(t) = x1(t)*EpoR_A*k1 - x2(t)^2*k2 │ x3'(t) = 1//2*x2(t)^2*k2 - x3(t)*k3 │ x4'(t) = x3(t)*k3 │ y1(t) = x2(t)*k5 + 2*x3(t)*k5 │ y2(t) = x1(t)*k6 + x2(t)*k6 + 2*x3(t)*k6 │ y3(t) = EpoR_A*k7 │ , ident_funcs = RingElem[k2//k6, k3, EpoR_A*k7, EpoR_A*k1, k5//k6]) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., k7 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), y3(t), EpoR_A, k1, k2, k3, k5, k6, k7] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001823893 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000106829 [ Info: Selecting generators in 0.000196218 [ Info: Inclusion checked with probability 0.995 in 0.002372078 seconds [ Info: The search for identifiable functions concluded in 0.010771787 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001862552 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.3739e-5 [ Info: Selecting generators in 0.000211078 [ Info: Inclusion checked with probability 0.995 in 0.002402137 seconds [ Info: The search for identifiable functions concluded in 0.011335801 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 1.060088311 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000135429 [ Info: Selecting generators in 0.000257217 [ Info: Inclusion checked with probability 0.995 in 0.002918642 seconds [ Info: The search for identifiable functions concluded in 1.103312039 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001941381 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002573646 [ Info: Selecting generators in 0.000249358 [ Info: Inclusion checked with probability 0.995 in 0.002455206 seconds [ Info: The search for identifiable functions concluded in 0.013786828 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00204971 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002633204 [ Info: Selecting generators in 0.000261068 [ Info: Inclusion checked with probability 0.995 in 0.002458397 seconds [ Info: The search for identifiable functions concluded in 0.013928077 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00210676 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002721324 [ Info: Selecting generators in 0.000268717 [ Info: Inclusion checked with probability 0.995 in 0.002552915 seconds [ Info: The search for identifiable functions concluded in 0.014270974 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[x1(t) + x2(t)] │ case = │ (ode = x1'(t) = x1(t) │ x2'(t) = x2(t) │ y(t) = x1(t) + x2(t) │ , ident_funcs = QQMPolyRingElem[x1(t) + x2(t)], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x1(t), x2(t), y(t) │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t)] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01773264 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.046847592 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000581744 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.023776323 [ Info: Selecting generators in 0.012509901 [ Info: Inclusion checked with probability 0.995 in 0.038573832 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000181738 [ Info: Selecting generators in 0.011702128 [ Info: Inclusion checked with probability 0.995 in 0.015463443 seconds [ Info: The search for identifiable functions concluded in 0.345326891 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), U(t)*a + I(t)*a, E(t)//(U(t) + I(t)), S(t)//(U(t) + I(t)), (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013852877 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.043308536 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000594784 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019150567 [ Info: Selecting generators in 0.011357532 [ Info: Inclusion checked with probability 0.995 in 0.03459295 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000181078 [ Info: Selecting generators in 0.010003175 [ Info: Inclusion checked with probability 0.995 in 0.013049306 seconds [ Info: The search for identifiable functions concluded in 1.333721427 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), U(t)*a + I(t)*a, E(t)//(U(t) + I(t)), S(t)//(U(t) + I(t)), (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013567711 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.039104287 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000596665 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.017566562 [ Info: Selecting generators in 0.010413801 [ Info: Inclusion checked with probability 0.995 in 0.031956775 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000180718 [ Info: Selecting generators in 0.009486779 [ Info: Inclusion checked with probability 0.995 in 0.012804707 seconds [ Info: The search for identifiable functions concluded in 0.282728728 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), U(t)*a + I(t)*a, E(t)//(U(t) + I(t)), S(t)//(U(t) + I(t)), (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012231603 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.03977906 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000591254 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019531323 [ Info: Selecting generators in 0.011675639 [ Info: Inclusion checked with probability 0.995 in 0.03564063 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.036832184 [ Info: Selecting generators in 0.022153349 [ Info: Inclusion checked with probability 0.995 in 0.01574797 seconds [ Info: The search for identifiable functions concluded in 1.349274958 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), E(t)*a, S(t)*a, U(t)*a + I(t)*a, (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), E(t), U(t), I(t), y(t), N, a, b, d, g] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.017594642 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.047577315 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000596524 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.023300288 [ Info: Selecting generators in 0.011852597 [ Info: Inclusion checked with probability 0.995 in 0.037931318 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.377126547 [ Info: Selecting generators in 0.015581372 [ Info: Inclusion checked with probability 0.995 in 0.012315533 seconds [ Info: The search for identifiable functions concluded in 0.721311278 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), E(t)*a, S(t)*a, U(t)*a + I(t)*a, (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), E(t), U(t), I(t), y(t), N, a, b, d, g] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013984607 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.039012568 seconds [ Info: Dimensions of the Wronskians [80] [ Info: Ranks of the Wronskians computed in 0.000616014 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.017728181 [ Info: Selecting generators in 0.010225872 [ Info: Inclusion checked with probability 0.995 in 0.031269201 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.176014618 [ Info: Selecting generators in 0.015504462 [ Info: Inclusion checked with probability 0.995 in 0.012047005 seconds [ Info: The search for identifiable functions concluded in 0.461767388 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[g, d, I(t), E(t)*a, S(t)*a, U(t)*a + I(t)*a, (N*a)//b] │ case = │ (ode = S'(t) = (-S(t)*U(t)*b - S(t)*I(t)*b)//N │ E'(t) = (S(t)*U(t)*b + S(t)*I(t)*b - E(t)*N*g)//N │ U'(t) = -E(t)*a*g + E(t)*g - U(t)*d │ I'(t) = E(t)*a*g - I(t)*d │ y(t) = I(t) │ , ident_funcs = RingElem[I(t), d, g, S(t)*a, E(t)*a, U(t)*a + I(t)*a, (N*a)//b], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 10 variables S(t), E(t), U(t), I(t), ..., g │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), E(t), U(t), I(t), y(t), N, a, b, d, g] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001134209 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00095286 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.716e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001511525 [ Info: Selecting generators in 0.000707383 [ Info: Inclusion checked with probability 0.995 in 0.001858372 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.7679e-5 [ Info: Selecting generators in 0.001339337 [ Info: Inclusion checked with probability 0.995 in 0.003019711 seconds [ Info: The search for identifiable functions concluded in 0.021900571 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)^2, x(t)//alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001210509 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00101214 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.141e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001252318 [ Info: Selecting generators in 0.000749823 [ Info: Inclusion checked with probability 0.995 in 0.001798353 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.422e-5 [ Info: Selecting generators in 0.00110873 [ Info: Inclusion checked with probability 0.995 in 0.002647965 seconds [ Info: The search for identifiable functions concluded in 0.020964109 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)^2, x(t)//alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001177358 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000931041 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.0809e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001236738 [ Info: Selecting generators in 0.000659493 [ Info: Inclusion checked with probability 0.995 in 0.001834592 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.1869e-5 [ Info: Selecting generators in 0.001170359 [ Info: Inclusion checked with probability 0.995 in 0.002637975 seconds [ Info: The search for identifiable functions concluded in 0.021173047 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)^2, x(t)//alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001110359 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000884771 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.79e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000981701 [ Info: Selecting generators in 0.000571505 [ Info: Inclusion checked with probability 0.995 in 0.001621155 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003843573 [ Info: Selecting generators in 0.002108699 [ Info: Inclusion checked with probability 0.995 in 0.002698095 seconds [ Info: The search for identifiable functions concluded in 0.023957711 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)*alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), alpha] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001071289 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000879372 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.74e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001141149 [ Info: Selecting generators in 0.000640834 [ Info: Inclusion checked with probability 0.995 in 0.001724023 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003954392 [ Info: Selecting generators in 0.002358217 [ Info: Inclusion checked with probability 0.995 in 0.002912242 seconds [ Info: The search for identifiable functions concluded in 0.025556236 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)*alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), alpha] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001245458 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00106662 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.272e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001392286 [ Info: Selecting generators in 0.000853122 [ Info: Inclusion checked with probability 0.995 in 0.002039911 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004757194 [ Info: Selecting generators in 0.002706945 [ Info: Inclusion checked with probability 0.995 in 0.003077391 seconds [ Info: The search for identifiable functions concluded in 0.030444069 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[alpha^2, x(t)*alpha] │ case = │ (ode = x'(t) = x(t)^2*alpha │ y(t) = x(t)^2 │ , ident_funcs = QQMPolyRingElem[alpha^2, x(t)*alpha], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 3 variables x(t), y(t), alpha │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x(t), y(t), alpha] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003448527 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002675854 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.168e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000124119 [ Info: Selecting generators in 0.003917573 [ Info: Inclusion checked with probability 0.995 in 0.004824544 seconds [ Info: The search for identifiable functions concluded in 0.030817805 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003351858 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002739384 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.2179e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000125089 [ Info: Selecting generators in 0.003895613 [ Info: Inclusion checked with probability 0.995 in 0.004975963 seconds [ Info: The search for identifiable functions concluded in 0.030854115 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003354107 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002683675 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.181e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000136149 [ Info: Selecting generators in 0.004017692 [ Info: Inclusion checked with probability 0.995 in 0.004773775 seconds [ Info: The search for identifiable functions concluded in 0.030459899 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003361938 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002777763 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.2269e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.021106018 [ Info: Selecting generators in 0.003569186 [ Info: Inclusion checked with probability 0.995 in 0.004491157 seconds [ Info: The search for identifiable functions concluded in 0.05121342 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003523067 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002665675 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.166e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.02202428 [ Info: Selecting generators in 0.003845473 [ Info: Inclusion checked with probability 0.995 in 0.004251479 seconds [ Info: The search for identifiable functions concluded in 0.051814945 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002964642 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002453286 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.789e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.021835631 [ Info: Selecting generators in 0.004046531 [ Info: Inclusion checked with probability 0.995 in 0.004863134 seconds [ Info: The search for identifiable functions concluded in 0.050592407 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k02 + k12, k01 + k21, k12*k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k02 + k12, k01 + k21, k12*k21], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003313998 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002680584 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.083e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.015852394 [ Info: Selecting generators in 0.005610676 [ Info: Inclusion checked with probability 0.995 in 0.005578177 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000220018 [ Info: Selecting generators in 0.013003316 [ Info: Inclusion checked with probability 0.995 in 0.008759926 seconds [ Info: The search for identifiable functions concluded in 1.1052899 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)//k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004328429 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003495237 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.873e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.030540349 [ Info: Selecting generators in 0.005585797 [ Info: Inclusion checked with probability 0.995 in 0.005872334 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000168759 [ Info: Selecting generators in 0.011558049 [ Info: Inclusion checked with probability 0.995 in 0.008677747 seconds [ Info: The search for identifiable functions concluded in 0.120634028 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)//k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003990691 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003556046 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.931e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.024221198 [ Info: Selecting generators in 0.003764214 [ Info: Inclusion checked with probability 0.995 in 0.004363088 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000153349 [ Info: Selecting generators in 0.010275571 [ Info: Inclusion checked with probability 0.995 in 0.007147342 seconds [ Info: The search for identifiable functions concluded in 0.101447481 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)//k21] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003073471 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002443937 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.713e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020612183 [ Info: Selecting generators in 0.003505117 [ Info: Inclusion checked with probability 0.995 in 0.00411314 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.071858183 [ Info: Selecting generators in 0.011888186 [ Info: Inclusion checked with probability 0.995 in 0.007087512 seconds [ Info: The search for identifiable functions concluded in 0.164160172 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002891203 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002305938 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.7149e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019406735 [ Info: Selecting generators in 0.003268139 [ Info: Inclusion checked with probability 0.995 in 0.003947483 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.068113109 [ Info: Selecting generators in 0.010661078 [ Info: Inclusion checked with probability 0.995 in 0.006855205 seconds [ Info: The search for identifiable functions concluded in 0.15491754 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002812843 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002285368 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.837e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019062068 [ Info: Selecting generators in 0.003636755 [ Info: Inclusion checked with probability 0.995 in 0.004293609 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.065662683 [ Info: Selecting generators in 0.011328872 [ Info: Inclusion checked with probability 0.995 in 0.006641897 seconds [ Info: The search for identifiable functions concluded in 0.156515745 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12] │ case = │ (ode = x1'(t) = -x1(t)*k01 - x1(t)*k21 + x2(t)*k12 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k02 + k12, k01 + k21, k12*k21, x2(t)*k12], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 9 variables x1(t), x2(t), y(t), u(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), k01, k02, k12, k21, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.0041512 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003669605 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.325e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000126779 [ Info: Selecting generators in 0.012387461 [ Info: Inclusion checked with probability 0.995 in 0.009167802 seconds [ Info: The search for identifiable functions concluded in 0.052020633 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, K_M*c, V_M//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003750305 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004015402 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.074e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000140229 [ Info: Selecting generators in 0.012435571 [ Info: Inclusion checked with probability 0.995 in 0.009558489 seconds [ Info: The search for identifiable functions concluded in 0.053884685 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, K_M*c, V_M//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004392808 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004255639 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.285e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000131158 [ Info: Selecting generators in 0.012685928 [ Info: Inclusion checked with probability 0.995 in 0.009014344 seconds [ Info: The search for identifiable functions concluded in 0.054464749 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, K_M*c, V_M//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003961182 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004472897 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 4.524e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.075489359 [ Info: Selecting generators in 0.019362445 [ Info: Inclusion checked with probability 0.995 in 0.008712096 seconds [ Info: The search for identifiable functions concluded in 0.136114619 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004278359 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004522897 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.029e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.072892294 [ Info: Selecting generators in 0.018344495 [ Info: Inclusion checked with probability 0.995 in 0.008815126 seconds [ Info: The search for identifiable functions concluded in 0.134330316 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004297089 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004262249 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.126e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.953586419 [ Info: Selecting generators in 0.025426217 [ Info: Inclusion checked with probability 0.995 in 0.01052104 seconds [ Info: The search for identifiable functions concluded in 1.02573718 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005979843 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005678346 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 4.1109e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.082483092 [ Info: Selecting generators in 0.01886016 [ Info: Inclusion checked with probability 0.995 in 0.008703417 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000173668 [ Info: Selecting generators in 0.021736772 [ Info: Inclusion checked with probability 0.995 in 0.016429083 seconds [ Info: The search for identifiable functions concluded in 0.254109232 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x1(t)*c, x2(t)//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004530617 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004551187 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.7069e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.071387007 [ Info: Selecting generators in 0.017049807 [ Info: Inclusion checked with probability 0.995 in 0.008115173 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000154238 [ Info: Selecting generators in 0.02097033 [ Info: Inclusion checked with probability 0.995 in 0.016918798 seconds [ Info: The search for identifiable functions concluded in 0.224559705 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x1(t)*c, x2(t)//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004729815 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004833893 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 4.1909e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.07744892 [ Info: Selecting generators in 0.018304955 [ Info: Inclusion checked with probability 0.995 in 0.009669817 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000160609 [ Info: Selecting generators in 0.021382826 [ Info: Inclusion checked with probability 0.995 in 0.016843299 seconds [ Info: The search for identifiable functions concluded in 0.23960393 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x1(t)*c, x2(t)//b1] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005660006 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004391208 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.268e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.069863292 [ Info: Selecting generators in 0.017023718 [ Info: Inclusion checked with probability 0.995 in 0.00835149 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.26272128 [ Info: Selecting generators in 0.024963591 [ Info: Inclusion checked with probability 0.995 in 0.016546742 seconds [ Info: The search for identifiable functions concluded in 0.491371635 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004504517 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004547496 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.068e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.035244859 [ Info: Selecting generators in 0.024524286 [ Info: Inclusion checked with probability 0.995 in 0.011029724 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.271174029 [ Info: Selecting generators in 0.022247567 [ Info: Inclusion checked with probability 0.995 in 0.015525342 seconds [ Info: The search for identifiable functions concluded in 1.487539267 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003979962 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00413127 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.674e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.066296406 [ Info: Selecting generators in 0.017316874 [ Info: Inclusion checked with probability 0.995 in 0.008570188 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.237737509 [ Info: Selecting generators in 0.02507659 [ Info: Inclusion checked with probability 0.995 in 0.014722439 seconds [ Info: The search for identifiable functions concluded in 0.456570928 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c] │ case = │ (ode = x1'(t) = (-x1(t)^2*k21 + x1(t)*x2(t)*k12 + x1(t)*u(t)*b1 - x1(t)*K_M*k21 - x1(t)*V_M + x2(t)*K_M*k12 + u(t)*K_M*b1)//(x1(t) + K_M) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ y(t) = x1(t)*c │ , ident_funcs = QQMPolyRingElem[k21, k12, k02, b1*c, V_M*c, K_M*c, x2(t)*c, x1(t)*c], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 11 variables x1(t), x2(t), y(t), u(t), ..., k21 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), u(t), K_M, V_M, b1, c, k02, k12, k21] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005684346 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004607676 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.597e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000209778 [ Info: Selecting generators in 0.013447322 [ Info: Inclusion checked with probability 0.995 in 0.011253923 seconds [ Info: The search for identifiable functions concluded in 0.132156778 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, (k12*k21 + k13*k31)//(k12 + k31), (k12*k21 - k13*k31)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006112521 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005073741 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.791e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000164128 [ Info: Selecting generators in 0.011655799 [ Info: Inclusion checked with probability 0.995 in 0.011062795 seconds [ Info: The search for identifiable functions concluded in 0.128892619 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, (k12*k21 + k13*k31)//(k12 + k31), (k12*k21 - k13*k31)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006113062 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005004492 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.686e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000216238 [ Info: Selecting generators in 0.015317004 [ Info: Inclusion checked with probability 0.995 in 0.922829923 seconds [ Info: The search for identifiable functions concluded in 1.052291316 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, (k12*k21 + k13*k31)//(k12 + k31), (k12*k21 - k13*k31)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007845185 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006990093 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.474e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.162593416 [ Info: Selecting generators in 0.020397955 [ Info: Inclusion checked with probability 0.995 in 0.008608207 seconds [ Info: The search for identifiable functions concluded in 0.324601239 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006147342 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005134241 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.013e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.116339848 [ Info: Selecting generators in 0.015864839 [ Info: Inclusion checked with probability 0.995 in 0.007495658 seconds [ Info: The search for identifiable functions concluded in 0.243742671 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.004861934 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004364068 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.447e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.105416633 [ Info: Selecting generators in 0.015811229 [ Info: Inclusion checked with probability 0.995 in 0.007722276 seconds [ Info: The search for identifiable functions concluded in 0.225100849 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00522594 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004305009 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.401e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.119734776 [ Info: Selecting generators in 0.016215135 [ Info: Inclusion checked with probability 0.995 in 0.008872675 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000229728 [ Info: Selecting generators in 0.936133856 [ Info: Inclusion checked with probability 0.995 in 0.022764972 seconds [ Info: The search for identifiable functions concluded in 1.407295744 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, x1(t)*k12 + x1(t)*k31 - x2(t)*k12 - x3(t)*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, (x2(t)*k12 - x3(t)*k13)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.007608578 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006597247 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.5539e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.162072631 [ Info: Selecting generators in 0.018389284 [ Info: Inclusion checked with probability 0.995 in 0.008600078 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000261967 [ Info: Selecting generators in 0.047768163 [ Info: Inclusion checked with probability 0.995 in 0.018324694 seconds [ Info: The search for identifiable functions concluded in 0.596704878 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, x1(t)*k12 + x1(t)*k31 - x2(t)*k12 - x3(t)*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, (x2(t)*k12 - x3(t)*k13)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005681956 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004334569 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.331e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.111101919 [ Info: Selecting generators in 0.016177056 [ Info: Inclusion checked with probability 0.995 in 0.007934414 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000241648 [ Info: Selecting generators in 0.048989112 [ Info: Inclusion checked with probability 0.995 in 0.019310826 seconds [ Info: The search for identifiable functions concluded in 0.499910943 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, k02*k03 + k02*k13 + k03*k12 + k12*k13, x1(t)*k12 + x1(t)*k31 - x2(t)*k12 - x3(t)*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, (x2(t)*k12 - x3(t)*k13)//(k02 - k03 + k12 - k13)] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00629726 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00516254 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.411e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.115043271 [ Info: Selecting generators in 0.817355741 [ Info: Inclusion checked with probability 0.995 in 0.023494816 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.791455168 [ Info: Selecting generators in 0.053499519 [ Info: Inclusion checked with probability 0.995 in 0.017263915 seconds [ Info: The search for identifiable functions concluded in 2.175385136 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006587407 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004762894 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 3.6919e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.170915787 [ Info: Selecting generators in 0.019944179 [ Info: Inclusion checked with probability 0.995 in 0.009623598 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.390686863 [ Info: Selecting generators in 0.071933343 [ Info: Inclusion checked with probability 0.995 in 0.019225456 seconds [ Info: The search for identifiable functions concluded in 2.887571041 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.006965163 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005946533 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.244e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.1256083 [ Info: Selecting generators in 0.016354894 [ Info: Inclusion checked with probability 0.995 in 0.007792036 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 2.629294369 [ Info: Selecting generators in 0.06076514 [ Info: Inclusion checked with probability 0.995 in 0.018168147 seconds [ Info: The search for identifiable functions concluded in 3.171031393 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13] │ case = │ (ode = x1'(t) = -x1(t)*k12 - x1(t)*k31 + x2(t)*k12 + x3(t)*k13 + u(t) │ x2'(t) = x1(t)*k21 - x2(t)*k02 - x2(t)*k12 │ x3'(t) = x1(t)*k31 - x3(t)*k03 - x3(t)*k13 │ y(t) = x1(t)//v │ , ident_funcs = QQMPolyRingElem[v, x1(t), k12 + k31, k02 + k03 + k13 - k31, k12*k21 + k13*k31, x2(t)*k12 + x3(t)*k13, k02*k03 + k02*k13 + k03*k12 + k12*k13, k02*k13*k31 + k03*k12*k21 + k12*k13*k21 + k12*k13*k31, x2(t)*k03*k12 + x2(t)*k12*k13 + x3(t)*k02*k13 + x3(t)*k12*k13], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 12 variables x1(t), x2(t), x3(t), y(t), ..., v │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), y(t), u(t), k02, k03, k12, k13, k21, k31, v] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.019039308 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011379491 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.6889e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000136359 [ Info: Selecting generators in 0.010097704 [ Info: Inclusion checked with probability 0.995 in 0.00842405 seconds [ Info: The search for identifiable functions concluded in 0.08792994 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.016139016 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008677767 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.224e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000122899 [ Info: Selecting generators in 0.008886535 [ Info: Inclusion checked with probability 0.995 in 0.006640696 seconds [ Info: The search for identifiable functions concluded in 0.074769375 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.015563871 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008330031 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.338e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000119199 [ Info: Selecting generators in 0.008795866 [ Info: Inclusion checked with probability 0.995 in 0.00632426 seconds [ Info: The search for identifiable functions concluded in 0.072578167 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014845538 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008011713 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.0659e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.062090787 [ Info: Selecting generators in 0.00846815 [ Info: Inclusion checked with probability 0.995 in 0.00633071 seconds [ Info: The search for identifiable functions concluded in 0.132355776 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.015930107 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007550708 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.0979e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.060532611 [ Info: Selecting generators in 0.009976625 [ Info: Inclusion checked with probability 0.995 in 0.007443909 seconds [ Info: The search for identifiable functions concluded in 0.133869931 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.016403553 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.009124823 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.2309e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.067047159 [ Info: Selecting generators in 0.010820447 [ Info: Inclusion checked with probability 0.995 in 0.008704227 seconds [ Info: The search for identifiable functions concluded in 0.148211624 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, a03 + a43, a04 + a24 + a42, a24*a43, a04*a42], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.017386364 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010319042 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.622e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.070344878 [ Info: Selecting generators in 0.010323322 [ Info: Inclusion checked with probability 0.995 in 0.007548348 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000185199 [ Info: Selecting generators in 0.027410248 [ Info: Inclusion checked with probability 0.995 in 0.0136123 seconds [ Info: The search for identifiable functions concluded in 0.291544894 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.015973048 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.009696247 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.672e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.917352036 [ Info: Selecting generators in 0.014240864 [ Info: Inclusion checked with probability 0.995 in 0.009707777 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000181238 [ Info: Selecting generators in 0.026807754 [ Info: Inclusion checked with probability 0.995 in 0.011970025 seconds [ Info: The search for identifiable functions concluded in 1.158998337 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.016127536 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011228393 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.9539e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.059810728 [ Info: Selecting generators in 0.00732051 [ Info: Inclusion checked with probability 0.995 in 0.005645746 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000134958 [ Info: Selecting generators in 0.020340586 [ Info: Inclusion checked with probability 0.995 in 0.009213032 seconds [ Info: The search for identifiable functions concluded in 0.236435121 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014746619 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008498389 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.5849e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.051918644 [ Info: Selecting generators in 0.009088853 [ Info: Inclusion checked with probability 0.995 in 0.006804045 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.429327328 [ Info: Selecting generators in 0.028926524 [ Info: Inclusion checked with probability 0.995 in 0.01360635 seconds [ Info: The search for identifiable functions concluded in 0.681697387 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.018092567 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.010317642 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 2.651e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.063624772 [ Info: Selecting generators in 0.010676578 [ Info: Inclusion checked with probability 0.995 in 0.008018024 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.523806065 [ Info: Selecting generators in 0.025176539 [ Info: Inclusion checked with probability 0.995 in 0.011669688 seconds [ Info: The search for identifiable functions concluded in 1.818914522 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.015430303 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007903275 seconds [ Info: Dimensions of the Wronskians [4, 5] [ Info: Ranks of the Wronskians computed in 5.2109e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.05969518 [ Info: Selecting generators in 0.009148902 [ Info: Inclusion checked with probability 0.995 in 0.007038132 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.402687398 [ Info: Selecting generators in 0.034629299 [ Info: Inclusion checked with probability 0.995 in 0.015568322 seconds [ Info: The search for identifiable functions concluded in 1.670823576 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24] │ case = │ (ode = x1'(t) = -x1(t)*a31 + x3(t)*a13 + u(t) │ x2'(t) = -x2(t)*a42 + x4(t)*a24 │ x3'(t) = x1(t)*a31 - x3(t)*a03 - x3(t)*a13 - x3(t)*a43 │ x4'(t) = x2(t)*a42 + x3(t)*a43 - x4(t)*a04 - x4(t)*a24 │ y1(t) = x1(t) │ y2(t) = x2(t) │ , ident_funcs = QQMPolyRingElem[a31, a13, x3(t), x2(t), x1(t), a03 + a43, a04 + a24 + a42, a24*a43, a04*a42, x2(t)*a42 - x4(t)*a24], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 14 variables x1(t), x2(t), x3(t), x4(t), ..., a43 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), u(t), a03, a04, a13, a24, a31, a42, a43] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003540866 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002914612 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.099e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000130929 [ Info: Selecting generators in 0.004855014 [ Info: Inclusion checked with probability 0.995 in 0.005598627 seconds [ Info: The search for identifiable functions concluded in 0.036288663 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003498637 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002909392 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.224e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000109399 [ Info: Selecting generators in 0.004028761 [ Info: Inclusion checked with probability 0.995 in 0.005204 seconds [ Info: The search for identifiable functions concluded in 0.034120464 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003245899 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002755263 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.179e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000111059 [ Info: Selecting generators in 0.004096501 [ Info: Inclusion checked with probability 0.995 in 0.005108751 seconds [ Info: The search for identifiable functions concluded in 0.033220402 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003265518 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002788023 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.697e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.018520183 [ Info: Selecting generators in 0.004341489 [ Info: Inclusion checked with probability 0.995 in 0.00520942 seconds [ Info: The search for identifiable functions concluded in 0.052994343 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003446817 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002676655 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.959e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.017709081 [ Info: Selecting generators in 0.00417949 [ Info: Inclusion checked with probability 0.995 in 0.00519577 seconds [ Info: The search for identifiable functions concluded in 0.049941062 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003806134 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002758734 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.155e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.018029017 [ Info: Selecting generators in 0.004274869 [ Info: Inclusion checked with probability 0.995 in 0.005099431 seconds [ Info: The search for identifiable functions concluded in 0.049963983 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = false [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003040551 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002491856 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.119e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01672528 [ Info: Selecting generators in 0.003766124 [ Info: Inclusion checked with probability 0.995 in 0.004834134 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000131549 [ Info: Selecting generators in 0.007980754 [ Info: Inclusion checked with probability 0.995 in 0.007605117 seconds [ Info: The search for identifiable functions concluded in 0.086755801 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)//N] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002897913 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002243958 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.0709e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016645691 [ Info: Selecting generators in 0.003723344 [ Info: Inclusion checked with probability 0.995 in 0.004716465 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000129208 [ Info: Selecting generators in 0.007989654 [ Info: Inclusion checked with probability 0.995 in 0.007592057 seconds [ Info: The search for identifiable functions concluded in 0.086381205 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)//N] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002811663 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002247119 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.436e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015455272 [ Info: Selecting generators in 0.003701054 [ Info: Inclusion checked with probability 0.995 in 0.003631335 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000129029 [ Info: Selecting generators in 0.007437569 [ Info: Inclusion checked with probability 0.995 in 0.007209571 seconds [ Info: The search for identifiable functions concluded in 0.077991995 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)//N] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002895822 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002255819 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.18e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015748299 [ Info: Selecting generators in 0.003877363 [ Info: Inclusion checked with probability 0.995 in 0.004876053 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.07011923 [ Info: Selecting generators in 0.009912665 [ Info: Inclusion checked with probability 0.995 in 0.006635447 seconds [ Info: The search for identifiable functions concluded in 0.156234487 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002811363 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00219482 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.142e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015134736 [ Info: Selecting generators in 0.003605395 [ Info: Inclusion checked with probability 0.995 in 0.004573907 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.045541595 [ Info: Selecting generators in 0.008547628 [ Info: Inclusion checked with probability 0.995 in 0.006986314 seconds [ Info: The search for identifiable functions concluded in 0.12664921 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002551146 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002273678 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.965e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.017622732 [ Info: Selecting generators in 0.003935262 [ Info: Inclusion checked with probability 0.995 in 0.005344569 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.072617586 [ Info: Selecting generators in 0.011088364 [ Info: Inclusion checked with probability 0.995 in 0.007732186 seconds [ Info: The search for identifiable functions concluded in 0.163922714 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[nu, mu, beta, N*k, I(t)*k, S(t)*k] │ case = │ (ode = S'(t) = (-S(t)*I(t)*beta - S(t)*N*mu + N^2*mu)//N │ I'(t) = (S(t)*I(t)*beta - I(t)*N*mu - I(t)*N*nu)//N │ y(t) = I(t)*k │ , ident_funcs = QQMPolyRingElem[nu, mu, beta, N*k, I(t)*k, S(t)*k], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables S(t), I(t), y(t), N, ..., nu │ over rational field └ with_states = true [ Info: QQMPolyRingElem[S(t), I(t), y(t), N, beta, k, mu, nu] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002836873 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002448556 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.2839e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000126749 [ Info: Selecting generators in 0.005142891 [ Info: Inclusion checked with probability 0.995 in 0.005852474 seconds [ Info: The search for identifiable functions concluded in 0.032888076 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002800403 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002409877 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.9969e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000113489 [ Info: Selecting generators in 0.005162621 [ Info: Inclusion checked with probability 0.995 in 0.005586387 seconds [ Info: The search for identifiable functions concluded in 0.032163882 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002663704 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002449897 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.998e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000116289 [ Info: Selecting generators in 0.004793235 [ Info: Inclusion checked with probability 0.995 in 0.004789824 seconds [ Info: The search for identifiable functions concluded in 0.030500489 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00315969 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002744314 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.134e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020331135 [ Info: Selecting generators in 0.004065141 [ Info: Inclusion checked with probability 0.995 in 0.004568416 seconds [ Info: The search for identifiable functions concluded in 0.051764376 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002484426 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002220478 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.692e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.022225078 [ Info: Selecting generators in 0.005429358 [ Info: Inclusion checked with probability 0.995 in 0.005009613 seconds [ Info: The search for identifiable functions concluded in 0.052700217 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002790083 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002448087 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.1689e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.022116468 [ Info: Selecting generators in 0.004563476 [ Info: Inclusion checked with probability 0.995 in 0.004716145 seconds [ Info: The search for identifiable functions concluded in 0.053003793 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, p2//p4], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002478786 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002238208 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.792e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020723142 [ Info: Selecting generators in 0.004543896 [ Info: Inclusion checked with probability 0.995 in 0.004630535 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000139879 [ Info: Selecting generators in 0.006235601 [ Info: Inclusion checked with probability 0.995 in 0.007131002 seconds [ Info: The search for identifiable functions concluded in 0.086029258 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002860663 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002430677 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.149e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.023615275 [ Info: Selecting generators in 0.005171761 [ Info: Inclusion checked with probability 0.995 in 0.005090262 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000148359 [ Info: Selecting generators in 0.006398289 [ Info: Inclusion checked with probability 0.995 in 0.007410759 seconds [ Info: The search for identifiable functions concluded in 0.094321999 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.023583955 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002468106 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.947e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.029204301 [ Info: Selecting generators in 0.006179481 [ Info: Inclusion checked with probability 0.995 in 0.005468588 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000171249 [ Info: Selecting generators in 0.007951554 [ Info: Inclusion checked with probability 0.995 in 0.008185202 seconds [ Info: The search for identifiable functions concluded in 0.154659522 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00314758 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002523516 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.896e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.02612318 [ Info: Selecting generators in 0.005422018 [ Info: Inclusion checked with probability 0.995 in 0.005055801 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.068405956 [ Info: Selecting generators in 0.008563768 [ Info: Inclusion checked with probability 0.995 in 0.007061113 seconds [ Info: The search for identifiable functions concluded in 0.171461751 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002801983 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002466396 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 1.958e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.021662613 [ Info: Selecting generators in 0.004702175 [ Info: Inclusion checked with probability 0.995 in 0.004789035 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.059937287 [ Info: Selecting generators in 0.007649637 [ Info: Inclusion checked with probability 0.995 in 0.006840174 seconds [ Info: The search for identifiable functions concluded in 0.150082306 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002485376 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00214012 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.081e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020145067 [ Info: Selecting generators in 0.004772794 [ Info: Inclusion checked with probability 0.995 in 0.004611146 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.058881847 [ Info: Selecting generators in 0.007457429 [ Info: Inclusion checked with probability 0.995 in 0.006362059 seconds [ Info: The search for identifiable functions concluded in 0.146117813 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[p5, p3, p1, x1(t), x2(t)*p4, p2//p4] │ case = │ (ode = x1'(t) = -x1(t)*x2(t)*p2 + x1(t)*p1 │ x2'(t) = x1(t)*x2(t)*p5 - x2(t)^2*p3*p4 + x2(t)*p3 │ y(t) = x1(t) │ , ident_funcs = RingElem[p5, p3, p1, x1(t), x2(t)*p4, p2//p4], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 8 variables x1(t), x2(t), y(t), p1, ..., p5 │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), y(t), p1, p2, p3, p4, p5] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014186585 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007143272 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.761e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000181248 [ Info: Selecting generators in 0.017088346 [ Info: Inclusion checked with probability 0.995 in 0.011571109 seconds [ Info: The search for identifiable functions concluded in 0.202152399 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, (k1*q1 + k1*q2 + mu1*q2)//q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01467361 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007211741 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.963e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000168769 [ Info: Selecting generators in 0.016760689 [ Info: Inclusion checked with probability 0.995 in 0.01151797 seconds [ Info: The search for identifiable functions concluded in 0.188237681 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, (k1*q1 + k1*q2 + mu1*q2)//q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014442212 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008020684 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.727e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000213878 [ Info: Selecting generators in 0.018908999 [ Info: Inclusion checked with probability 0.995 in 0.012723818 seconds [ Info: The search for identifiable functions concluded in 0.210049793 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, (k1*q1 + k1*q2 + mu1*q2)//q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.016009327 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008770486 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.4219e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.205526586 [ Info: Selecting generators in 0.024293698 [ Info: Inclusion checked with probability 0.995 in 0.012838388 seconds [ Info: The search for identifiable functions concluded in 0.420697161 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.018148756 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008875875 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 3.082e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.24697298 [ Info: Selecting generators in 0.021692992 [ Info: Inclusion checked with probability 0.995 in 0.011443671 seconds [ Info: The search for identifiable functions concluded in 1.524887111 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014967307 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007721266 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 3.1619e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.190946506 [ Info: Selecting generators in 0.018210426 [ Info: Inclusion checked with probability 0.995 in 0.009904775 seconds [ Info: The search for identifiable functions concluded in 0.380478505 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, c + k1 + mu1 + mu2, k2*q2, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2], with_states = false) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = false [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012635329 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.006372239 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.581e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.198919859 [ Info: Selecting generators in 0.021882511 [ Info: Inclusion checked with probability 0.995 in 0.011444621 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:00 Points: 11   ⌝ # Computing specializations.. Time: 0:00:01 Points: 278   ✓ # Computing specializations.. Time: 0:00:01 [ Info: Search for polynomial generators concluded in 0.000271057 [ Info: Selecting generators in 0.053139843 [ Info: Inclusion checked with probability 0.995 in 0.032324991 seconds [ Info: The search for identifiable functions concluded in 2.442727612 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, (x2(t)*x4(t)*k1 - x3(t)^2*k2 + x3(t)*x4(t)*c - x3(t)*x4(t)*mu2)//(x4(t)*q2)] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.013701279 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007451779 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.83e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.187449139 [ Info: Selecting generators in 0.018461594 [ Info: Inclusion checked with probability 0.995 in 0.01042808 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:01 Points: 296   ✓ # Computing specializations.. Time: 0:00:01 [ Info: Search for polynomial generators concluded in 0.000256268 [ Info: Selecting generators in 0.06173326 [ Info: Inclusion checked with probability 0.995 in 0.034897097 seconds [ Info: The search for identifiable functions concluded in 2.155635264 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, (x2(t)*x4(t)*k1 - x3(t)^2*k2 + x3(t)*x4(t)*c - x3(t)*x4(t)*mu2)//(x4(t)*q2)] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.015551541 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007705967 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 3.329e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.2020101 [ Info: Selecting generators in 0.020067839 [ Info: Inclusion checked with probability 0.995 in 0.011358842 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000321887 [ Info: Selecting generators in 0.066294156 [ Info: Inclusion checked with probability 0.995 in 0.039150096 seconds [ Info: The search for identifiable functions concluded in 2.180098201 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, (x2(t)*x4(t)*k1 - x3(t)^2*k2 + x3(t)*x4(t)*c - x3(t)*x4(t)*mu2)//(x4(t)*q2)] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :weak │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.01673803 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.008787386 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.7489e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.213149233 [ Info: Selecting generators in 0.022917571 [ Info: Inclusion checked with probability 0.995 in 0.012429512 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:00 Points: 310   ✓ # Computing specializations.. Time: 0:00:01 [ Info: Search for polynomial generators concluded in 3.5021004 [ Info: Selecting generators in 0.072096662 [ Info: Inclusion checked with probability 0.995 in 0.030865495 seconds [ Info: The search for identifiable functions concluded in 5.778094655 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.012975366 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00732346 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 2.5949e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.179782062 [ Info: Selecting generators in 0.018024068 [ Info: Inclusion checked with probability 0.995 in 0.010587979 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 2.316547057 [ Info: Selecting generators in 0.070702794 [ Info: Inclusion checked with probability 0.995 in 0.031806107 seconds [ Info: The search for identifiable functions concluded in 4.38554084 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014899238 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.007819085 seconds [ Info: Dimensions of the Wronskians [4, 7] [ Info: Ranks of the Wronskians computed in 3.13e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.192084605 [ Info: Selecting generators in 0.021631143 [ Info: Inclusion checked with probability 0.995 in 0.011740588 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 3.643503299 [ Info: Selecting generators in 0.07643728 [ Info: Inclusion checked with probability 0.995 in 0.031182172 seconds [ Info: The search for identifiable functions concluded in 5.819055884 seconds ┌ Info: Test, result_funcs = │ AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2] │ case = │ (ode = x1'(t) = -x1(t)*x4(t)*beta - x1(t)*d + s │ x2'(t) = x1(t)*x4(t)*beta*q1 - x2(t)*k1 - x2(t)*mu1 │ x3'(t) = x1(t)*x4(t)*beta*q2 + x2(t)*k1 - x3(t)*mu2 │ x4'(t) = x3(t)*k2 - x4(t)*c │ y1(t) = x1(t) │ y2(t) = x4(t) │ , ident_funcs = QQMPolyRingElem[s, d, beta, x4(t), x1(t), c + k1 + mu1 + mu2, k2*q2, x3(t)*k2 - x4(t)*c, c*k1 + c*mu1 + c*mu2 + k1*mu2 + mu1*mu2, c*k1*mu2 + c*mu1*mu2, k1*k2*q1 + k1*k2*q2 + k2*mu1*q2, x2(t)*k1*k2 + x3(t)*k1*k2 + x3(t)*k2*mu1 + x4(t)*k1*mu2 + x4(t)*mu1*mu2], with_states = true) │ simplify = :standard │ R = │ Multivariate polynomial ring in 16 variables x1(t), x2(t), x3(t), x4(t), ..., s │ over rational field └ with_states = true [ Info: QQMPolyRingElem[x1(t), x2(t), x3(t), x4(t), y1(t), y2(t), beta, c, d, k1, k2, mu1, mu2, q1, q2, s] [ Info: Computing IO-equations [ Info: Computed IO-equations in 1.92581948 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.981181735 seconds [ Info: Dimensions of the Wronskians [279] [ Info: Ranks of the Wronskians computed in 0.007382959 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:04 ⌝ # Computing specializations.. Time: 0:00:05 ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 ⌝ # Computing specializations.. Time: 0:00:01 ⌟ # Computing specializations.. Time: 0:00:02 ⌞ # Computing specializations.. Time: 0:00:02 ⌜ # Computing specializations.. Time: 0:00:02 ⌝ # Computing specializations.. Time: 0:00:03 ⌟ # Computing specializations.. Time: 0:00:04 ⌞ # Computing specializations.. Time: 0:00:04 ⌜ # Computing specializations.. Time: 0:00:05 ✓ # Computing specializations.. Time: 0:00:05 ⌜ # Computing specializations.. Time: 0:00:00 Points: 2   ⌝ # Computing specializations.. Time: 0:00:01 Points: 3   ⌟ # Computing specializations.. Time: 0:00:02 Points: 4   ⌞ # Computing specializations.. Time: 0:00:02 Points: 5   ⌜ # Computing specializations.. Time: 0:00:03 Points: 6   ⌝ # Computing specializations.. 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A stacktrace will print followed by a 1.0 second profile ====================================================================================== cmd: /opt/julia/bin/julia 21 running 1 of 1 signal (10): User defined signal 1 unknown function (ip: 0x724733f6760d) malloc at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) ijl_gc_counted_malloc at /source/src/gc.c:3688 ijl_malloc at /source/src/gc.c:3755 flint_malloc at /workspace/srcdir/flint-3.3.1/src/generic_files/memory_manager.c:80 mpoly_gcd_info_init at /workspace/srcdir/flint-3.3.1/src/mpoly/gcd_info.c:21 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1723 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 _nmod_mpoly_vec_content_mpoly at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly_factor/mpolyv.c:153 _try_missing_var at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1011 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1846 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 _nmod_mpoly_vec_content_mpoly at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly_factor/mpolyv.c:153 _try_missing_var at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1011 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1846 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 _nmod_mpoly_vec_content_mpoly at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly_factor/mpolyv.c:153 _try_missing_var at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1011 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1846 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 _nmod_mpoly_vec_content_mpoly at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly_factor/mpolyv.c:153 _try_missing_var at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1011 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1846 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 _nmod_mpoly_vec_content_mpoly at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly_factor/mpolyv.c:153 _try_missing_var at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1011 _nmod_mpoly_gcd_algo_small at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:1846 _nmod_mpoly_gcd_algo at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2246 nmod_mpoly_gcd at /workspace/srcdir/flint-3.3.1/src/nmod_mpoly/gcd.c:2272 gcd at /home/pkgeval/.julia/packages/Nemo/i8LKC/src/flint/nmod_mpoly.jl:346 // at /home/pkgeval/.julia/packages/AbstractAlgebra/eRqDm/src/Fraction.jl:56 derivative at /home/pkgeval/.julia/packages/AbstractAlgebra/eRqDm/src/Fraction.jl:667 derivative at /home/pkgeval/.julia/packages/AbstractAlgebra/eRqDm/src/Fraction.jl:660 [inlined] _check_algebraicity at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/Field.jl:138 check_algebraicity_modp at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/Field.jl:214 issubfield_mod_p at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/Field.jl:284 issubfield_mod_p at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/Field.jl:284 [inlined] #groebner_basis_coeffs#147 at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/simplification.jl:147 groebner_basis_coeffs at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/simplification.jl:147 unknown function (ip: 0x7247155d3509) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 #simplified_generating_set#149 at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/simplification.jl:319 simplified_generating_set at /home/pkgeval/.julia/packages/RationalFunctionFields/SAAsh/src/simplification.jl:319 unknown function (ip: 0x724714d81969) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 #_find_identifiable_functions#368 at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/src/identifiable_functions.jl:120 _find_identifiable_functions at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/src/identifiable_functions.jl:86 [inlined] #366 at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/src/identifiable_functions.jl:63 unknown function (ip: 0x724714d79602) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 with_logstate at ./logging.jl:519 with_logger at ./logging.jl:632 [inlined] #find_identifiable_functions#365 at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/src/identifiable_functions.jl:61 find_identifiable_functions at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/src/identifiable_functions.jl:49 unknown function (ip: 0x724714d794a9) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 jl_apply at /source/src/julia.h:1982 [inlined] do_call at /source/src/interpreter.c:126 eval_value at /source/src/interpreter.c:223 eval_body at /source/src/interpreter.c:489 eval_body at /source/src/interpreter.c:544 eval_body at /source/src/interpreter.c:544 jl_interpret_toplevel_thunk at /source/src/interpreter.c:775 jl_toplevel_eval_flex at /source/src/toplevel.c:934 jl_toplevel_eval_flex at /source/src/toplevel.c:877 ijl_toplevel_eval_in at /source/src/toplevel.c:985 eval at ./boot.jl:385 [inlined] include_string at ./loading.jl:2149 _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 _include at ./loading.jl:2209 include at ./client.jl:487 unknown function (ip: 0x72473307f125) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 macro expansion at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/test/runtests.jl:152 [inlined] macro expansion at /source/usr/share/julia/stdlib/v1.10/Test/src/Test.jl:1582 [inlined] macro expansion at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/test/runtests.jl:150 [inlined] macro expansion at ./timing.jl:279 [inlined] top-level scope at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/test/runtests.jl:149 _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_invoke at /source/src/gf.c:2904 jl_toplevel_eval_flex at /source/src/toplevel.c:925 jl_toplevel_eval_flex at /source/src/toplevel.c:877 ijl_toplevel_eval_in at /source/src/toplevel.c:985 eval at ./boot.jl:385 [inlined] include_string at ./loading.jl:2149 _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 _include at ./loading.jl:2209 include at ./client.jl:487 unknown function (ip: 0x72473307f125) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 jl_apply at /source/src/julia.h:1982 [inlined] do_call at /source/src/interpreter.c:126 eval_value at /source/src/interpreter.c:223 eval_stmt_value at /source/src/interpreter.c:174 [inlined] eval_body at /source/src/interpreter.c:635 jl_interpret_toplevel_thunk at /source/src/interpreter.c:775 jl_toplevel_eval_flex at /source/src/toplevel.c:934 jl_toplevel_eval_flex at /source/src/toplevel.c:877 ijl_toplevel_eval_in at /source/src/toplevel.c:985 eval at ./boot.jl:385 [inlined] exec_options at ./client.jl:289 _start at ./client.jl:550 jfptr__start_83133.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 jl_apply at /source/src/julia.h:1982 [inlined] true_main at /source/src/jlapi.c:582 jl_repl_entrypoint at /source/src/jlapi.c:731 main at /source/cli/loader_exe.c:58 unknown function (ip: 0x724733ef7249) __libc_start_main at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) unknown function (ip: 0x4010b8) unknown function (ip: (nil)) ============================================================== Profile collected. A report will print at the next yield point ============================================================== ====================================================================================== Information request received. A stacktrace will print followed by a 1.0 second profile ====================================================================================== cmd: /opt/julia/bin/julia 1 running 0 of 1 signal (10): User defined signal 1 epoll_wait at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) uv__io_poll at /workspace/srcdir/libuv/src/unix/epoll.c:236 uv_run at /workspace/srcdir/libuv/src/unix/core.c:400 ijl_task_get_next at /source/src/partr.c:478 poptask at ./task.jl:999 wait at ./task.jl:1008 #wait#647 at ./condition.jl:130 wait at ./condition.jl:125 [inlined] wait at ./process.jl:661 jfptr_wait_74856.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 subprocess_handler at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:2048 #130 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1992 withenv at ./env.jl:257 #117 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1840 with_temp_env at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1721 #115 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1810 #mktempdir#24 at ./file.jl:766 unknown function (ip: 0x7c1352f5be80) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 mktempdir at ./file.jl:762 mktempdir at ./file.jl:762 [inlined] #sandbox#114 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1768 sandbox at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1759 unknown function (ip: 0x7c1352f54785) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 #test#127 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1971 test at /source/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1915 [inlined] #test#146 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:444 test at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:423 unknown function (ip: 0x7c1352f54270) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 #test#77 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:159 unknown function (ip: 0x7c1352f53b30) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 test at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:148 #test#75 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:147 [inlined] test at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:147 [inlined] #test#74 at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:146 [inlined] test at /source/usr/share/julia/stdlib/v1.10/Pkg/src/API.jl:146 unknown function (ip: 0x7c1352f50229) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 jl_apply at /source/src/julia.h:1982 [inlined] do_call at /source/src/interpreter.c:126 eval_value at /source/src/interpreter.c:223 eval_stmt_value at /source/src/interpreter.c:174 [inlined] eval_body at /source/src/interpreter.c:635 eval_body at /source/src/interpreter.c:544 eval_body at /source/src/interpreter.c:544 jl_interpret_toplevel_thunk at /source/src/interpreter.c:775 jl_toplevel_eval_flex at /source/src/toplevel.c:934 jl_toplevel_eval_flex at /source/src/toplevel.c:877 ijl_toplevel_eval_in at /source/src/toplevel.c:985 eval at ./boot.jl:385 [inlined] include_string at ./loading.jl:2149 _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 _include at ./loading.jl:2209 include at ./Base.jl:495 jfptr_include_46673.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 exec_options at ./client.jl:316 _start at ./client.jl:550 jfptr__start_83133.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:2878 [inlined] ijl_apply_generic at /source/src/gf.c:3079 jl_apply at /source/src/julia.h:1982 [inlined] true_main at /source/src/jlapi.c:582 jl_repl_entrypoint at /source/src/jlapi.c:731 main at /source/cli/loader_exe.c:58 unknown function (ip: 0x7c1353fa1249) __libc_start_main at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) unknown function (ip: 0x4010b8) unknown function (ip: (nil)) ============================================================== Profile collected. A report will print at the next yield point ============================================================== ┌ Warning: There were no samples collected in one or more groups. │ This may be due to idle threads, or you may need to run your │ program longer (perhaps by running it multiple times), │ or adjust the delay between samples with `Profile.init()`. └ @ Profile /opt/julia/share/julia/stdlib/v1.10/Profile/src/Profile.jl:1225 Overhead ╎ [+additional indent] Count File:Line; Function ========================================================= Thread 1 Task 0x00007c13473fc010 Total snapshots: 1. Utilization: 0% ╎1 @Base/client.jl:550; _start() ╎ 1 @Base/client.jl:316; exec_options(opts::Base.JLOptions) ╎ 1 @Base/Base.jl:495; include(mod::Module, _path::String) ╎ 1 @Base/loading.jl:2209; _include(mapexpr::Function, mod::Module, _path::S… ╎ 1 @Base/loading.jl:2149; include_string(mapexpr::typeof(identity), mod::M… ╎ 1 @Base/boot.jl:385; eval ╎ ╎ 1 @Pkg/src/API.jl:146; kwcall(::@NamedTuple{julia_args::Cmd}, ::typeof(… ╎ ╎ 1 @Pkg/src/API.jl:146; #test#74 ╎ ╎ 1 @Pkg/src/API.jl:147; test ╎ ╎ 1 @Pkg/src/API.jl:147; #test#75 ╎ ╎ 1 @Pkg/src/API.jl:148; kwcall(::@NamedTuple{julia_args::Cmd}, ::typ… ╎ ╎ ╎ 1 @Pkg/src/API.jl:159; test(pkgs::Vector{Pkg.Types.PackageSpec}; i… ╎ ╎ ╎ 1 @Pkg/src/API.jl:423; kwcall(::@NamedTuple{julia_args::Cmd, io::… ╎ ╎ ╎ 1 @Pkg/src/API.jl:444; test(ctx::Pkg.Types.Context, pkgs::Vector… ╎ ╎ ╎ 1 …/src/Operations.jl:1915; test ╎ ╎ ╎ 1 …src/Operations.jl:1971; test(ctx::Pkg.Types.Context, pkgs::… ╎ ╎ ╎ ╎ 1 …src/Operations.jl:1759; kwcall(::@NamedTuple{preferences::… ╎ ╎ ╎ ╎ 1 …src/Operations.jl:1768; sandbox(fn::Function, ctx::Pkg.Ty… ╎ ╎ ╎ ╎ 1 @Base/file.jl:762; mktempdir ╎ ╎ ╎ ╎ 1 @Base/file.jl:762; mktempdir(fn::Function, parent::Strin… ╎ ╎ ╎ ╎ 1 @Base/file.jl:766; mktempdir(fn::Pkg.Operations.var"#11… ╎ ╎ ╎ ╎ ╎ 1 …c/Operations.jl:1810; (::Pkg.Operations.var"#115#120"… ╎ ╎ ╎ ╎ ╎ 1 …c/Operations.jl:1721; with_temp_env(fn::Pkg.Operatio… ╎ ╎ ╎ ╎ ╎ 1 …/Operations.jl:1840; (::Pkg.Operations.var"#117#122… ╎ ╎ ╎ ╎ ╎ 1 @Base/env.jl:257; withenv(::Pkg.Operations.var"#130… ╎ ╎ ╎ ╎ ╎ 1 …Operations.jl:1992; (::Pkg.Operations.var"#130#13… ╎ ╎ ╎ ╎ ╎ ╎ 1 …Operations.jl:2048; subprocess_handler(cmd::Cmd,… ╎ ╎ ╎ ╎ ╎ ╎ 1 …se/process.jl:661; wait(x::Base.Process) ╎ ╎ ╎ ╎ ╎ ╎ 1 …/condition.jl:125; wait ╎ ╎ ╎ ╎ ╎ ╎ 1 …condition.jl:130; wait(c::Base.GenericConditi… ╎ ╎ ╎ ╎ ╎ ╎ 1 …ase/task.jl:1008; wait() ╎ ╎ ╎ ╎ ╎ ╎ ╎ 1 …ase/task.jl:999; poptask(W::Base.IntrusiveL… [21] signal (15): Terminated in expression starting at /home/pkgeval/.julia/packages/StructuralIdentifiability/MQy2n/test/identifiable_functions.jl:1096 n_ll_mod_preinv at /workspace/srcdir/flint-3.3.1/src/ulong_extras/ll_mod_preinv.c:24 unknown function (ip: 0x200000003) n_mulmod2_preinv at /workspace/srcdir/flint-3.3.1/src/ulong_extras.h:180 [inlined] _nmod_poly_divrem_basecase_preinv1_2 at /workspace/srcdir/flint-3.3.1/src/nmod_poly/divrem_basecase.c:190 unknown function (ip: (nil)) Allocations: 1950564348 (Pool: 1949635341; Big: 929007); GC: 707 PkgEval terminated after 2723.31s: test duration exceeded the time limit