Package evaluation to test StructuralIdentifiability on Julia 1.13.0-DEV.1307 (5a5fc987d0*) started at 2025-10-14T15:24:25.355 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Set-up completed after 9.72s ################################################################################ # Installation # Installing StructuralIdentifiability... Resolving package versions... Updating `~/.julia/environments/v1.13/Project.toml` [220ca800] + StructuralIdentifiability v0.5.16 Updating `~/.julia/environments/v1.13/Manifest.toml` ⌅ [c3fe647b] + AbstractAlgebra v0.46.5 [a9b6321e] + Atomix v1.1.2 [861a8166] + Combinatorics v1.0.3 [864edb3b] + DataStructures v0.19.1 [e2ba6199] + ExprTools v0.1.10 ⌅ [0b43b601] + Groebner v0.9.5 [18e54dd8] + IntegerMathUtils v0.1.3 [c8e1da08] + IterTools v1.10.0 [692b3bcd] + JLLWrappers v1.7.1 [1914dd2f] + MacroTools v0.5.16 ⌅ [2edaba10] + Nemo v0.51.1 [bac558e1] + OrderedCollections v1.8.1 [3e851597] + ParamPunPam v0.5.5 [aea7be01] + PrecompileTools v1.3.3 [21216c6a] + Preferences v1.5.0 [27ebfcd6] + Primes v0.5.7 [92933f4c] + ProgressMeter v1.11.0 [fb686558] + RandomExtensions v0.4.4 [220ca800] + StructuralIdentifiability v0.5.16 [a759f4b9] + TimerOutputs v0.5.29 [013be700] + UnsafeAtomics v0.3.0 [e134572f] + FLINT_jll v301.300.102+0 [656ef2d0] + OpenBLAS32_jll v0.3.29+0 [56f22d72] + Artifacts v1.11.0 [ade2ca70] + Dates v1.11.0 [8ba89e20] + Distributed v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.13.0 [56ddb016] + Logging v1.11.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.13.0 [fa267f1f] + TOML v1.0.3 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.3.0+1 [781609d7] + GMP_jll v6.3.0+2 [3a97d323] + MPFR_jll v4.2.2+0 [4536629a] + OpenBLAS_jll v0.3.29+0 [bea87d4a] + SuiteSparse_jll v7.10.1+0 [8e850b90] + libblastrampoline_jll v5.15.0+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 To see why use `status --outdated -m` Installation completed after 5.42s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompilation completed after 222.89s ################################################################################ # Testing # Testing StructuralIdentifiability Status `/tmp/jl_obohTD/Project.toml` ⌅ [c3fe647b] AbstractAlgebra v0.46.5 [4c88cf16] Aqua v0.8.14 [2a0fbf3d] CPUSummary v0.2.7 [861a8166] Combinatorics v1.0.3 [864edb3b] DataStructures v0.19.1 ⌅ [0b43b601] Groebner v0.9.5 [c8e1da08] IterTools v1.10.0 [1914dd2f] MacroTools v0.5.16 ⌅ [2edaba10] Nemo v0.51.1 [3e851597] ParamPunPam v0.5.5 [aea7be01] PrecompileTools v1.3.3 [27ebfcd6] Primes v0.5.7 [276daf66] SpecialFunctions v2.6.1 [220ca800] StructuralIdentifiability v0.5.16 ⌅ [98d24dd4] TestSetExtensions v2.0.0 [a759f4b9] TimerOutputs v0.5.29 [ade2ca70] Dates v1.11.0 [37e2e46d] LinearAlgebra v1.13.0 [56ddb016] Logging v1.11.0 [44cfe95a] Pkg v1.13.0 [9a3f8284] Random v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_obohTD/Manifest.toml` ⌅ [c3fe647b] AbstractAlgebra v0.46.5 [4c88cf16] Aqua v0.8.14 [a9b6321e] Atomix v1.1.2 [2a0fbf3d] CPUSummary v0.2.7 [861a8166] Combinatorics v1.0.3 [f70d9fcc] CommonWorldInvalidations v1.0.0 [34da2185] Compat v4.18.1 [adafc99b] CpuId v0.3.1 [864edb3b] DataStructures v0.19.1 [ab62b9b5] DeepDiffs v1.2.0 [ffbed154] DocStringExtensions v0.9.5 [e2ba6199] ExprTools v0.1.10 ⌅ [0b43b601] Groebner v0.9.5 [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 v0.51.1 [bac558e1] OrderedCollections v1.8.1 [3e851597] ParamPunPam v0.5.5 [aea7be01] PrecompileTools v1.3.3 [21216c6a] Preferences v1.5.0 [27ebfcd6] Primes v0.5.7 [92933f4c] ProgressMeter v1.11.0 [fb686558] RandomExtensions v0.4.4 [431bcebd] SciMLPublic v1.0.0 [276daf66] SpecialFunctions v2.6.1 [aedffcd0] Static v1.3.0 [220ca800] StructuralIdentifiability v0.5.16 ⌅ [98d24dd4] TestSetExtensions v2.0.0 [a759f4b9] TimerOutputs v0.5.29 [013be700] UnsafeAtomics v0.3.0 [e134572f] FLINT_jll v301.300.102+0 [656ef2d0] OpenBLAS32_jll v0.3.29+0 [efe28fd5] OpenSpecFun_jll v0.5.6+0 [0dad84c5] ArgTools v1.1.2 [56f22d72] Artifacts v1.11.0 [2a0f44e3] Base64 v1.11.0 [ade2ca70] Dates v1.11.0 [8ba89e20] Distributed v1.11.0 [f43a241f] Downloads v1.7.0 [7b1f6079] FileWatching v1.11.0 [b77e0a4c] InteractiveUtils v1.11.0 [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0 [b27032c2] LibCURL v0.6.4 [76f85450] LibGit2 v1.11.0 [8f399da3] Libdl v1.11.0 [37e2e46d] LinearAlgebra v1.13.0 [56ddb016] Logging v1.11.0 [d6f4376e] Markdown v1.11.0 [ca575930] NetworkOptions v1.3.0 [44cfe95a] Pkg v1.13.0 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [ea8e919c] SHA v0.7.0 [9e88b42a] Serialization v1.11.0 [6462fe0b] Sockets v1.11.0 [2f01184e] SparseArrays v1.13.0 [f489334b] StyledStrings v1.11.0 [fa267f1f] TOML v1.0.3 [a4e569a6] Tar v1.10.0 [8dfed614] Test v1.11.0 [cf7118a7] UUIDs v1.11.0 [4ec0a83e] Unicode v1.11.0 [e66e0078] CompilerSupportLibraries_jll v1.3.0+1 [781609d7] GMP_jll v6.3.0+2 [deac9b47] LibCURL_jll v8.16.0+0 [e37daf67] LibGit2_jll v1.9.1+0 [29816b5a] LibSSH2_jll v1.11.3+1 [3a97d323] MPFR_jll v4.2.2+0 [14a3606d] MozillaCACerts_jll v2025.9.9 [4536629a] OpenBLAS_jll v0.3.29+0 [05823500] OpenLibm_jll v0.8.7+0 [458c3c95] OpenSSL_jll v3.5.4+0 [efcefdf7] PCRE2_jll v10.46.0+0 [bea87d4a] SuiteSparse_jll v7.10.1+0 [83775a58] Zlib_jll v1.3.1+2 [3161d3a3] Zstd_jll v1.5.7+1 [8e850b90] libblastrampoline_jll v5.15.0+0 [8e850ede] nghttp2_jll v1.67.1+0 [3f19e933] p7zip_jll v17.6.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. Testing Running tests... Resolving package versions... Updating `/tmp/jl_obohTD/Project.toml` ⌅ [c3fe647b] ↓ AbstractAlgebra v0.46.5 ⇒ v0.44.13 [loaded: v0.46.5] [961ee093] + ModelingToolkit v10.25.0 ⌅ [2edaba10] ↓ Nemo v0.51.1 ⇒ v0.49.5 [loaded: v0.51.1] Updating `/tmp/jl_obohTD/Manifest.toml` [47edcb42] + ADTypes v1.18.0 ⌅ [c3fe647b] ↓ AbstractAlgebra v0.46.5 ⇒ v0.44.13 [loaded: v0.46.5] [1520ce14] + AbstractTrees v0.4.5 [7d9f7c33] + Accessors v0.1.42 [79e6a3ab] + Adapt v4.4.0 [66dad0bd] + AliasTables v1.1.3 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.20.0 [4c555306] + ArrayLayouts v1.12.0 [e2ed5e7c] + Bijections v0.2.2 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [8e7c35d0] + BlockArrays v1.7.2 [70df07ce] + BracketingNonlinearSolve v1.5.0 [d360d2e6] + ChainRulesCore v1.26.0 [fb6a15b2] + CloseOpenIntervals v0.1.13 [a80b9123] + CommonMark v0.9.1 [38540f10] + CommonSolve v0.2.4 [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 [9a962f9c] + DataAPI v1.16.0 [2b5f629d] + DiffEqBase v6.190.2 [459566f4] + DiffEqCallbacks v4.10.1 [77a26b50] + DiffEqNoiseProcess v5.24.1 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [a0c0ee7d] + DifferentiationInterface v0.7.9 [8d63f2c5] + DispatchDoctor v0.4.26 [31c24e10] + Distributions v0.25.122 [5b8099bc] + DomainSets v0.7.16 [7c1d4256] + DynamicPolynomials v0.6.4 [06fc5a27] + DynamicQuantities v1.10.0 [4e289a0a] + EnumX v1.0.5 [f151be2c] + EnzymeCore v0.8.14 [55351af7] + ExproniconLite v0.10.14 [7034ab61] + FastBroadcast v0.3.5 [9aa1b823] + FastClosures v0.3.2 [a4df4552] + FastPower v1.1.3 [1a297f60] + FillArrays v1.14.0 [64ca27bc] + FindFirstFunctions v1.4.2 [6a86dc24] + FiniteDiff v2.29.0 [1fa38f19] + Format v1.3.7 ⌃ [f6369f11] + ForwardDiff v0.10.39 [069b7b12] + FunctionWrappers v1.1.3 [77dc65aa] + FunctionWrappersWrappers v0.1.3 [46192b85] + GPUArraysCore v0.2.0 [c27321d9] + Glob v1.3.1 [86223c79] + Graphs v1.13.1 [34004b35] + HypergeometricFunctions v0.3.28 [3263718b] + ImplicitDiscreteSolve v1.2.0 [d25df0c9] + Inflate v0.1.5 [8197267c] + IntervalSets v0.7.11 [3587e190] + InverseFunctions v0.1.17 [82899510] + IteratorInterfaceExtensions v1.0.0 [ae98c720] + Jieko v0.2.1 [98e50ef6] + JuliaFormatter v2.1.6 ⌅ [70703baa] + JuliaSyntax v0.4.10 [ccbc3e58] + JumpProcesses v9.19.1 [b964fa9f] + LaTeXStrings v1.4.0 [23fbe1c1] + Latexify v0.16.10 [10f19ff3] + LayoutPointers v0.1.17 [87fe0de2] + LineSearch v0.1.4 [d3d80556] + LineSearches v7.4.0 [d8e11817] + MLStyle v0.4.17 [d125e4d3] + ManualMemory v0.1.8 [bb5d69b7] + MaybeInplace v0.1.4 [e1d29d7a] + Missings v1.2.0 [961ee093] + ModelingToolkit v10.25.0 [2e0e35c7] + Moshi v0.3.7 [46d2c3a1] + MuladdMacro v0.2.4 [102ac46a] + MultivariatePolynomials v0.5.13 [d8a4904e] + MutableArithmetics v1.6.6 [d41bc354] + NLSolversBase v7.10.0 [77ba4419] + NaNMath v1.1.3 ⌅ [2edaba10] ↓ Nemo v0.51.1 ⇒ v0.49.5 [loaded: v0.51.1] [be0214bd] + NonlinearSolveBase v2.0.0 [6fe1bfb0] + OffsetArrays v1.17.0 [429524aa] + Optim v1.13.2 [bbf590c4] + OrdinaryDiffEqCore v1.36.0 [90014a1f] + PDMats v0.11.35 [d96e819e] + Parameters v0.12.3 [e409e4f3] + PoissonRandom v0.4.7 [f517fe37] + Polyester v0.7.18 [1d0040c9] + PolyesterWeave v0.2.2 [85a6dd25] + PositiveFactorizations v0.2.4 [d236fae5] + PreallocationTools v0.4.34 [43287f4e] + PtrArrays v1.3.0 [1fd47b50] + QuadGK v2.11.2 [74087812] + Random123 v1.7.1 [e6cf234a] + RandomNumbers v1.6.0 [3cdcf5f2] + RecipesBase v1.3.4 [731186ca] + RecursiveArrayTools v3.37.1 [189a3867] + Reexport v1.2.2 [ae029012] + Requires v1.3.1 [ae5879a3] + ResettableStacks v1.1.1 [79098fc4] + Rmath v0.8.0 [7e49a35a] + RuntimeGeneratedFunctions v0.5.15 [9dfe8606] + SCCNonlinearSolve v1.6.0 [94e857df] + SIMDTypes v0.1.0 [0bca4576] + SciMLBase v2.121.1 [19f34311] + SciMLJacobianOperators v0.1.11 [c0aeaf25] + SciMLOperators v1.9.0 [53ae85a6] + SciMLStructures v1.7.0 [efcf1570] + Setfield v1.1.2 [727e6d20] + SimpleNonlinearSolve v2.9.0 [699a6c99] + SimpleTraits v0.9.5 [ce78b400] + SimpleUnPack v1.1.0 [a2af1166] + SortingAlgorithms v1.2.2 [0d7ed370] + StaticArrayInterface v1.8.0 [90137ffa] + StaticArrays v1.9.15 [1e83bf80] + StaticArraysCore v1.4.3 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.7.1 [2913bbd2] + StatsBase v0.34.6 [4c63d2b9] + StatsFuns v1.5.0 [7792a7ef] + StrideArraysCore v0.5.8 [2efcf032] + SymbolicIndexingInterface v0.3.45 ⌃ [19f23fe9] + SymbolicLimits v0.2.3 ⌅ [d1185830] + SymbolicUtils v3.31.0 [0c5d862f] + Symbolics v6.55.0 [ed4db957] + TaskLocalValues v0.1.3 [8ea1fca8] + TermInterface v2.0.0 [1c621080] + TestItems v1.0.0 [8290d209] + ThreadingUtilities v0.5.5 [410a4b4d] + Tricks v0.1.12 [781d530d] + TruncatedStacktraces v1.4.0 [5c2747f8] + URIs v1.6.1 [3a884ed6] + UnPack v1.0.2 [1986cc42] + Unitful v1.25.0 [a7c27f48] + Unityper v0.1.6 ⌅ [e134572f] ↓ FLINT_jll v301.300.102+0 ⇒ v300.200.201+0 [loaded: v301.300.102+0] [61579ee1] + Ghostscript_jll v9.55.1+0 [aacddb02] + JpegTurbo_jll v3.1.3+0 [f50d1b31] + Rmath_jll v0.5.1+0 [9fa8497b] + Future v1.11.0 [a63ad114] + Mmap v1.11.0 [1a1011a3] + SharedArrays v1.11.0 [4607b0f0] + SuiteSparse Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m` Resolving package versions... Updating `/tmp/jl_obohTD/Project.toml` [0c5d862f] + Symbolics v6.55.0 Manifest No packages added to or removed from `/tmp/jl_obohTD/Manifest.toml` [ 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/0tPYp/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 2.172712 seconds (943.57 k allocations: 47.802 MiB, 99.51% compilation time) 0.001835 seconds (7.17 k allocations: 322.047 KiB) 0.001828 seconds (10.80 k allocations: 484.703 KiB) 0.001862 seconds (10.76 k allocations: 480.141 KiB) 0.002300 seconds (14.53 k allocations: 635.641 KiB) 0.001241 seconds (7.95 k allocations: 360.602 KiB) 0.000825 seconds (7.45 k allocations: 300.641 KiB) 15.576970 seconds (6.82 M allocations: 350.760 MiB, 1.21% gc time, 99.79% 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 0.249793 seconds (112.44 k allocations: 6.028 MiB, 98.02% compilation time) [ Info: Summary of the model: [ Info: State variables: x1, x2 [ Info: Parameters: [ Info: Inputs: u [ Info: Outputs: y 0.009459 seconds (9.76 k allocations: 520.023 KiB, 91.53% compilation time) [ Info: Summary of the model: [ Info: State variables: x [ Info: Parameters: a, b [ Info: Inputs: u [ Info: Outputs: y Coefficient extraction for rational functions: Test Failed at /home/pkgeval/.julia/packages/StructuralIdentifiability/0tPYp/test/extract_coefficients.jl:27 Expression: Set(C) == Set([x // 1, (y + 3) // 1, y ^ 2 // 1, one(R) // 1, 3 * one(R) // 1, -((x ^ 2 + y ^ 2)) // 1]) Evaluated: Set(AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[1//3, -1//3*x^2 - 1//3*y^2, 1//3*y^2, 1//3*x, 1, 1//3*y + 1]) == Set(AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}[y^2, 3, y + 3, 1, x, -x^2 - y^2]) Stacktrace: [1] top-level scope @ ~/.julia/packages/StructuralIdentifiability/0tPYp/test/extract_coefficients.jl:2 [2] macro expansion @ /opt/julia/share/julia/stdlib/v1.13/Test/src/Test.jl:1961 [inlined] [3] macro expansion @ ~/.julia/packages/StructuralIdentifiability/0tPYp/test/extract_coefficients.jl:27 [inlined] [4] macro expansion @ /opt/julia/share/julia/stdlib/v1.13/Test/src/Test.jl:753 [inlined] [ 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}(y2(t)_1 => -a*y2(t)_0 + a*u(t)_0 + y2(t)_1 - u(t)_1, y1(t)_2 => -y1(t)_0 + y1(t)_2) [ 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 0.003094659 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 7.00549597 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 0.070098777 seconds [ Info: Global identifiability assessed in 59.169094461 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002551814 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Global identifiability assessed in 0.866759822 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Global identifiability assessed in 4.9769e-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 0.038420219 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.563441278 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 3.031e-5 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:13 ✓ # Computing specializations.. Time: 0:00:15 [ Info: Search for polynomial generators concluded in 12.366772153 [ Info: Selecting generators in 0.013634201 [ Info: Inclusion checked with probability 0.9955 in 0.062196328 seconds [ Info: Global identifiability assessed in 95.865620455 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 1.665606732 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 1.601262166 seconds [ Info: Dimensions of the Wronskians [676] [ Info: Ranks of the Wronskians computed in 0.10427518 seconds [ Info: Global identifiability assessed in 33.846574834 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.014841629 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.029886067 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000265768 seconds [ Info: Global identifiability assessed in 0.07772971 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 15.495881065 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00400182 seconds [ Info: Dimensions of the Wronskians [2, 3, 2] [ Info: Ranks of the Wronskians computed in 2.648e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.897714211 [ Info: Selecting generators in 0.000457505 [ Info: Inclusion checked with probability 0.9955 in 0.003211928 seconds [ Info: Global identifiability assessed in 17.767797216 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.002846381 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00196348 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.1679e-5 seconds [ Info: Global identifiability assessed in 0.007575123 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.003246517 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002252207 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.874e-5 seconds [ Info: Global identifiability assessed in 0.008784581 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.005975139 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004722302 seconds [ Info: Dimensions of the Wronskians [6] [ Info: Ranks of the Wronskians computed in 2.334e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.184883034 [ Info: Selecting generators in 0.017009537 [ Info: Inclusion checked with probability 0.9955 in 0.005746802 seconds [ Info: Global identifiability assessed in 2.641049293 seconds [ Info: Assessing local identifiability [ Info: Assessing global identifiability [ Info: Functions to check involve states [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.008558343 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003953209 seconds [ Info: Dimensions of the Wronskians [2, 5] [ Info: Ranks of the Wronskians computed in 2.918e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.009237076 [ Info: Selecting generators in 0.005118108 [ Info: Inclusion checked with probability 0.9955 in 0.004550844 seconds [ Info: Global identifiability assessed in 0.057642514 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: Computing IO-equations [ Info: Computed IO-equations in 0.001932301 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001515514 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.4889e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000110199 [ Info: Selecting generators in 1.191423509 [ Info: Inclusion checked with probability 0.995 in 0.001422015 seconds [ Info: The search for identifiable functions concluded in 2.796531905 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 0.001877771 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001696022 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.006e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000118558 [ Info: Selecting generators in 0.000714033 [ Info: Inclusion checked with probability 0.995 in 0.001202088 seconds [ Info: The search for identifiable functions concluded in 0.01181059 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 0.001254777 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001092999 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.933e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000111649 [ Info: Selecting generators in 0.000692883 [ Info: Inclusion checked with probability 0.995 in 0.001183588 seconds [ Info: The search for identifiable functions concluded in 0.009429614 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 0.001188768 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001090919 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.5949e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000656843 [ Info: Selecting generators in 0.000702113 [ Info: Inclusion checked with probability 0.995 in 0.001145868 seconds [ Info: The search for identifiable functions concluded in 0.009599212 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 0.001853511 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001605763 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.64e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000603274 [ Info: Selecting generators in 0.001155028 [ Info: Inclusion checked with probability 0.995 in 0.001677083 seconds [ Info: The search for identifiable functions concluded in 0.013840749 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 0.001674873 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001575493 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.309e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000491575 [ Info: Selecting generators in 0.000743092 [ Info: Inclusion checked with probability 0.995 in 0.001275127 seconds [ Info: The search for identifiable functions concluded in 0.012519583 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 0.001821482 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001309486 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.844e-5 seconds [ Info: The search for identifiable functions concluded in 0.025332163 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001815432 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001277117 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.8e-5 seconds [ Info: The search for identifiable functions concluded in 0.004329356 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001658043 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001353956 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.594e-5 seconds [ Info: The search for identifiable functions concluded in 0.004086349 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001652253 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001272107 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.677e-5 seconds [ Info: The search for identifiable functions concluded in 0.004010499 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001706212 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001296687 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.4629e-5 seconds [ Info: The search for identifiable functions concluded in 0.004049839 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001669163 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001187258 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.319e-5 seconds [ Info: The search for identifiable functions concluded in 0.003770201 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.00192706 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001399676 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.63e-5 seconds [ Info: The search for identifiable functions concluded in 0.00491619 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.0019352 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001400766 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 2.07e-5 seconds [ Info: The search for identifiable functions concluded in 0.004663473 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001765112 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001231198 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.573e-5 seconds [ Info: The search for identifiable functions concluded in 0.004095509 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001683093 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001295077 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.47e-5 seconds [ Info: The search for identifiable functions concluded in 0.004029989 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001718893 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001255217 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.834e-5 seconds [ Info: The search for identifiable functions concluded in 0.004126438 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.001691453 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001249887 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.764e-5 seconds [ Info: The search for identifiable functions concluded in 0.00396553 seconds [ Info: Computing IO-equations [ Info: Computed IO-equations in 0.326727252 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001765872 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.461e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.9589e-5 [ Info: Selecting generators in 0.000630954 [ Info: Inclusion checked with probability 0.995 in 0.001112628 seconds [ Info: The search for identifiable functions concluded in 0.33676334 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 0.002459455 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001524975 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.784e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.8459e-5 [ Info: Selecting generators in 0.000604054 [ Info: Inclusion checked with probability 0.995 in 0.001091179 seconds [ Info: The search for identifiable functions concluded in 0.010476544 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 0.002484634 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001650743 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.9699e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 8.4579e-5 [ Info: Selecting generators in 0.000658253 [ Info: Inclusion checked with probability 0.995 in 0.001281517 seconds [ Info: The search for identifiable functions concluded in 0.011255645 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 0.002716203 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001682623 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.298e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000491285 [ Info: Selecting generators in 0.000699673 [ Info: Inclusion checked with probability 0.995 in 0.001233258 seconds [ Info: The search for identifiable functions concluded in 0.012215476 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 0.002712363 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001613964 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.173e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000481575 [ Info: Selecting generators in 0.000745402 [ Info: Inclusion checked with probability 0.995 in 0.001193338 seconds [ Info: The search for identifiable functions concluded in 0.012048947 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 0.002697032 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001743203 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.2619e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000519865 [ Info: Selecting generators in 0.000797842 [ Info: Inclusion checked with probability 0.995 in 0.001289187 seconds [ Info: The search for identifiable functions concluded in 0.012642052 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 0.001526054 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00203145 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.527e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000119119 [ Info: Selecting generators in 0.002178028 [ Info: Inclusion checked with probability 0.995 in 0.003246547 seconds [ Info: The search for identifiable functions concluded in 0.01872548 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 0.001358366 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001254427 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.994e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000109269 [ Info: Selecting generators in 0.00201691 [ Info: Inclusion checked with probability 0.995 in 0.003115758 seconds [ Info: The search for identifiable functions concluded in 0.017320134 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 0.001403086 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001322687 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.942e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000115199 [ Info: Selecting generators in 0.002296497 [ Info: Inclusion checked with probability 0.995 in 0.003122199 seconds [ Info: The search for identifiable functions concluded in 0.017413243 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 0.001486595 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001454175 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.3869e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.266049828 [ Info: Selecting generators in 0.003616363 [ Info: Inclusion checked with probability 0.995 in 0.002864581 seconds [ Info: The search for identifiable functions concluded in 0.286759118 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 0.001388656 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001408525 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.058e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015087976 [ Info: Selecting generators in 0.003670973 [ Info: Inclusion checked with probability 0.995 in 0.003090748 seconds [ Info: The search for identifiable functions concluded in 0.033802667 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 0.001391156 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001340406 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.996e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016847459 [ Info: Selecting generators in 0.003467955 [ Info: Inclusion checked with probability 0.995 in 0.003066199 seconds [ Info: The search for identifiable functions concluded in 0.036158923 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 0.001395036 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001185868 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.9869e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000111279 [ Info: Selecting generators in 0.002160058 [ Info: Inclusion checked with probability 0.995 in 0.002312477 seconds [ Info: The search for identifiable functions concluded in 1.00034848 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 0.001423766 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001177688 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.862e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000100539 [ Info: Selecting generators in 0.00203649 [ Info: Inclusion checked with probability 0.995 in 0.002173548 seconds [ Info: The search for identifiable functions concluded in 0.014002817 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 0.001316717 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001190768 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.898e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000111069 [ Info: Selecting generators in 0.00201082 [ Info: Inclusion checked with probability 0.995 in 0.002340846 seconds [ Info: The search for identifiable functions concluded in 0.014399834 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 0.001360817 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001169768 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.285e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.25216959 [ Info: Selecting generators in 0.002652573 [ Info: Inclusion checked with probability 0.995 in 0.002376816 seconds [ Info: The search for identifiable functions concluded in 0.267057768 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 0.001329977 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001163028 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.064e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006178367 [ Info: Selecting generators in 0.002130229 [ Info: Inclusion checked with probability 0.995 in 0.002387806 seconds [ Info: The search for identifiable functions concluded in 0.020512352 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 0.001304727 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001197068 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.03e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005052878 [ Info: Selecting generators in 0.002202718 [ Info: Inclusion checked with probability 0.995 in 0.002221127 seconds [ Info: The search for identifiable functions concluded in 0.018560911 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 0.002255027 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001741662 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.797e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000101009 [ Info: Selecting generators in 0.000507915 [ Info: Inclusion checked with probability 0.995 in 0.002376006 seconds [ Info: The search for identifiable functions concluded in 0.017002817 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 0.002106869 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001557684 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.531e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000127499 [ Info: Selecting generators in 0.000580534 [ Info: Inclusion checked with probability 0.995 in 0.002688373 seconds [ Info: The search for identifiable functions concluded in 0.01674677 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 0.002175478 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001675582 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.769e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000107649 [ Info: Selecting generators in 0.000528535 [ Info: Inclusion checked with probability 0.995 in 0.002248627 seconds [ Info: The search for identifiable functions concluded in 0.016375614 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 0.0020349 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001552054 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.726e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.28261504 [ Info: Selecting generators in 0.00102364 [ Info: Inclusion checked with probability 0.995 in 0.002842571 seconds [ Info: The search for identifiable functions concluded in 0.300172052 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 0.002691862 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00199547 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.084e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006967289 [ Info: Selecting generators in 0.000685063 [ Info: Inclusion checked with probability 0.995 in 0.002400546 seconds [ Info: The search for identifiable functions concluded in 0.02557852 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 0.002142139 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001692193 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.07e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006539654 [ Info: Selecting generators in 0.000663274 [ Info: Inclusion checked with probability 0.995 in 0.002237158 seconds [ Info: The search for identifiable functions concluded in 0.022966517 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 0.002796661 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00203172 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.28e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000108348 [ Info: Selecting generators in 0.003108309 [ Info: Inclusion checked with probability 0.995 in 0.002919701 seconds [ Info: The search for identifiable functions concluded in 0.022312873 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 0.003082279 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002077359 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.3829e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000114799 [ Info: Selecting generators in 0.003349206 [ Info: Inclusion checked with probability 0.995 in 0.003083118 seconds [ Info: The search for identifiable functions concluded in 0.023430552 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 0.002663433 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00200167 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.685e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000110339 [ Info: Selecting generators in 0.003118588 [ Info: Inclusion checked with probability 0.995 in 0.00287896 seconds [ Info: The search for identifiable functions concluded in 0.021869898 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 0.002811681 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002124449 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.99e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015482243 [ Info: Selecting generators in 0.003517584 [ Info: Inclusion checked with probability 0.995 in 0.00294016 seconds [ Info: The search for identifiable functions concluded in 0.039032873 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 0.00296784 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002185598 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.987e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.015299885 [ Info: Selecting generators in 0.003666462 [ Info: Inclusion checked with probability 0.995 in 0.003272287 seconds [ Info: The search for identifiable functions concluded in 0.039183833 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 0.00296694 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002236187 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.42e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014104167 [ Info: Selecting generators in 0.003609683 [ Info: Inclusion checked with probability 0.995 in 0.003219447 seconds [ Info: The search for identifiable functions concluded in 0.037559488 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 0.016264155 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005334946 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.243e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000140579 [ Info: Selecting generators in 0.00983432 [ Info: Inclusion checked with probability 0.995 in 0.005522894 seconds [ Info: The search for identifiable functions concluded in 0.31415111 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 0.007037209 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004959039 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.89e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000127198 [ Info: Selecting generators in 0.009335925 [ Info: Inclusion checked with probability 0.995 in 0.005622033 seconds [ Info: The search for identifiable functions concluded in 0.046318169 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 0.007142128 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005741172 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.713e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000143799 [ Info: Selecting generators in 0.010677052 [ Info: Inclusion checked with probability 0.995 in 0.005853711 seconds [ Info: The search for identifiable functions concluded in 0.050026232 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 0.00788329 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005596603 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.842e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002270017 [ Info: Selecting generators in 0.010502444 [ Info: Inclusion checked with probability 0.995 in 0.006108188 seconds [ Info: The search for identifiable functions concluded in 0.053019271 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 0.007651852 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005478934 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.941e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002182398 [ Info: Selecting generators in 0.010303825 [ Info: Inclusion checked with probability 0.995 in 0.00586397 seconds [ Info: The search for identifiable functions concluded in 0.052331068 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 0.007778191 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005609194 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.534e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002357926 [ Info: Selecting generators in 0.011147406 [ Info: Inclusion checked with probability 0.995 in 0.006314995 seconds [ Info: The search for identifiable functions concluded in 0.054502967 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 0.005572104 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003595774 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.3249e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000116359 [ Info: Selecting generators in 0.002041759 [ Info: Inclusion checked with probability 0.995 in 0.003580254 seconds [ Info: The search for identifiable functions concluded in 0.026959896 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 0.005377826 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003532164 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.742e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000137499 [ Info: Selecting generators in 0.002488934 [ Info: Inclusion checked with probability 0.995 in 0.003552504 seconds [ Info: The search for identifiable functions concluded in 0.026291722 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 0.005359156 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003610653 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.691e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000126458 [ Info: Selecting generators in 0.002271637 [ Info: Inclusion checked with probability 0.995 in 0.003520615 seconds [ Info: The search for identifiable functions concluded in 0.026382602 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 0.005373286 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003543514 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.86e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001432455 [ Info: Selecting generators in 0.002526155 [ Info: Inclusion checked with probability 0.995 in 0.003813591 seconds [ Info: The search for identifiable functions concluded in 0.355778046 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 0.005232816 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003205447 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 0.001304646 [ Info: Selecting generators in 0.002074709 [ Info: Inclusion checked with probability 0.995 in 0.003577523 seconds [ Info: The search for identifiable functions concluded in 0.028201094 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 0.005600023 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003157968 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 2.181e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001324597 [ Info: Selecting generators in 0.002392116 [ Info: Inclusion checked with probability 0.995 in 0.003461465 seconds [ Info: The search for identifiable functions concluded in 0.027797558 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 0.00497372 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002958259 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.2519e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000121138 [ Info: Selecting generators in 0.002800332 [ Info: Inclusion checked with probability 0.995 in 0.003649673 seconds [ Info: The search for identifiable functions concluded in 0.03049731 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 0.005657963 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003464165 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.454e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000124409 [ Info: Selecting generators in 0.002797881 [ Info: Inclusion checked with probability 0.995 in 0.003489335 seconds [ Info: The search for identifiable functions concluded in 0.031430821 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 0.005220317 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003068588 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.44e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000120849 [ Info: Selecting generators in 0.002691773 [ Info: Inclusion checked with probability 0.995 in 0.003308276 seconds [ Info: The search for identifiable functions concluded in 0.030606029 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 0.005260497 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003078288 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.267e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.018608501 [ Info: Selecting generators in 0.003742812 [ Info: Inclusion checked with probability 0.995 in 0.003227437 seconds [ Info: The search for identifiable functions concluded in 0.050067711 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 0.005293856 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003245077 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 2.853e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019268344 [ Info: Selecting generators in 0.003706703 [ Info: Inclusion checked with probability 0.995 in 0.003163588 seconds [ Info: The search for identifiable functions concluded in 0.051925473 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 0.005213307 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003063309 seconds [ Info: Dimensions of the Wronskians [4] [ Info: Ranks of the Wronskians computed in 1.762e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01670902 [ Info: Selecting generators in 0.003576094 [ Info: Inclusion checked with probability 0.995 in 0.003452235 seconds [ Info: The search for identifiable functions concluded in 0.046714885 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 0.002712042 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002056349 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.247e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000104659 [ Info: Selecting generators in 0.001723482 [ Info: Inclusion checked with probability 0.995 in 0.002636204 seconds [ Info: The search for identifiable functions concluded in 0.019336014 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 0.002487455 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00199074 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.115e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000109499 [ Info: Selecting generators in 0.001743782 [ Info: Inclusion checked with probability 0.995 in 0.00298719 seconds [ Info: The search for identifiable functions concluded in 0.019030977 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 0.002517704 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001856551 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.108e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000128649 [ Info: Selecting generators in 0.00195409 [ Info: Inclusion checked with probability 0.995 in 0.003527865 seconds [ Info: The search for identifiable functions concluded in 0.019479892 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 0.002519454 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00194613 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 2.429e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01372099 [ Info: Selecting generators in 0.003510504 [ Info: Inclusion checked with probability 0.995 in 0.003110958 seconds [ Info: The search for identifiable functions concluded in 0.034567439 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 0.002714112 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00195274 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.729e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.011970958 [ Info: Selecting generators in 0.003029519 [ Info: Inclusion checked with probability 0.995 in 0.003337046 seconds [ Info: The search for identifiable functions concluded in 0.031635709 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 0.002809651 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002417446 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.9849e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.013646042 [ Info: Selecting generators in 0.003190367 [ Info: Inclusion checked with probability 0.995 in 0.002873711 seconds [ Info: The search for identifiable functions concluded in 0.034383381 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 0.016244685 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.033617648 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000278518 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:05 ✓ # Computing specializations.. Time: 0:00:05 [ Info: Search for polynomial generators concluded in 0.000223738 [ Info: Selecting generators in 0.019746869 [ Info: Inclusion checked with probability 0.995 in 0.031224593 seconds [ Info: The search for identifiable functions concluded in 11.803962756 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 0.016147226 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.034303241 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000280947 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000140599 [ Info: Selecting generators in 0.016649141 [ Info: Inclusion checked with probability 0.995 in 0.026201704 seconds [ Info: The search for identifiable functions concluded in 0.521056639 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 0.014714411 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.029944326 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000351156 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000142698 [ Info: Selecting generators in 0.017674261 [ Info: Inclusion checked with probability 0.995 in 0.027732599 seconds [ Info: The search for identifiable functions concluded in 0.160720578 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 0.014777209 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.031085725 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000347347 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.173136987 [ Info: Selecting generators in 0.016314005 [ Info: Inclusion checked with probability 0.995 in 0.026094444 seconds [ Info: The search for identifiable functions concluded in 1.333868445 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 0.014629411 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.029390231 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000275307 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.045665876 [ Info: Selecting generators in 0.015951658 [ Info: Inclusion checked with probability 0.995 in 0.027316523 seconds [ Info: The search for identifiable functions concluded in 0.204437864 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 0.014356824 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.046439838 seconds [ Info: Dimensions of the Wronskians [69] [ Info: Ranks of the Wronskians computed in 0.000296927 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.046845295 [ Info: Selecting generators in 0.020210425 [ Info: Inclusion checked with probability 0.995 in 0.0266276 seconds [ Info: The search for identifiable functions concluded in 0.605908668 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 1.537806055 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.09039707 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.213426283 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: 8   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000182628 [ Info: Selecting generators in 0.940289243 [ Info: Inclusion checked with probability 0.995 in 2.948616672 seconds [ Info: The search for identifiable functions concluded in 17.676982303 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 1.530099535 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.446305421 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.181665876 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: 7   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000155528 [ Info: Selecting generators in 1.101217861 [ Info: Inclusion checked with probability 0.995 in 2.43809493 seconds [ Info: The search for identifiable functions concluded in 17.865557509 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 1.836501197 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.680230011 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.188291509 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: 7   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.000168468 [ Info: Selecting generators in 1.103347732 [ Info: Inclusion checked with probability 0.995 in 2.631444062 seconds [ Info: The search for identifiable functions concluded in 18.485325261 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 1.893843309 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 8.539079729 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.179500619 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: 7   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.030753268 [ Info: Selecting generators in 1.221936581 [ Info: Inclusion checked with probability 0.995 in 2.68735551 seconds [ Info: The search for identifiable functions concluded in 18.694744568 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 1.755266898 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 9.016277713 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.186442699 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: 4   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.029861677 [ Info: Selecting generators in 0.619421185 [ Info: Inclusion checked with probability 0.995 in 2.870274918 seconds [ Info: The search for identifiable functions concluded in 19.12167488 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 1.895573358 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 9.061209633 seconds [ Info: Dimensions of the Wronskians [830, 3] [ Info: Ranks of the Wronskians computed in 0.187976213 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: 2   ⌝ # Computing specializations.. Time: 0:00:00 Points: 8   ✓ # Computing specializations.. Time: 0:00:00 [ Info: Search for polynomial generators concluded in 0.029753599 [ Info: Selecting generators in 0.595381871 [ Info: Inclusion checked with probability 0.995 in 2.82927756 seconds [ Info: The search for identifiable functions concluded in 19.115699595 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 0.014321924 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012053347 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.242e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000136929 [ Info: Selecting generators in 0.008546923 [ Info: Inclusion checked with probability 0.995 in 0.008587303 seconds [ Info: The search for identifiable functions concluded in 0.083787311 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 0.013987688 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011747721 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.114e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000139129 [ Info: Selecting generators in 0.009097958 [ Info: Inclusion checked with probability 0.995 in 0.009079548 seconds [ Info: The search for identifiable functions concluded in 0.085021418 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 0.013593792 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012128777 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.53e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000141348 [ Info: Selecting generators in 0.008619692 [ Info: Inclusion checked with probability 0.995 in 0.009100118 seconds [ Info: The search for identifiable functions concluded in 0.081257056 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 0.013462724 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.011615982 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 2.9769e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.040211583 [ Info: Selecting generators in 0.019153085 [ Info: Inclusion checked with probability 0.995 in 0.010764021 seconds [ Info: The search for identifiable functions concluded in 0.921700321 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 0.01579699 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.012064498 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 3.485e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.036195943 [ Info: Selecting generators in 0.013701931 [ Info: Inclusion checked with probability 0.995 in 0.008703932 seconds [ Info: The search for identifiable functions concluded in 0.127054641 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 0.014499693 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01179653 seconds [ Info: Dimensions of the Wronskians [15] [ Info: Ranks of the Wronskians computed in 5.3819e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.035989565 [ Info: Selecting generators in 0.013899659 [ Info: Inclusion checked with probability 0.995 in 0.008982639 seconds [ Info: The search for identifiable functions concluded in 0.125400858 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 0.025684499 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.018110187 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.035e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000148028 [ Info: Selecting generators in 0.014323655 [ Info: Inclusion checked with probability 0.995 in 0.016039068 seconds [ Info: The search for identifiable functions concluded in 0.413523445 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 0.02372578 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01675274 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 7.8519e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000148629 [ Info: Selecting generators in 0.010703811 [ Info: Inclusion checked with probability 0.995 in 0.014365714 seconds [ Info: The search for identifiable functions concluded in 0.111178092 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 0.02265556 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.016609872 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.269e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000142868 [ Info: Selecting generators in 0.010125808 [ Info: Inclusion checked with probability 0.995 in 0.015150656 seconds [ Info: The search for identifiable functions concluded in 0.107812607 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 0.022961627 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.015884209 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 8.0059e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.049245831 [ Info: Selecting generators in 0.017034907 [ Info: Inclusion checked with probability 0.995 in 0.013935469 seconds [ Info: The search for identifiable functions concluded in 0.162179825 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 0.022227995 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01580362 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 7.9029e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.050118772 [ Info: Selecting generators in 0.019013197 [ Info: Inclusion checked with probability 0.995 in 0.015556522 seconds [ Info: The search for identifiable functions concluded in 0.167891637 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 0.024102986 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.01782788 seconds [ Info: Dimensions of the Wronskians [3, 36] [ Info: Ranks of the Wronskians computed in 9.4749e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.055050211 [ Info: Selecting generators in 0.019769889 [ Info: Inclusion checked with probability 0.995 in 0.016342554 seconds [ Info: The search for identifiable functions concluded in 0.184729526 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 0.013448163 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017402204 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.7049e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000187848 [ Info: Selecting generators in 0.095478201 [ Info: Inclusion checked with probability 0.995 in 0.019346594 seconds [ Info: The search for identifiable functions concluded in 0.589171034 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*s - s)//(a*e)] │ 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 0.012953478 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017350934 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.7219e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000181898 [ Info: Selecting generators in 0.089141456 [ Info: Inclusion checked with probability 0.995 in 0.017807029 seconds [ Info: The search for identifiable functions concluded in 1.459633555 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*s - s)//(a*e)] │ 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 0.011099057 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.015867189 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.7809e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000185828 [ Info: Selecting generators in 0.08869806 [ Info: Inclusion checked with probability 0.995 in 0.019239004 seconds [ Info: The search for identifiable functions concluded in 0.530451309 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*s - s)//(a*e)] │ 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 0.01184796 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.016902068 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.7019e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.083371924 [ Info: Selecting generators in 0.082736231 [ Info: Inclusion checked with probability 0.995 in 0.016598902 seconds [ Info: The search for identifiable functions concluded in 0.612794775 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 0.011673212 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.019584491 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 6.5469e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 3.284703494 [ Info: Selecting generators in 0.105918985 [ Info: Inclusion checked with probability 0.995 in 0.018262694 seconds [ Info: The search for identifiable functions concluded in 3.829153841 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 0.013042788 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.017241165 seconds [ Info: Dimensions of the Wronskians [32] [ Info: Ranks of the Wronskians computed in 7.1369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 1.317307079 [ Info: Selecting generators in 0.0749259 [ Info: Inclusion checked with probability 0.995 in 0.015284225 seconds [ Info: The search for identifiable functions concluded in 1.846884888 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 2.891830639 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.070671793 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 8.148e-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 Points: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 19   ⌟ # Computing specializations.. Time: 0:00:01 Points: 29   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 49   ⌝ # Computing specializations.. Time: 0:00:02 Points: 60   ⌟ # Computing specializations.. Time: 0:00:02 Points: 70   ⌞ # Computing specializations.. Time: 0:00:02 Points: 80   ⌜ # Computing specializations.. Time: 0:00:03 Points: 90   ✓ # Computing specializations.. Time: 0:00:03 ⌜ # 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: 10   ⌝ # Computing specializations.. Time: 0:00:00 Points: 18   ⌟ # Computing specializations.. Time: 0:00:00 Points: 28   ⌞ # Computing specializations.. Time: 0:00:01 Points: 38   ⌜ # Computing specializations.. Time: 0:00:01 Points: 48   ⌝ # Computing specializations.. Time: 0:00:02 Points: 57   ⌟ # Computing specializations.. Time: 0:00:02 Points: 67   ⌞ # Computing specializations.. Time: 0:00:02 Points: 77   ⌜ # Computing specializations.. Time: 0:00:03 Points: 86   ⌝ # Computing specializations.. Time: 0:00:03 Points: 95   ⌟ # Computing specializations.. Time: 0:00:03 Points: 104   ⌞ # Computing specializations.. Time: 0:00:04 Points: 114   ⌜ # Computing specializations.. Time: 0:00:04 Points: 124   ⌝ # Computing specializations.. Time: 0:00:05 Points: 135   ⌟ # Computing specializations.. Time: 0:00:05 Points: 145   ⌞ # Computing specializations.. Time: 0:00:05 Points: 155   ⌜ # Computing specializations.. Time: 0:00:06 Points: 165   ⌝ # Computing specializations.. Time: 0:00:06 Points: 173   ⌟ # Computing specializations.. Time: 0:00:06 Points: 184   ⌞ # Computing specializations.. Time: 0:00:07 Points: 194   ⌜ # Computing specializations.. Time: 0:00:07 Points: 205   ⌝ # Computing specializations.. Time: 0:00:07 Points: 215   ⌟ # Computing specializations.. Time: 0:00:08 Points: 225   ⌞ # Computing specializations.. Time: 0:00:09 Points: 235   ⌜ # Computing specializations.. Time: 0:00:12 Points: 245   ⌝ # Computing specializations.. Time: 0:00:12 Points: 257   ⌟ # Computing specializations.. Time: 0:00:12 Points: 267   ⌞ # Computing specializations.. Time: 0:00:12 Points: 276   ⌜ # Computing specializations.. Time: 0:00:13 Points: 286   ⌝ # Computing specializations.. Time: 0:00:13 Points: 296   ⌟ # Computing specializations.. Time: 0:00:13 Points: 306   ⌞ # Computing specializations.. Time: 0:00:14 Points: 314   ⌜ # Computing specializations.. Time: 0:00:15 Points: 325   ⌝ # Computing specializations.. Time: 0:00:15 Points: 335   ⌟ # Computing specializations.. Time: 0:00:15 Points: 344   ⌞ # Computing specializations.. Time: 0:00:16 Points: 353   ⌜ # Computing specializations.. Time: 0:00:16 Points: 364   ⌝ # Computing specializations.. Time: 0:00:17 Points: 374   ⌟ # Computing specializations.. Time: 0:00:17 Points: 384   ⌞ # Computing specializations.. Time: 0:00:17 Points: 392   ⌜ # Computing specializations.. Time: 0:00:18 Points: 402   ⌝ # Computing specializations.. Time: 0:00:18 Points: 412   ⌟ # Computing specializations.. Time: 0:00:18 Points: 420   ⌞ # Computing specializations.. Time: 0:00:19 Points: 431   ⌜ # Computing specializations.. Time: 0:00:19 Points: 441   ⌝ # Computing specializations.. Time: 0:00:20 Points: 450   ⌟ # Computing specializations.. Time: 0:00:20 Points: 459   ⌞ # Computing specializations.. Time: 0:00:20 Points: 468   ⌜ # Computing specializations.. Time: 0:00:21 Points: 478   ⌝ # Computing specializations.. Time: 0:00:21 Points: 488   ⌟ # Computing specializations.. Time: 0:00:21 Points: 497   ⌞ # Computing specializations.. Time: 0:00:22 Points: 506   ⌜ # Computing specializations.. Time: 0:00:22 Points: 515   ⌝ # Computing specializations.. Time: 0:00:22 Points: 526   ⌟ # Computing specializations.. Time: 0:00:23 Points: 536   ⌞ # Computing specializations.. Time: 0:00:23 Points: 546   ⌜ # Computing specializations.. Time: 0:00:24 Points: 556   ⌝ # Computing specializations.. Time: 0:00:24 Points: 567   ⌟ # Computing specializations.. Time: 0:00:24 Points: 577   ⌞ # Computing specializations.. Time: 0:00:25 Points: 589   ⌜ # Computing specializations.. Time: 0:00:25 Points: 600   ⌝ # Computing specializations.. Time: 0:00:26 Points: 611   ⌟ # Computing specializations.. Time: 0:00:26 Points: 621   ⌞ # Computing specializations.. Time: 0:00:26 Points: 632   ✓ # Computing specializations.. Time: 0:00:27 [ Info: Search for polynomial generators concluded in 0.000259847 [ Info: Selecting generators in 0.040098114 [ Info: Inclusion checked with probability 0.995 in 9.446635416 seconds [ Info: The search for identifiable functions concluded in 60.657064769 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 2.778822142 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.076813721 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000106379 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: 7   ⌝ # Computing specializations.. Time: 0:00:00 Points: 17   ⌟ # Computing specializations.. Time: 0:00:01 Points: 27   ⌞ # Computing specializations.. Time: 0:00:01 Points: 37   ⌜ # Computing specializations.. Time: 0:00:01 Points: 47   ⌝ # Computing specializations.. Time: 0:00:02 Points: 58   ⌟ # Computing specializations.. Time: 0:00:02 Points: 67   ⌞ # Computing specializations.. Time: 0:00:02 Points: 77   ⌜ # Computing specializations.. Time: 0:00:03 Points: 87   ✓ # Computing specializations.. Time: 0:00:03 ⌜ # 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: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 19   ⌟ # Computing specializations.. Time: 0:00:01 Points: 29   ⌞ # Computing specializations.. Time: 0:00:01 Points: 38   ⌜ # Computing specializations.. Time: 0:00:01 Points: 47   ⌝ # Computing specializations.. Time: 0:00:02 Points: 56   ⌟ # Computing specializations.. Time: 0:00:02 Points: 66   ⌞ # Computing specializations.. Time: 0:00:03 Points: 75   ⌜ # Computing specializations.. Time: 0:00:03 Points: 85   ⌝ # Computing specializations.. Time: 0:00:03 Points: 95   ⌟ # Computing specializations.. Time: 0:00:04 Points: 104   ⌞ # Computing specializations.. Time: 0:00:04 Points: 113   ⌜ # Computing specializations.. Time: 0:00:04 Points: 122   ⌝ # Computing specializations.. Time: 0:00:05 Points: 132   ⌟ # Computing specializations.. Time: 0:00:05 Points: 141   ⌞ # Computing specializations.. Time: 0:00:05 Points: 150   ⌜ # Computing specializations.. Time: 0:00:06 Points: 160   ⌝ # Computing specializations.. Time: 0:00:06 Points: 168   ⌟ # Computing specializations.. Time: 0:00:07 Points: 179   ⌞ # Computing specializations.. Time: 0:00:07 Points: 189   ⌜ # Computing specializations.. Time: 0:00:07 Points: 200   ⌝ # Computing specializations.. Time: 0:00:08 Points: 210   ⌟ # Computing specializations.. Time: 0:00:08 Points: 221   ⌞ # Computing specializations.. Time: 0:00:08 Points: 231   ⌜ # Computing specializations.. Time: 0:00:09 Points: 240   ⌝ # Computing specializations.. Time: 0:00:09 Points: 249   ⌟ # Computing specializations.. Time: 0:00:10 Points: 258   ⌞ # Computing specializations.. Time: 0:00:10 Points: 268   ⌜ # Computing specializations.. Time: 0:00:10 Points: 278   ⌝ # Computing specializations.. Time: 0:00:11 Points: 289   ⌟ # Computing specializations.. Time: 0:00:11 Points: 298   ⌞ # Computing specializations.. Time: 0:00:11 Points: 309   ⌜ # Computing specializations.. Time: 0:00:12 Points: 319   ⌝ # Computing specializations.. Time: 0:00:12 Points: 328   ⌟ # Computing specializations.. Time: 0:00:13 Points: 338   ⌞ # Computing specializations.. Time: 0:00:13 Points: 346   ⌜ # Computing specializations.. Time: 0:00:13 Points: 357   ⌝ # Computing specializations.. Time: 0:00:14 Points: 367   ⌟ # Computing specializations.. Time: 0:00:14 Points: 378   ⌞ # Computing specializations.. Time: 0:00:15 Points: 388   ⌜ # Computing specializations.. Time: 0:00:15 Points: 399   ⌝ # Computing specializations.. Time: 0:00:15 Points: 409   ⌟ # Computing specializations.. Time: 0:00:16 Points: 418   ⌞ # Computing specializations.. Time: 0:00:16 Points: 428   ⌜ # Computing specializations.. Time: 0:00:16 Points: 436   ⌝ # Computing specializations.. Time: 0:00:17 Points: 446   ⌟ # Computing specializations.. Time: 0:00:17 Points: 456   ⌞ # Computing specializations.. Time: 0:00:17 Points: 468   ⌜ # Computing specializations.. Time: 0:00:18 Points: 479   ⌝ # Computing specializations.. Time: 0:00:18 Points: 491   ⌟ # Computing specializations.. Time: 0:00:19 Points: 503   ⌞ # Computing specializations.. Time: 0:00:19 Points: 516   ⌜ # Computing specializations.. Time: 0:00:19 Points: 528   ⌝ # Computing specializations.. Time: 0:00:20 Points: 538   ⌟ # Computing specializations.. Time: 0:00:20 Points: 548   ⌞ # Computing specializations.. Time: 0:00:21 Points: 559   ⌜ # Computing specializations.. Time: 0:00:21 Points: 570   ⌝ # Computing specializations.. Time: 0:00:21 Points: 582   ⌟ # Computing specializations.. Time: 0:00:22 Points: 593   ⌞ # Computing specializations.. Time: 0:00:22 Points: 604   ⌜ # Computing specializations.. Time: 0:00:22 Points: 614   ⌝ # Computing specializations.. Time: 0:00:23 Points: 623   ⌟ # Computing specializations.. Time: 0:00:23 Points: 632   ✓ # Computing specializations.. Time: 0:00:24 [ Info: Search for polynomial generators concluded in 0.000281078 [ Info: Selecting generators in 0.036428221 [ Info: Inclusion checked with probability 0.995 in 8.967904975 seconds [ Info: The search for identifiable functions concluded in 55.027818007 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 1.999931002 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.053440609 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000112249 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 Points: 10   ⌝ # Computing specializations.. Time: 0:00:00 Points: 20   ⌟ # Computing specializations.. Time: 0:00:01 Points: 29   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 47   ⌝ # Computing specializations.. Time: 0:00:02 Points: 56   ⌟ # Computing specializations.. Time: 0:00:02 Points: 65   ⌞ # Computing specializations.. Time: 0:00:02 Points: 74   ⌜ # Computing specializations.. Time: 0:00:03 Points: 84   ⌝ # Computing specializations.. Time: 0:00:03 Points: 93   ✓ # Computing specializations.. Time: 0:00:03 ⌜ # 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 Points: 15   ⌟ # Computing specializations.. Time: 0:00:01 Points: 24   ⌞ # Computing specializations.. Time: 0:00:01 Points: 34   ⌜ # Computing specializations.. Time: 0:00:01 Points: 43   ⌝ # Computing specializations.. Time: 0:00:02 Points: 52   ⌟ # Computing specializations.. Time: 0:00:02 Points: 61   ⌞ # Computing specializations.. Time: 0:00:03 Points: 71   ⌜ # Computing specializations.. Time: 0:00:03 Points: 80   ⌝ # Computing specializations.. Time: 0:00:03 Points: 89   ⌟ # Computing specializations.. Time: 0:00:04 Points: 98   ⌞ # Computing specializations.. Time: 0:00:04 Points: 107   ⌜ # Computing specializations.. Time: 0:00:04 Points: 115   ⌝ # Computing specializations.. Time: 0:00:05 Points: 125   ⌟ # Computing specializations.. Time: 0:00:05 Points: 134   ⌞ # Computing specializations.. Time: 0:00:06 Points: 143   ⌜ # Computing specializations.. Time: 0:00:06 Points: 151   ⌝ # Computing specializations.. Time: 0:00:06 Points: 161   ⌟ # Computing specializations.. Time: 0:00:07 Points: 170   ⌞ # Computing specializations.. Time: 0:00:07 Points: 180   ⌜ # Computing specializations.. Time: 0:00:07 Points: 188   ⌝ # Computing specializations.. Time: 0:00:08 Points: 198   ⌟ # Computing specializations.. Time: 0:00:08 Points: 208   ⌞ # Computing specializations.. Time: 0:00:09 Points: 217   ⌜ # Computing specializations.. Time: 0:00:09 Points: 226   ⌝ # Computing specializations.. Time: 0:00:09 Points: 235   ⌟ # Computing specializations.. Time: 0:00:10 Points: 244   ⌞ # Computing specializations.. Time: 0:00:10 Points: 254   ⌜ # Computing specializations.. Time: 0:00:11 Points: 262   ⌝ # Computing specializations.. Time: 0:00:11 Points: 272   ⌟ # Computing specializations.. Time: 0:00:11 Points: 281   ⌞ # Computing specializations.. Time: 0:00:12 Points: 291   ⌜ # Computing specializations.. Time: 0:00:12 Points: 300   ⌝ # Computing specializations.. Time: 0:00:12 Points: 309   ⌟ # Computing specializations.. Time: 0:00:13 Points: 318   ⌞ # Computing specializations.. Time: 0:00:13 Points: 326   ⌜ # Computing specializations.. Time: 0:00:13 Points: 335   ⌝ # Computing specializations.. Time: 0:00:14 Points: 342   ⌟ # Computing specializations.. Time: 0:00:14 Points: 351   ⌞ # Computing specializations.. Time: 0:00:15 Points: 360   ⌜ # Computing specializations.. Time: 0:00:15 Points: 370   ⌝ # Computing specializations.. Time: 0:00:15 Points: 379   ⌟ # Computing specializations.. Time: 0:00:16 Points: 389   ⌞ # Computing specializations.. Time: 0:00:16 Points: 398   ⌜ # Computing specializations.. Time: 0:00:17 Points: 408   ⌝ # Computing specializations.. Time: 0:00:17 Points: 417   ⌟ # Computing specializations.. Time: 0:00:17 Points: 425   ⌞ # Computing specializations.. Time: 0:00:18 Points: 434   ⌜ # Computing specializations.. Time: 0:00:18 Points: 442   ⌝ # Computing specializations.. Time: 0:00:18 Points: 451   ⌟ # Computing specializations.. Time: 0:00:19 Points: 460   ⌞ # Computing specializations.. Time: 0:00:19 Points: 470   ⌜ # Computing specializations.. Time: 0:00:20 Points: 479   ⌝ # Computing specializations.. Time: 0:00:20 Points: 489   ⌟ # Computing specializations.. Time: 0:00:20 Points: 499   ⌞ # Computing specializations.. Time: 0:00:21 Points: 509   ⌜ # Computing specializations.. Time: 0:00:21 Points: 519   ⌝ # Computing specializations.. Time: 0:00:21 Points: 527   ⌟ # Computing specializations.. Time: 0:00:22 Points: 536   ⌞ # Computing specializations.. Time: 0:00:22 Points: 544   ⌜ # Computing specializations.. Time: 0:00:22 Points: 553   ⌝ # Computing specializations.. Time: 0:00:23 Points: 562   ⌟ # Computing specializations.. Time: 0:00:23 Points: 572   ⌞ # Computing specializations.. Time: 0:00:24 Points: 581   ⌜ # Computing specializations.. Time: 0:00:24 Points: 591   ⌝ # Computing specializations.. Time: 0:00:24 Points: 601   ⌟ # Computing specializations.. Time: 0:00:25 Points: 610   ⌞ # Computing specializations.. Time: 0:00:25 Points: 619   ⌜ # Computing specializations.. Time: 0:00:26 Points: 628   ⌝ # Computing specializations.. Time: 0:00:26 Points: 637   ✓ # Computing specializations.. Time: 0:00:27 [ Info: Search for polynomial generators concluded in 0.000357996 [ Info: Selecting generators in 0.056594867 [ Info: Inclusion checked with probability 0.995 in 8.432800996 seconds [ Info: The search for identifiable functions concluded in 62.617516631 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 2.611996377 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.077875572 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000138989 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: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 19   ⌟ # Computing specializations.. Time: 0:00:01 Points: 29   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 49   ⌝ # Computing specializations.. Time: 0:00:02 Points: 59   ⌟ # Computing specializations.. Time: 0:00:02 Points: 69   ⌞ # Computing specializations.. Time: 0:00:02 Points: 79   ⌜ # Computing specializations.. Time: 0:00:03 Points: 89   ✓ # Computing specializations.. Time: 0:00:03 ⌜ # 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: 10   ⌝ # Computing specializations.. Time: 0:00:00 Points: 17   ⌟ # Computing specializations.. Time: 0:00:00 Points: 28   ⌞ # Computing specializations.. Time: 0:00:01 Points: 38   ⌜ # Computing specializations.. Time: 0:00:01 Points: 48   ⌝ # Computing specializations.. Time: 0:00:02 Points: 58   ⌟ # Computing specializations.. Time: 0:00:02 Points: 68   ⌞ # Computing specializations.. Time: 0:00:02 Points: 78   ⌜ # Computing specializations.. Time: 0:00:03 Points: 89   ⌝ # Computing specializations.. Time: 0:00:03 Points: 99   ⌟ # Computing specializations.. Time: 0:00:04 Points: 110   ⌞ # Computing specializations.. Time: 0:00:04 Points: 121   ⌜ # Computing specializations.. Time: 0:00:04 Points: 132   ⌝ # Computing specializations.. Time: 0:00:05 Points: 142   ⌟ # Computing specializations.. Time: 0:00:05 Points: 153   ⌞ # Computing specializations.. Time: 0:00:05 Points: 162   ⌜ # Computing specializations.. Time: 0:00:06 Points: 174   ⌝ # Computing specializations.. Time: 0:00:06 Points: 185   ⌟ # Computing specializations.. Time: 0:00:07 Points: 196   ⌞ # Computing specializations.. Time: 0:00:07 Points: 206   ⌜ # Computing specializations.. Time: 0:00:07 Points: 217   ⌝ # Computing specializations.. Time: 0:00:08 Points: 226   ⌟ # Computing specializations.. Time: 0:00:08 Points: 236   ⌞ # Computing specializations.. Time: 0:00:09 Points: 246   ⌜ # Computing specializations.. Time: 0:00:09 Points: 258   ⌝ # Computing specializations.. Time: 0:00:09 Points: 269   ⌟ # Computing specializations.. Time: 0:00:10 Points: 280   ⌞ # Computing specializations.. Time: 0:00:10 Points: 290   ⌜ # Computing specializations.. Time: 0:00:10 Points: 301   ⌝ # Computing specializations.. Time: 0:00:11 Points: 311   ⌟ # Computing specializations.. Time: 0:00:11 Points: 323   ⌞ # Computing specializations.. Time: 0:00:12 Points: 333   ⌜ # Computing specializations.. Time: 0:00:12 Points: 345   ⌝ # Computing specializations.. Time: 0:00:13 Points: 356   ⌟ # Computing specializations.. Time: 0:00:13 Points: 367   ⌞ # Computing specializations.. Time: 0:00:13 Points: 376   ⌜ # Computing specializations.. Time: 0:00:14 Points: 387   ⌝ # Computing specializations.. Time: 0:00:14 Points: 398   ⌟ # Computing specializations.. Time: 0:00:14 Points: 410   ⌞ # Computing specializations.. Time: 0:00:15 Points: 421   ⌜ # Computing specializations.. Time: 0:00:15 Points: 433   ⌝ # Computing specializations.. Time: 0:00:16 Points: 444   ⌟ # Computing specializations.. Time: 0:00:16 Points: 455   ⌞ # Computing specializations.. Time: 0:00:16 Points: 465   ⌜ # Computing specializations.. Time: 0:00:17 Points: 476   ⌝ # Computing specializations.. Time: 0:00:17 Points: 486   ⌟ # Computing specializations.. Time: 0:00:17 Points: 496   ⌞ # Computing specializations.. Time: 0:00:18 Points: 506   ⌜ # Computing specializations.. Time: 0:00:18 Points: 515   ⌝ # Computing specializations.. Time: 0:00:18 Points: 525   ⌟ # Computing specializations.. Time: 0:00:19 Points: 533   ⌞ # Computing specializations.. Time: 0:00:19 Points: 545   ⌜ # Computing specializations.. Time: 0:00:20 Points: 556   ⌝ # Computing specializations.. Time: 0:00:20 Points: 567   ⌟ # Computing specializations.. Time: 0:00:20 Points: 577   ⌞ # Computing specializations.. Time: 0:00:21 Points: 588   ⌜ # Computing specializations.. Time: 0:00:21 Points: 598   ⌝ # Computing specializations.. Time: 0:00:21 Points: 607   ⌟ # Computing specializations.. Time: 0:00:22 Points: 617   ⌞ # Computing specializations.. Time: 0:00:22 Points: 625   ⌜ # Computing specializations.. Time: 0:00:22 Points: 635   ✓ # Computing specializations.. Time: 0:00:23 [ Info: Search for polynomial generators concluded in 2.06917668 [ Info: Selecting generators in 0.034306563 [ Info: Inclusion checked with probability 0.995 in 8.304534915 seconds [ Info: The search for identifiable functions concluded in 54.032945079 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 2.390299553 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.073561806 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000123099 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: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 18   ⌟ # Computing specializations.. Time: 0:00:01 Points: 28   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 49   ⌝ # Computing specializations.. Time: 0:00:02 Points: 60   ⌟ # Computing specializations.. Time: 0:00:02 Points: 70   ⌞ # Computing specializations.. Time: 0:00:02 Points: 80   ⌜ # Computing specializations.. Time: 0:00:03 Points: 90   ✓ # Computing specializations.. Time: 0:00:03 ⌜ # 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: 8   ⌝ # Computing specializations.. Time: 0:00:00 Points: 18   ⌟ # Computing specializations.. Time: 0:00:01 Points: 28   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 49   ⌝ # Computing specializations.. Time: 0:00:02 Points: 60   ⌟ # Computing specializations.. Time: 0:00:02 Points: 70   ⌞ # Computing specializations.. Time: 0:00:03 Points: 80   ⌜ # Computing specializations.. Time: 0:00:03 Points: 90   ⌝ # Computing specializations.. Time: 0:00:03 Points: 101   ⌟ # Computing specializations.. Time: 0:00:04 Points: 111   ⌞ # Computing specializations.. Time: 0:00:04 Points: 121   ⌜ # Computing specializations.. Time: 0:00:05 Points: 131   ⌝ # Computing specializations.. Time: 0:00:05 Points: 142   ⌟ # Computing specializations.. Time: 0:00:05 Points: 152   ⌞ # Computing specializations.. Time: 0:00:06 Points: 162   ⌜ # Computing specializations.. Time: 0:00:06 Points: 171   ⌝ # Computing specializations.. Time: 0:00:06 Points: 180   ⌟ # Computing specializations.. Time: 0:00:07 Points: 190   ⌞ # Computing specializations.. Time: 0:00:07 Points: 198   ⌜ # Computing specializations.. Time: 0:00:07 Points: 208   ⌝ # Computing specializations.. Time: 0:00:08 Points: 216   ⌟ # Computing specializations.. Time: 0:00:08 Points: 226   ⌞ # Computing specializations.. Time: 0:00:09 Points: 236   ⌜ # Computing specializations.. Time: 0:00:09 Points: 246   ⌝ # Computing specializations.. Time: 0:00:09 Points: 255   ⌟ # Computing specializations.. Time: 0:00:10 Points: 264   ⌞ # Computing specializations.. Time: 0:00:10 Points: 274   ⌜ # Computing specializations.. Time: 0:00:10 Points: 282   ⌝ # Computing specializations.. Time: 0:00:11 Points: 292   ⌟ # Computing specializations.. Time: 0:00:11 Points: 302   ⌞ # Computing specializations.. Time: 0:00:12 Points: 313   ⌜ # Computing specializations.. Time: 0:00:12 Points: 323   ⌝ # Computing specializations.. Time: 0:00:12 Points: 332   ⌟ # Computing specializations.. Time: 0:00:13 Points: 342   ⌞ # Computing specializations.. Time: 0:00:13 Points: 352   ⌜ # Computing specializations.. Time: 0:00:13 Points: 362   ⌝ # Computing specializations.. Time: 0:00:14 Points: 370   ⌟ # Computing specializations.. Time: 0:00:14 Points: 380   ⌞ # Computing specializations.. Time: 0:00:15 Points: 390   ⌜ # Computing specializations.. Time: 0:00:15 Points: 400   ⌝ # Computing specializations.. Time: 0:00:15 Points: 410   ⌟ # Computing specializations.. Time: 0:00:16 Points: 420   ⌞ # Computing specializations.. Time: 0:00:16 Points: 430   ⌜ # Computing specializations.. Time: 0:00:16 Points: 438   ⌝ # Computing specializations.. Time: 0:00:17 Points: 448   ⌟ # Computing specializations.. Time: 0:00:17 Points: 458   ⌞ # Computing specializations.. Time: 0:00:17 Points: 469   ⌜ # Computing specializations.. Time: 0:00:18 Points: 479   ⌝ # Computing specializations.. Time: 0:00:18 Points: 488   ⌟ # Computing specializations.. Time: 0:00:18 Points: 498   ⌞ # Computing specializations.. Time: 0:00:19 Points: 507   ⌜ # Computing specializations.. Time: 0:00:19 Points: 517   ⌝ # Computing specializations.. Time: 0:00:20 Points: 527   ⌟ # Computing specializations.. Time: 0:00:20 Points: 537   ⌞ # Computing specializations.. Time: 0:00:20 Points: 547   ⌜ # Computing specializations.. Time: 0:00:21 Points: 558   ⌝ # Computing specializations.. Time: 0:00:21 Points: 567   ⌟ # Computing specializations.. Time: 0:00:21 Points: 578   ⌞ # Computing specializations.. Time: 0:00:22 Points: 588   ⌜ # Computing specializations.. Time: 0:00:22 Points: 599   ⌝ # Computing specializations.. Time: 0:00:23 Points: 608   ⌟ # Computing specializations.. Time: 0:00:23 Points: 619   ⌞ # Computing specializations.. Time: 0:00:23 Points: 629   ⌜ # Computing specializations.. Time: 0:00:24 Points: 638   ✓ # Computing specializations.. Time: 0:00:24 [ Info: Search for polynomial generators concluded in 2.679684516 [ Info: Selecting generators in 0.034423172 [ Info: Inclusion checked with probability 0.995 in 8.252495642 seconds [ Info: The search for identifiable functions concluded in 55.63654154 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 2.473396364 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.072097801 seconds [ Info: Dimensions of the Wronskians [34, 2] [ Info: Ranks of the Wronskians computed in 0.000122628 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: 7   ⌝ # Computing specializations.. Time: 0:00:00 Points: 17   ⌟ # Computing specializations.. Time: 0:00:01 Points: 26   ⌞ # Computing specializations.. Time: 0:00:01 Points: 35   ⌜ # Computing specializations.. Time: 0:00:01 Points: 44   ⌝ # Computing specializations.. Time: 0:00:02 Points: 54   ⌟ # Computing specializations.. Time: 0:00:02 Points: 63   ⌞ # Computing specializations.. Time: 0:00:03 Points: 73   ⌜ # Computing specializations.. Time: 0:00:03 Points: 82   ⌝ # Computing specializations.. Time: 0:00:03 Points: 92   ✓ # Computing specializations.. Time: 0:00:04 ⌜ # 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: 10   ⌝ # Computing specializations.. Time: 0:00:00 Points: 19   ⌟ # Computing specializations.. Time: 0:00:01 Points: 29   ⌞ # Computing specializations.. Time: 0:00:01 Points: 39   ⌜ # Computing specializations.. Time: 0:00:01 Points: 49   ⌝ # Computing specializations.. Time: 0:00:02 Points: 58   ⌟ # Computing specializations.. Time: 0:00:02 Points: 68   ⌞ # Computing specializations.. Time: 0:00:02 Points: 77   ⌜ # Computing specializations.. Time: 0:00:03 Points: 87   ⌝ # Computing specializations.. Time: 0:00:03 Points: 95   ⌟ # Computing specializations.. Time: 0:00:03 Points: 104   ⌞ # Computing specializations.. Time: 0:00:04 Points: 113   ⌜ # Computing specializations.. Time: 0:00:04 Points: 123   ⌝ # Computing specializations.. Time: 0:00:05 Points: 131   ⌟ # Computing specializations.. Time: 0:00:05 Points: 141   ⌞ # Computing specializations.. Time: 0:00:05 Points: 151   ⌜ # Computing specializations.. Time: 0:00:06 Points: 160   ⌝ # Computing specializations.. Time: 0:00:06 Points: 169   ⌟ # Computing specializations.. Time: 0:00:06 Points: 179   ⌞ # Computing specializations.. Time: 0:00:07 Points: 188   ⌜ # Computing specializations.. Time: 0:00:07 Points: 197   ⌝ # Computing specializations.. Time: 0:00:08 Points: 206   ⌟ # Computing specializations.. Time: 0:00:08 Points: 216   ⌞ # Computing specializations.. Time: 0:00:08 Points: 225   ⌜ # Computing specializations.. Time: 0:00:09 Points: 233   ⌝ # Computing specializations.. Time: 0:00:09 Points: 242   ⌟ # Computing specializations.. Time: 0:00:09 Points: 249   ⌞ # Computing specializations.. Time: 0:00:10 Points: 258   ⌜ # Computing specializations.. Time: 0:00:10 Points: 267   ⌝ # Computing specializations.. Time: 0:00:11 Points: 276   ⌟ # Computing specializations.. Time: 0:00:11 Points: 285   ⌞ # Computing specializations.. Time: 0:00:11 Points: 293   ⌜ # Computing specializations.. Time: 0:00:12 Points: 301   ⌝ # Computing specializations.. Time: 0:00:12 Points: 309   ⌟ # Computing specializations.. Time: 0:00:12 Points: 318   ⌞ # Computing specializations.. Time: 0:00:13 Points: 326   ⌜ # Computing specializations.. Time: 0:00:13 Points: 336   ⌝ # Computing specializations.. Time: 0:00:14 Points: 345   ⌟ # Computing specializations.. Time: 0:00:14 Points: 355   ⌞ # Computing specializations.. Time: 0:00:14 Points: 364   ⌜ # Computing specializations.. Time: 0:00:15 Points: 372   ⌝ # Computing specializations.. Time: 0:00:15 Points: 381   ⌟ # Computing specializations.. Time: 0:00:16 Points: 388   ⌞ # Computing specializations.. Time: 0:00:16 Points: 397   ⌜ # Computing specializations.. Time: 0:00:16 Points: 406   ⌝ # Computing specializations.. Time: 0:00:17 Points: 416   ⌟ # Computing specializations.. Time: 0:00:17 Points: 425   ⌞ # Computing specializations.. Time: 0:00:17 Points: 433   ⌜ # Computing specializations.. Time: 0:00:18 Points: 442   ⌝ # Computing specializations.. Time: 0:00:18 Points: 451   ⌟ # Computing specializations.. Time: 0:00:18 Points: 460   ⌞ # Computing specializations.. Time: 0:00:19 Points: 468   ⌜ # Computing specializations.. Time: 0:00:19 Points: 478   ⌝ # Computing specializations.. Time: 0:00:20 Points: 488   ⌟ # Computing specializations.. Time: 0:00:20 Points: 498   ⌞ # Computing specializations.. Time: 0:00:21 Points: 507   ⌜ # Computing specializations.. Time: 0:00:21 Points: 517   ⌝ # Computing specializations.. Time: 0:00:21 Points: 526   ⌟ # Computing specializations.. Time: 0:00:22 Points: 534   ⌞ # Computing specializations.. Time: 0:00:22 Points: 543   ⌜ # Computing specializations.. Time: 0:00:22 Points: 552   ⌝ # Computing specializations.. Time: 0:00:23 Points: 562   ⌟ # Computing specializations.. Time: 0:00:23 Points: 570   ⌞ # Computing specializations.. Time: 0:00:23 Points: 580   ⌜ # Computing specializations.. Time: 0:00:24 Points: 589   ⌝ # Computing specializations.. Time: 0:00:24 Points: 599   ⌟ # Computing specializations.. Time: 0:00:25 Points: 608   ⌞ # Computing specializations.. Time: 0:00:25 Points: 618   ⌜ # Computing specializations.. Time: 0:00:25 Points: 627   ⌝ # Computing specializations.. Time: 0:00:26 Points: 637   ✓ # Computing specializations.. Time: 0:00:26 [ Info: Search for polynomial generators concluded in 1.348690196 [ Info: Selecting generators in 0.047545629 [ Info: Inclusion checked with probability 0.995 in 7.964795552 seconds [ Info: The search for identifiable functions concluded in 57.462570442 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 0.002733822 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.5549e-5 [ Info: Selecting generators in 0.000165298 [ Info: Inclusion checked with probability 0.995 in 0.001472075 seconds [ Info: The search for identifiable functions concluded in 0.029934297 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 0.001175818 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000109719 [ Info: Selecting generators in 0.000142508 [ Info: Inclusion checked with probability 0.995 in 0.001257857 seconds [ Info: The search for identifiable functions concluded in 0.007162478 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 0.001577925 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.413e-5 [ Info: Selecting generators in 0.000163448 [ Info: Inclusion checked with probability 0.995 in 0.001241177 seconds [ Info: The search for identifiable functions concluded in 0.007263537 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 0.001499545 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000754163 [ Info: Selecting generators in 0.000175778 [ Info: Inclusion checked with probability 0.995 in 0.001476015 seconds [ Info: The search for identifiable functions concluded in 0.010049078 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 0.001255597 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000469205 [ Info: Selecting generators in 0.000187338 [ Info: Inclusion checked with probability 0.995 in 0.001377376 seconds [ Info: The search for identifiable functions concluded in 0.008070719 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 0.001148468 seconds [ Info: No parameters, so Wronskian computation is not needed [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000505345 [ Info: Selecting generators in 0.000175468 [ Info: Inclusion checked with probability 0.995 in 0.001433505 seconds [ Info: The search for identifiable functions concluded in 0.00796469 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 0.001559804 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001741533 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 2.682e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000501155 [ Info: Selecting generators in 0.000668743 [ Info: Inclusion checked with probability 0.995 in 0.001164509 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.7199e-5 [ Info: Selecting generators in 0.000437206 [ Info: Inclusion checked with probability 0.995 in 0.002076769 seconds [ Info: The search for identifiable functions concluded in 0.023102706 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 0.001271107 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00099393 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.69e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000435066 [ Info: Selecting generators in 0.000599084 [ Info: Inclusion checked with probability 0.995 in 0.001107009 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.6169e-5 [ Info: Selecting generators in 0.000416296 [ Info: Inclusion checked with probability 0.995 in 0.00198594 seconds [ Info: The search for identifiable functions concluded in 0.015907179 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 0.001177838 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00104628 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.627e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000466495 [ Info: Selecting generators in 0.000657803 [ Info: Inclusion checked with probability 0.995 in 0.001126578 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.1429e-5 [ Info: Selecting generators in 0.000444616 [ Info: Inclusion checked with probability 0.995 in 0.001945001 seconds [ Info: The search for identifiable functions concluded in 0.015953999 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 0.001162548 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00099038 seconds [ Info: Dimensions of the Wronskians [2] [ 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 0.000413216 [ Info: Selecting generators in 0.000626943 [ Info: Inclusion checked with probability 0.995 in 0.001073689 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.224338822 [ Info: Selecting generators in 0.000550024 [ Info: Inclusion checked with probability 0.995 in 0.001584764 seconds [ Info: The search for identifiable functions concluded in 0.239467359 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 0.00093787 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000826382 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.372e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000358666 [ Info: Selecting generators in 0.000486365 [ Info: Inclusion checked with probability 0.995 in 0.000890941 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000515605 [ Info: Selecting generators in 0.000361347 [ Info: Inclusion checked with probability 0.995 in 0.001495045 seconds [ Info: The search for identifiable functions concluded in 0.01283521 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 0.000931081 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000807082 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.3179e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000349597 [ Info: Selecting generators in 0.000463076 [ Info: Inclusion checked with probability 0.995 in 0.000881602 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000504085 [ Info: Selecting generators in 0.000369646 [ Info: Inclusion checked with probability 0.995 in 0.001463075 seconds [ Info: The search for identifiable functions concluded in 0.012667072 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 0.001878401 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001488685 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.266e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005404686 [ Info: Selecting generators in 0.001860341 [ Info: Inclusion checked with probability 0.995 in 0.002235207 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000108669 [ Info: Selecting generators in 0.002554224 [ Info: Inclusion checked with probability 0.995 in 0.003597693 seconds [ Info: The search for identifiable functions concluded in 0.03555406 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 0.001719832 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001416966 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.2919e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005076309 [ Info: Selecting generators in 0.001609144 [ Info: Inclusion checked with probability 0.995 in 0.002131018 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000104339 [ Info: Selecting generators in 0.002404196 [ Info: Inclusion checked with probability 0.995 in 0.003740423 seconds [ Info: The search for identifiable functions concluded in 0.033864957 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 0.001756412 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001373867 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.269e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005359176 [ Info: Selecting generators in 0.001660714 [ Info: Inclusion checked with probability 0.995 in 0.002092839 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000103739 [ Info: Selecting generators in 0.002370166 [ Info: Inclusion checked with probability 0.995 in 0.003539104 seconds [ Info: The search for identifiable functions concluded in 0.033445652 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 0.001743112 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001420095 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.38e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005499984 [ Info: Selecting generators in 0.001709192 [ Info: Inclusion checked with probability 0.995 in 0.002140868 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.017934639 [ Info: Selecting generators in 0.002448415 [ Info: Inclusion checked with probability 0.995 in 0.003461445 seconds [ Info: The search for identifiable functions concluded in 0.052147462 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 0.001722792 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001507755 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.354e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00494477 [ Info: Selecting generators in 0.001629833 [ Info: Inclusion checked with probability 0.995 in 0.002056719 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.019081188 [ Info: Selecting generators in 0.003143998 [ Info: Inclusion checked with probability 0.995 in 0.003850521 seconds [ Info: The search for identifiable functions concluded in 0.05346916 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 0.002116738 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00196237 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.341e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00588544 [ Info: Selecting generators in 0.00196889 [ Info: Inclusion checked with probability 0.995 in 0.002427975 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020633242 [ Info: Selecting generators in 0.00300138 [ Info: Inclusion checked with probability 0.995 in 0.004136588 seconds [ Info: The search for identifiable functions concluded in 0.06133536 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 0.002043499 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001752372 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.328e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005910691 [ Info: Selecting generators in 0.00194529 [ Info: Inclusion checked with probability 0.995 in 0.002444375 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000115409 [ Info: Selecting generators in 0.002829312 [ Info: Inclusion checked with probability 0.995 in 0.00400151 seconds [ Info: The search for identifiable functions concluded in 0.03962638 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 0.00197389 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001613333 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.308e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005628683 [ Info: Selecting generators in 0.001872311 [ Info: Inclusion checked with probability 0.995 in 0.002401426 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000113779 [ Info: Selecting generators in 0.002807711 [ Info: Inclusion checked with probability 0.995 in 0.003940871 seconds [ Info: The search for identifiable functions concluded in 0.038126474 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 0.00198006 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001625003 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.378e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00596315 [ Info: Selecting generators in 0.001890301 [ Info: Inclusion checked with probability 0.995 in 0.002321217 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000111809 [ Info: Selecting generators in 0.002752542 [ Info: Inclusion checked with probability 0.995 in 0.00397279 seconds [ Info: The search for identifiable functions concluded in 0.038655779 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 0.00199232 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001705723 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.285e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006082478 [ Info: Selecting generators in 0.001879911 [ Info: Inclusion checked with probability 0.995 in 0.002324626 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.01984326 [ Info: Selecting generators in 0.003129179 [ Info: Inclusion checked with probability 0.995 in 0.003854751 seconds [ Info: The search for identifiable functions concluded in 0.058299311 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 0.00197739 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001643913 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.2699e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00589605 [ Info: Selecting generators in 0.001898951 [ Info: Inclusion checked with probability 0.995 in 0.002275327 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020410053 [ Info: Selecting generators in 0.002839681 [ Info: Inclusion checked with probability 0.995 in 0.003807932 seconds [ Info: The search for identifiable functions concluded in 0.058074823 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 0.00197544 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001646014 seconds [ Info: Dimensions of the Wronskians [5] [ Info: Ranks of the Wronskians computed in 1.279e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006131768 [ Info: Selecting generators in 0.00188737 [ Info: Inclusion checked with probability 0.995 in 0.002361176 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.020144037 [ Info: Selecting generators in 0.002867671 [ Info: Inclusion checked with probability 0.995 in 0.0039812 seconds [ Info: The search for identifiable functions concluded in 0.058403089 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 0.005836171 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004533114 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.067e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001742442 [ Info: Selecting generators in 0.007790101 [ Info: Inclusion checked with probability 0.995 in 0.004367496 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000141288 [ Info: Selecting generators in 0.010040239 [ Info: Inclusion checked with probability 0.995 in 0.007790272 seconds [ Info: The search for identifiable functions concluded in 0.294718061 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 0.005786682 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004388056 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.0079e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001694593 [ Info: Selecting generators in 0.007838811 [ Info: Inclusion checked with probability 0.995 in 0.004504794 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000146839 [ Info: Selecting generators in 0.010126278 [ Info: Inclusion checked with probability 0.995 in 0.007936299 seconds [ Info: The search for identifiable functions concluded in 0.086029751 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 0.00587863 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.004576263 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.158e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.001815302 [ Info: Selecting generators in 0.00790283 [ Info: Inclusion checked with probability 0.995 in 0.004618534 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000142788 [ Info: Selecting generators in 0.010457184 [ Info: Inclusion checked with probability 0.995 in 0.51437861 seconds [ Info: The search for identifiable functions concluded in 0.594928366 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 0.007697192 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.00600187 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 3.592e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002339696 [ Info: Selecting generators in 0.007516274 [ Info: Inclusion checked with probability 0.995 in 0.00397474 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.003436075 [ Info: Selecting generators in 0.009592583 [ Info: Inclusion checked with probability 0.995 in 0.007090728 seconds [ Info: The search for identifiable functions concluded in 0.097494115 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 0.005236447 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003686113 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.194e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002167508 [ Info: Selecting generators in 0.010380715 [ Info: Inclusion checked with probability 0.995 in 0.005442265 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004676152 [ Info: Selecting generators in 0.011037739 [ Info: Inclusion checked with probability 0.995 in 0.007031049 seconds [ Info: The search for identifiable functions concluded in 0.09301736 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 0.005244007 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003634803 seconds [ Info: Dimensions of the Wronskians [13] [ Info: Ranks of the Wronskians computed in 2.071e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002052799 [ Info: Selecting generators in 0.006689912 [ Info: Inclusion checked with probability 0.995 in 0.003845331 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004904841 [ Info: Selecting generators in 0.013476094 [ Info: Inclusion checked with probability 0.995 in 0.007157348 seconds [ Info: The search for identifiable functions concluded in 0.09598018 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 0.001342666 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000886511 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.193e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.271e-5 [ Info: Selecting generators in 0.000357587 [ Info: Inclusion checked with probability 0.995 in 0.001688063 seconds [ Info: The search for identifiable functions concluded in 0.009628743 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 0.001389026 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000941931 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.2539e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 7.4489e-5 [ Info: Selecting generators in 0.000379836 [ Info: Inclusion checked with probability 0.995 in 0.001716293 seconds [ Info: The search for identifiable functions concluded in 0.009365485 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 0.001672043 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001187908 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.566e-5 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 6.6849e-5 [ Info: Selecting generators in 0.000376346 [ Info: Inclusion checked with probability 0.995 in 0.001589834 seconds [ Info: The search for identifiable functions concluded in 0.009799421 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 0.001298817 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000830881 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.155e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.0049106 [ Info: Selecting generators in 0.000441126 [ Info: Inclusion checked with probability 0.995 in 0.001700472 seconds [ Info: The search for identifiable functions concluded in 0.013763551 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 0.001327647 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000836241 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 2.898e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004504995 [ Info: Selecting generators in 0.000460645 [ Info: Inclusion checked with probability 0.995 in 0.001781112 seconds [ Info: The search for identifiable functions concluded in 0.013528074 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 0.001466325 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.000872311 seconds [ Info: Dimensions of the Wronskians [1] [ Info: Ranks of the Wronskians computed in 1.141e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.004189238 [ Info: Selecting generators in 0.000602764 [ Info: Inclusion checked with probability 0.995 in 0.002282937 seconds [ Info: The search for identifiable functions concluded in 0.014133447 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 0.002371656 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001528355 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.253e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.00199882 [ Info: Selecting generators in 0.000589055 [ Info: Inclusion checked with probability 0.995 in 0.001236988 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.3849e-5 [ Info: Selecting generators in 0.003465995 [ Info: Inclusion checked with probability 0.995 in 0.002574294 seconds [ Info: The search for identifiable functions concluded in 0.025461012 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 0.002285147 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001503945 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.252e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002804781 [ Info: Selecting generators in 0.000878671 [ Info: Inclusion checked with probability 0.995 in 0.001701653 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000128868 [ Info: Selecting generators in 0.004691952 [ Info: Inclusion checked with probability 0.995 in 0.003540614 seconds [ Info: The search for identifiable functions concluded in 0.033000836 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 0.003047739 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002104458 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.78e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002686823 [ Info: Selecting generators in 0.000764282 [ Info: Inclusion checked with probability 0.995 in 0.001717393 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000108959 [ Info: Selecting generators in 0.00502567 [ Info: Inclusion checked with probability 0.995 in 0.003510254 seconds [ Info: The search for identifiable functions concluded in 0.034092835 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 0.003212407 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002091909 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.8369e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002595654 [ Info: Selecting generators in 0.000881341 [ Info: Inclusion checked with probability 0.995 in 0.001676523 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.027751489 [ Info: Selecting generators in 0.005092068 [ Info: Inclusion checked with probability 0.995 in 0.003583664 seconds [ Info: The search for identifiable functions concluded in 0.062577007 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 0.003190268 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002090389 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.557e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002599864 [ Info: Selecting generators in 0.000898661 [ Info: Inclusion checked with probability 0.995 in 0.001648434 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.026797609 [ Info: Selecting generators in 0.004883121 [ Info: Inclusion checked with probability 0.995 in 0.003465065 seconds [ Info: The search for identifiable functions concluded in 0.060485129 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 0.003165128 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.002050219 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.601e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.002711282 [ Info: Selecting generators in 0.000883091 [ Info: Inclusion checked with probability 0.995 in 0.001721742 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.032544561 [ Info: Selecting generators in 0.006085388 [ Info: Inclusion checked with probability 0.995 in 0.004096689 seconds [ Info: The search for identifiable functions concluded in 0.069147491 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 0.002374096 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001564824 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.43e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000495605 [ Info: Selecting generators in 0.000720273 [ Info: Inclusion checked with probability 0.995 in 0.001247158 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000105519 [ Info: Selecting generators in 0.001614783 [ Info: Inclusion checked with probability 0.995 in 0.002613004 seconds [ Info: The search for identifiable functions concluded in 0.023112706 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 0.002274187 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001470215 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.717e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000462045 [ Info: Selecting generators in 0.000731943 [ Info: Inclusion checked with probability 0.995 in 0.001216067 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000108129 [ Info: Selecting generators in 0.001519094 [ Info: Inclusion checked with probability 0.995 in 0.002551614 seconds [ Info: The search for identifiable functions concluded in 0.022328414 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 0.002171778 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001377737 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.579e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000415266 [ Info: Selecting generators in 0.000651633 [ Info: Inclusion checked with probability 0.995 in 0.001170518 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 9.4279e-5 [ Info: Selecting generators in 0.001479385 [ Info: Inclusion checked with probability 0.995 in 0.002516764 seconds [ Info: The search for identifiable functions concluded in 0.021203176 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 0.002183758 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001377586 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.6089e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000463015 [ Info: Selecting generators in 0.000698183 [ Info: Inclusion checked with probability 0.995 in 0.001179488 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006313877 [ Info: Selecting generators in 0.001793841 [ Info: Inclusion checked with probability 0.995 in 0.002597113 seconds [ Info: The search for identifiable functions concluded in 0.028084066 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 0.002226448 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001463715 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.655e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000472476 [ Info: Selecting generators in 0.000745192 [ Info: Inclusion checked with probability 0.995 in 0.001261997 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006420335 [ Info: Selecting generators in 0.001727253 [ Info: Inclusion checked with probability 0.995 in 0.002490045 seconds [ Info: The search for identifiable functions concluded in 0.02865126 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 0.002296837 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001496875 seconds [ Info: Dimensions of the Wronskians [2] [ Info: Ranks of the Wronskians computed in 1.8e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.000474306 [ Info: Selecting generators in 0.000726163 [ Info: Inclusion checked with probability 0.995 in 0.001278037 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006374135 [ Info: Selecting generators in 0.001684403 [ Info: Inclusion checked with probability 0.995 in 0.002522155 seconds [ Info: The search for identifiable functions concluded in 0.028923908 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 0.001444196 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001291877 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.9469e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006199588 [ Info: Selecting generators in 0.002513275 [ Info: Inclusion checked with probability 0.995 in 0.002534184 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000127338 [ Info: Selecting generators in 0.00292023 [ Info: Inclusion checked with probability 0.995 in 0.003603154 seconds [ Info: The search for identifiable functions concluded in 0.037861747 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 0.001475695 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001318226 seconds [ Info: Dimensions of the Wronskians [3] [ 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 0.006720962 [ Info: Selecting generators in 0.002724102 [ Info: Inclusion checked with probability 0.995 in 0.002646283 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000122268 [ Info: Selecting generators in 0.00295488 [ Info: Inclusion checked with probability 0.995 in 0.003627173 seconds [ Info: The search for identifiable functions concluded in 0.039280553 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 0.001507185 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001315067 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.969e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006005349 [ Info: Selecting generators in 0.002219248 [ Info: Inclusion checked with probability 0.995 in 0.002150338 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000131039 [ Info: Selecting generators in 0.002731723 [ Info: Inclusion checked with probability 0.995 in 0.003454595 seconds [ Info: The search for identifiable functions concluded in 0.036037986 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 0.001373077 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001184928 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.7999e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.005722452 [ Info: Selecting generators in 0.002265637 [ Info: Inclusion checked with probability 0.995 in 0.002147089 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016320035 [ Info: Selecting generators in 0.002765772 [ Info: Inclusion checked with probability 0.995 in 0.003381736 seconds [ Info: The search for identifiable functions concluded in 0.051231022 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 0.001365666 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001215477 seconds [ Info: Dimensions of the Wronskians [3] [ 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 0.00596461 [ Info: Selecting generators in 0.002373846 [ Info: Inclusion checked with probability 0.995 in 0.002334676 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016019808 [ Info: Selecting generators in 0.002889061 [ Info: Inclusion checked with probability 0.995 in 0.003442895 seconds [ Info: The search for identifiable functions concluded in 0.050950275 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 0.001398736 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.001222027 seconds [ Info: Dimensions of the Wronskians [3] [ Info: Ranks of the Wronskians computed in 1.8809e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.006057978 [ Info: Selecting generators in 0.002391106 [ Info: Inclusion checked with probability 0.995 in 0.002326707 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.016447424 [ Info: Selecting generators in 0.002723022 [ Info: Inclusion checked with probability 0.995 in 0.003141908 seconds [ Info: The search for identifiable functions concluded in 0.051659488 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 0.006277577 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005214807 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.14e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.013999258 [ Info: Selecting generators in 0.004796152 [ Info: Inclusion checked with probability 0.995 in 0.004432805 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000164858 [ Info: Selecting generators in 0.028796289 [ Info: Inclusion checked with probability 0.995 in 0.010205796 seconds [ Info: The search for identifiable functions concluded in 0.134490171 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 0.006177588 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005443405 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.284e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014112137 [ Info: Selecting generators in 0.005449095 [ Info: Inclusion checked with probability 0.995 in 0.004451535 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000183918 [ Info: Selecting generators in 0.030837018 [ Info: Inclusion checked with probability 0.995 in 0.010708502 seconds [ Info: The search for identifiable functions concluded in 0.139349491 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 0.006344576 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005548424 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.14e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014387594 [ Info: Selecting generators in 0.004828721 [ Info: Inclusion checked with probability 0.995 in 0.004528354 seconds [ Info: Simplifying generating set. Simplification level: weak [ Info: Search for polynomial generators concluded in 0.000209008 [ Info: Selecting generators in 0.030207125 [ Info: Inclusion checked with probability 0.995 in 0.010560803 seconds [ Info: The search for identifiable functions concluded in 0.141006904 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 0.006966359 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.005483175 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 2.2969e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.014752151 [ Info: Selecting generators in 0.004847301 [ Info: Inclusion checked with probability 0.995 in 0.004692142 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.912482096 [ Info: Selecting generators in 0.028097946 [ Info: Inclusion checked with probability 0.995 in 0.008660692 seconds [ Info: The search for identifiable functions concluded in 1.052765208 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 0.005036259 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003592134 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 1.669e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.009173517 [ Info: Selecting generators in 0.003135428 [ Info: Inclusion checked with probability 0.995 in 0.003006529 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.069414628 [ Info: Selecting generators in 0.019591692 [ Info: Inclusion checked with probability 0.995 in 0.006503195 seconds [ Info: The search for identifiable functions concluded in 0.159458648 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 0.00393967 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.003358966 seconds [ Info: Dimensions of the Wronskians [7] [ Info: Ranks of the Wronskians computed in 1.3299e-5 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.008960119 [ Info: Selecting generators in 0.003048279 [ Info: Inclusion checked with probability 0.995 in 0.002780222 seconds [ Info: Simplifying generating set. Simplification level: standard [ Info: Search for polynomial generators concluded in 0.07224887 [ Info: Selecting generators in 0.019893199 [ Info: Inclusion checked with probability 0.995 in 0.006354445 seconds [ Info: The search for identifiable functions concluded in 0.160501748 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 0.139715908 seconds [ Info: Computing Wronskians [ Info: Computed Wronskians in 0.301074777 seconds [ Info: Dimensions of the Wronskians [145, 18, 9] [ Info: Ranks of the Wronskians computed in 0.001699023 seconds [ Info: Simplifying generating set. Simplification level: standard ⌜ # Computing specializations.. Time: 0:00:05 ✓ # Computing specializations.. Time: 0:00:05 [ Info: Search for polynomial generators concluded in 9.517773321 [ Info: Selecting generators in 0.055794496 [ Info: Inclusion checked with probability 0.995 in 6.540557637 seconds [ Info: Simplifying generating set. Simplification level: weak ⌜ # Computing specializations.. Time: 0:00:16 ✓ # Computing specializations.. Time: 0:00:16 ====================================================================================== Information request received. A stacktrace will print followed by a 1.0 second profile. --trace-compile is enabled during profile collection. ====================================================================================== cmd: /opt/julia/bin/julia 51 running 1 of 1 signal (10): User defined signal 1 _ZN4llvm10SSAUpdater17AddAvailableValueEPNS_10BasicBlockEPNS_5ValueE at /opt/julia/bin/../lib/julia/libLLVM.so.20.1jl (unknown line) unknown function (ip: 0x4284676f) at (unknown file) unknown function (ip: (nil)) at (unknown file) ============================================================== Profile collected. A report will print at the next yield point. Disabling --trace-compile ============================================================== [ Info: Search for polynomial generators concluded in 0.000429275 [ Info: Selecting generators in 0.229715649 ====================================================================================== Information request received. A stacktrace will print followed by a 1.0 second profile. --trace-compile is enabled during profile collection. ====================================================================================== cmd: /opt/julia/bin/julia 1 running 0 of 1 signal (10): User defined signal 1 epoll_pwait at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) uv__io_poll at /workspace/srcdir/libuv/src/unix/linux.c:1404 uv_run at /workspace/srcdir/libuv/src/unix/core.c:430 ijl_task_get_next at /source/src/scheduler.c:457 wait at ./task.jl:1217 wait_forever at ./task.jl:1139 jfptr_wait_forever_53569.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:4116 [inlined] ijl_apply_generic at /source/src/gf.c:4313 jl_apply at /source/src/julia.h:2275 [inlined] start_task at /source/src/task.c:1281 unknown function (ip: (nil)) at (unknown file) ============================================================== Profile collected. A report will print at the next yield point. Disabling --trace-compile ============================================================== ┌ 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/v1.13/Profile/src/Profile.jl:1362 Overhead ╎ [+additional indent] Count File:Line Function ========================================================= Thread 1 (default) Task 0x00007a7b411e7850 Total snapshots: 436. Utilization: 0% ╎436 @Base/task.jl:1139 wait_forever() 435╎ 436 @Base/task.jl:1217 wait() [1] signal 15: Terminated in expression starting at /PkgEval.jl/scripts/evaluate.jl:210 epoll_pwait at /lib/x86_64-linux-gnu/libc.so.6 (unknown line) uv__io_poll at /workspace/srcdir/libuv/src/unix/linux.c:1404 uv_run at /workspace/srcdir/libuv/src/unix/core.c:430 ijl_task_get_next at /source/src/scheduler.c:457 wait at ./task.jl:1217 wait_forever at ./task.jl:1139 jfptr_wait_forever_53569.1 at /opt/julia/lib/julia/sys.so (unknown line) _jl_invoke at /source/src/gf.c:4116 [inlined] ijl_apply_generic at /source/src/gf.c:4313 jl_apply at /source/src/julia.h:2275 [inlined] start_task at /source/src/task.c:1281 unknown function (ip: (nil)) at (unknown file) Allocations: 23606437 (Pool: 23605798; Big: 639); GC: 20 [51] signal 15: Terminated in expression starting at /home/pkgeval/.julia/packages/StructuralIdentifiability/0tPYp/test/identifiable_functions.jl:1077 PkgEval terminated after 2727.15s: test duration exceeded the time limit