diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json
index fe6e7698..b971e79c 100644
--- a/dev/.documenter-siteinfo.json
+++ b/dev/.documenter-siteinfo.json
@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-09T22:11:41","documenter_version":"1.3.0"}}
\ No newline at end of file
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-18T22:36:54","documenter_version":"1.4.0"}}
\ No newline at end of file
diff --git a/dev/assets/Manifest.toml b/dev/assets/Manifest.toml
index a873cf29..e78747ec 100644
--- a/dev/assets/Manifest.toml
+++ b/dev/assets/Manifest.toml
@@ -16,9 +16,9 @@ version = "0.0.1"
 
 [[deps.AbstractAlgebra]]
 deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"]
-git-tree-sha1 = "e4eebce3c99ad5718d33a434874b82610d18e2b6"
+git-tree-sha1 = "20b4984a6fa7e22346b4f420125342142d367913"
 uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
-version = "0.40.7"
+version = "0.40.9"
 
 [[deps.AbstractTrees]]
 git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
@@ -106,9 +106,9 @@ version = "7.9.0"
 
 [[deps.ArrayLayouts]]
 deps = ["FillArrays", "LinearAlgebra"]
-git-tree-sha1 = "0330bc3e828a05d1073553fb56f9695d73077370"
+git-tree-sha1 = "33207a8be6267bc389d0701e97a9bce6a4de68eb"
 uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
-version = "1.9.1"
+version = "1.9.2"
 weakdeps = ["SparseArrays"]
 
     [deps.ArrayLayouts.extensions]
@@ -274,9 +274,9 @@ version = "1.16.0"
 
 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "0f4b5d62a88d8f59003e43c25a8a90de9eb76317"
+git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
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@@ -289,9 +289,9 @@ uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
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-git-tree-sha1 = "4fa023dbb15b3485426bbc6c43e030c14250d664"
+git-tree-sha1 = "531c53fd0405716712a8b4960216c3b7b5ec89b9"
 uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
-version = "6.149.0"
+version = "6.149.1"
 
     [deps.DiffEqBase.extensions]
     DiffEqBaseChainRulesCoreExt = "ChainRulesCore"
@@ -319,9 +319,9 @@ version = "6.149.0"
 
 [[deps.DiffEqCallbacks]]
 deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "Functors", "LinearAlgebra", "Markdown", "NonlinearSolve", "Parameters", "RecipesBase", "RecursiveArrayTools", "SciMLBase", "StaticArraysCore"]
-git-tree-sha1 = "2df0433103c89ee2dad56f4ef9c7755521464a39"
+git-tree-sha1 = "ec436ca77daad49b71147d873638c206543c2312"
 uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def"
-version = "3.5.0"
+version = "3.6.1"
 
     [deps.DiffEqCallbacks.weakdeps]
     OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
@@ -367,15 +367,15 @@ version = "0.9.3"
 
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-git-tree-sha1 = "4a40af50e8b24333b9ec6892546d9ca5724228eb"
+git-tree-sha1 = "f15a91e6e3919055efa4f206f942a73fedf5dfe6"
 uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-version = "1.3.0"
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 [[deps.DomainSets]]
 deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays"]
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+git-tree-sha1 = "a0c11553b6c58bfc0283d8279dd3798150b77ac5"
 uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
-version = "0.7.11"
+version = "0.7.12"
 
 [[deps.Downloads]]
 deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
@@ -390,9 +390,9 @@ version = "0.6.8"
 
 [[deps.DynamicPolynomials]]
 deps = ["Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Pkg", "Reexport", "Test"]
-git-tree-sha1 = "0bb0a6f812213ecc8fbbcf472f4a993036858971"
+git-tree-sha1 = "0c056035f7de73b203a5295a22137f96fc32ad46"
 uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
-version = "0.5.5"
+version = "0.5.6"
 
 [[deps.DynamicQuantities]]
 deps = ["Compat", "PackageExtensionCompat", "Tricks"]
@@ -488,9 +488,9 @@ version = "1.2.0"
 
 [[deps.FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "Setfield", "SparseArrays"]
-git-tree-sha1 = "bc0c5092d6caaea112d3c8e3b238d61563c58d5f"
+git-tree-sha1 = "2de436b72c3422940cbe1367611d137008af7ec3"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.23.0"
+version = "2.23.1"
 
     [deps.FiniteDiff.extensions]
     FiniteDiffBandedMatricesExt = "BandedMatrices"
@@ -721,9 +721,9 @@ version = "0.4.6"
 
 [[deps.Latexify]]
 deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
-git-tree-sha1 = "cad560042a7cc108f5a4c24ea1431a9221f22c1b"
+git-tree-sha1 = "e0b5cd21dc1b44ec6e64f351976f961e6f31d6c4"
 uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
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@@ -905,9 +905,9 @@ version = "0.1.2"
 
 [[deps.MatrixFactorizations]]
 deps = ["ArrayLayouts", "LinearAlgebra", "Printf", "Random"]
-git-tree-sha1 = "eecef9daff3b2b58cc666ee0c85d1b9889b6e98e"
+git-tree-sha1 = "6731e0574fa5ee21c02733e397beb133df90de35"
 uuid = "a3b82374-2e81-5b9e-98ce-41277c0e4c87"
-version = "2.1.2"
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 [[deps.MaybeInplace]]
 deps = ["ArrayInterface", "LinearAlgebra", "MacroTools", "SparseArrays"]
@@ -931,9 +931,9 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
 [[deps.ModelingToolkit]]
 deps = ["AbstractTrees", "ArrayInterface", "Combinatorics", "Compat", "ConstructionBase", "DataStructures", "DiffEqBase", "DiffEqCallbacks", "DiffRules", "Distributed", "Distributions", "DocStringExtensions", "DomainSets", "DynamicQuantities", "ExprTools", "FindFirstFunctions", "ForwardDiff", "FunctionWrappersWrappers", "Graphs", "InteractiveUtils", "JuliaFormatter", "JumpProcesses", "LabelledArrays", "Latexify", "Libdl", "LinearAlgebra", "MLStyle", "NaNMath", "OrdinaryDiffEq", "PrecompileTools", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "SciMLStructures", "Serialization", "Setfield", "SimpleNonlinearSolve", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "SymbolicUtils", "Symbolics", "URIs", "UnPack", "Unitful"]
-git-tree-sha1 = "89c783f325e131233928bf108e17b75a8ec34857"
+git-tree-sha1 = "43f984aae6f3d2bee9832f14da78eb965f6765e8"
 uuid = "961ee093-0014-501f-94e3-6117800e7a78"
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     [deps.ModelingToolkit.extensions]
     MTKBifurcationKitExt = "BifurcationKit"
@@ -960,9 +960,9 @@ version = "0.5.4"
 
 [[deps.MutableArithmetics]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "2d106538aebe1c165e16d277914e10c550e9d9b7"
+git-tree-sha1 = "c2e2d748aea87f006a87c1654878349baa04aaf0"
 uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
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+version = "1.4.3"
 
 [[deps.NLSolversBase]]
 deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
@@ -987,10 +987,10 @@ uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
 
 [[deps.NonlinearSolve]]
-deps = ["ADTypes", "ArrayInterface", "ConcreteStructs", "DiffEqBase", "FastBroadcast", "FastClosures", "FiniteDiff", "ForwardDiff", "LazyArrays", "LineSearches", "LinearAlgebra", "LinearSolve", "MaybeInplace", "PrecompileTools", "Preferences", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SimpleNonlinearSolve", "SparseArrays", "SparseDiffTools", "StaticArraysCore", "TimerOutputs"]
-git-tree-sha1 = "b9e12aa04c90a05d2aaded6f7c4d8b39e77751db"
+deps = ["ADTypes", "ArrayInterface", "ConcreteStructs", "DiffEqBase", "FastBroadcast", "FastClosures", "FiniteDiff", "ForwardDiff", "LazyArrays", "LineSearches", "LinearAlgebra", "LinearSolve", "MaybeInplace", "PrecompileTools", "Preferences", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SimpleNonlinearSolve", "SparseArrays", "SparseDiffTools", "StaticArraysCore", "SymbolicIndexingInterface", "TimerOutputs"]
+git-tree-sha1 = "4891b745bd621f88aac661f2504d014931b443ba"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-version = "3.9.1"
+version = "3.10.0"
 
     [deps.NonlinearSolve.extensions]
     NonlinearSolveBandedMatricesExt = "BandedMatrices"
@@ -1019,9 +1019,9 @@ version = "3.9.1"
     Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [[deps.OffsetArrays]]
-git-tree-sha1 = "6a731f2b5c03157418a20c12195eb4b74c8f8621"
+git-tree-sha1 = "e64b4f5ea6b7389f6f046d13d4896a8f9c1ba71e"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "1.13.0"
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 weakdeps = ["Adapt"]
 
     [deps.OffsetArrays.extensions]
@@ -1114,9 +1114,9 @@ version = "0.4.4"
 
 [[deps.Polyester]]
 deps = ["ArrayInterface", "BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "ManualMemory", "PolyesterWeave", "Requires", "Static", "StaticArrayInterface", "StrideArraysCore", "ThreadingUtilities"]
-git-tree-sha1 = "09f59c6dda37c7f73efddc5bdf6f92bc940eb484"
+git-tree-sha1 = "2ba5f33cbb51a85ef58a850749492b08f9bf2193"
 uuid = "f517fe37-dbe3-4b94-8317-1923a5111588"
-version = "0.7.12"
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 [[deps.PolyesterWeave]]
 deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"]
@@ -1126,9 +1126,9 @@ version = "0.2.1"
 
 [[deps.PreallocationTools]]
 deps = ["Adapt", "ArrayInterface", "ForwardDiff"]
-git-tree-sha1 = "b6665214f2d0739f2d09a17474dd443b9139784a"
+git-tree-sha1 = "a660e9daab5db07adf3dedfe09b435cc530d855e"
 uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
-version = "0.4.20"
+version = "0.4.21"
 
     [deps.PreallocationTools.extensions]
     PreallocationToolsReverseDiffExt = "ReverseDiff"
@@ -1232,9 +1232,9 @@ version = "3.13.0"
 
 [[deps.RecursiveFactorization]]
 deps = ["LinearAlgebra", "LoopVectorization", "Polyester", "PrecompileTools", "StrideArraysCore", "TriangularSolve"]
-git-tree-sha1 = "8bc86c78c7d8e2a5fe559e3721c0f9c9e303b2ed"
+git-tree-sha1 = "6db1a75507051bc18bfa131fbc7c3f169cc4b2f6"
 uuid = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
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 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
@@ -1267,9 +1267,9 @@ version = "0.4.0+0"
 
 [[deps.RuntimeGeneratedFunctions]]
 deps = ["ExprTools", "SHA", "Serialization"]
-git-tree-sha1 = "6aacc5eefe8415f47b3e34214c1d79d2674a0ba2"
+git-tree-sha1 = "04c968137612c4a5629fa531334bb81ad5680f00"
 uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
-version = "0.5.12"
+version = "0.5.13"
 
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -1288,9 +1288,9 @@ version = "0.6.42"
 
 [[deps.SciMLBase]]
 deps = ["ADTypes", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
-git-tree-sha1 = "d15c65e25615272e1b1c5edb1d307484c7942824"
+git-tree-sha1 = "816176bca8a93f8f50a33853e0933d6c4ec116d0"
 uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-version = "2.31.0"
+version = "2.33.1"
 
     [deps.SciMLBase.extensions]
     SciMLBaseChainRulesCoreExt = "ChainRulesCore"
@@ -1384,9 +1384,9 @@ version = "1.10.0"
 
 [[deps.SparseDiffTools]]
 deps = ["ADTypes", "Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "Graphs", "LinearAlgebra", "PackageExtensionCompat", "Random", "Reexport", "SciMLOperators", "Setfield", "SparseArrays", "StaticArrayInterface", "StaticArrays", "Tricks", "UnPack", "VertexSafeGraphs"]
-git-tree-sha1 = "a616ac46c38da60ac05cecf52064d44732edd05e"
+git-tree-sha1 = "e2a3d8dfaffce3d3b8b5a0967c0cfcc89d34e425"
 uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
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+version = "2.17.1"
 
     [deps.SparseDiffTools.extensions]
     SparseDiffToolsEnzymeExt = "Enzyme"
@@ -1481,9 +1481,9 @@ weakdeps = ["ChainRulesCore", "InverseFunctions"]
 
 [[deps.StrideArraysCore]]
 deps = ["ArrayInterface", "CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static", "StaticArrayInterface", "ThreadingUtilities"]
-git-tree-sha1 = "b164d4dc04d7072066b725b7906e56331b170004"
+git-tree-sha1 = "b518da45c50dfab8384125ba829f1739bda41034"
 uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
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 [[deps.StringManipulation]]
 deps = ["PrecompileTools"]
@@ -1495,7 +1495,7 @@ version = "0.3.4"
 deps = ["AbstractAlgebra", "Combinatorics", "DataStructures", "Dates", "Groebner", "IterTools", "LinearAlgebra", "Logging", "MacroTools", "Nemo", "ParamPunPam", "PrecompileTools", "Primes", "Random", "TimerOutputs"]
 path = "/home/runner/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl"
 uuid = "220ca800-aa68-49bb-acd8-6037fa93a544"
-version = "0.5.6"
+version = "0.5.7"
 weakdeps = ["ModelingToolkit", "SymbolicUtils", "Symbolics"]
 
     [deps.StructuralIdentifiability.extensions]
@@ -1512,9 +1512,9 @@ version = "7.2.1+1"
 
 [[deps.SymbolicIndexingInterface]]
 deps = ["Accessors", "ArrayInterface", "MacroTools", "RuntimeGeneratedFunctions", "StaticArraysCore"]
-git-tree-sha1 = "4b7f4c80449d8baae8857d55535033981862619c"
+git-tree-sha1 = "40ea524431a92328cd73582d1820a5b08247a40f"
 uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
-version = "0.3.15"
+version = "0.3.16"
 
 [[deps.SymbolicLimits]]
 deps = ["SymbolicUtils"]
@@ -1530,9 +1530,9 @@ version = "1.5.1"
 
 [[deps.Symbolics]]
 deps = ["ArrayInterface", "Bijections", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "DynamicPolynomials", "ForwardDiff", "IfElse", "LaTeXStrings", "LambertW", "Latexify", "Libdl", "LinearAlgebra", "LogExpFunctions", "MacroTools", "Markdown", "NaNMath", "PrecompileTools", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "SymbolicLimits", "SymbolicUtils"]
-git-tree-sha1 = "280c17e091a24283a59eedfc00a02026ec984b09"
+git-tree-sha1 = "4104548fff14d7370b278ee767651d6ec61eb195"
 uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
-version = "5.27.1"
+version = "5.28.0"
 
     [deps.Symbolics.extensions]
     SymbolicsGroebnerExt = "Groebner"
@@ -1600,9 +1600,9 @@ weakdeps = ["Random", "Test"]
 
 [[deps.TriangularSolve]]
 deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
-git-tree-sha1 = "7ee8ed8904e7dd5d31bb46294ef5644d9e2e44e4"
+git-tree-sha1 = "66c68a20907800c0b7c04ff8a6164115e8747de2"
 uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
-version = "0.1.21"
+version = "0.2.0"
 
 [[deps.Tricks]]
 git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f"
@@ -1656,9 +1656,9 @@ version = "0.2.1"
 
 [[deps.VectorizationBase]]
 deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static", "StaticArrayInterface"]
-git-tree-sha1 = "7209df901e6ed7489fe9b7aa3e46fb788e15db85"
+git-tree-sha1 = "ac377f0a248753a1b1d58bbc92a64f5a726dfb71"
 uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
-version = "0.21.65"
+version = "0.21.66"
 
 [[deps.VertexSafeGraphs]]
 deps = ["Graphs"]
diff --git a/dev/export/export/index.html b/dev/export/export/index.html
index 1397fbe4..2e14f209 100644
--- a/dev/export/export/index.html
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-</script><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script 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href="../../utils/local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/global_identifiability/">Global Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/elimination/">Elimination</a></li><li><a class="tocitem" href="../../utils/ode/">ODE Tools</a></li><li><a class="tocitem" href="../../utils/power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../../utils/primality/">Primality Checks</a></li><li><a class="tocitem" href="../../utils/wronskian/">Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output Equation tools</a></li><li><a class="tocitem" href="../../utils/util/">Other Utilities</a></li></ul></li><li><span class="tocitem">Export</span><ul><li class="is-active"><a class="tocitem" href>Exporting to Other Systems</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Export</a></li><li class="is-active"><a href>Exporting to Other Systems</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Exporting to Other Systems</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/export/export.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Exporting-to-Other-Systems"><a class="docs-heading-anchor" href="#Exporting-to-Other-Systems">Exporting to Other Systems</a><a id="Exporting-to-Other-Systems-1"></a><a class="docs-heading-anchor-permalink" href="#Exporting-to-Other-Systems" title="Permalink"></a></h1><p>Here we put some helpful utilities to export your code to other identifiability software.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_maple" href="#StructuralIdentifiability.print_for_maple"><code>StructuralIdentifiability.print_for_maple</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_maple(ode, package)</code></pre><p>Prints the ODE in the format accepted by maple packages</p><ul><li>SIAN (https://github.com/pogudingleb/SIAN) if package=:SIAN</li><li>DifferentialAlgebra if package=:DifferentialAlgebra</li><li>DifferentialThomas if package=:DifferentialThomas</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODEexport.jl#L1-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_DAISY" href="#StructuralIdentifiability.print_for_DAISY"><code>StructuralIdentifiability.print_for_DAISY</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_DAISY(ode)</code></pre><p>Prints the ODE in the format accepted by DAISY (https://daisy.dei.unipd.it/)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODEexport.jl#L90-L94">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_GenSSI" href="#StructuralIdentifiability.print_for_GenSSI"><code>StructuralIdentifiability.print_for_GenSSI</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_GenSSI(ode)</code></pre><p>Prints the ODE in the format accepted by GenSSI 2.0 (https://github.com/genssi-developer/GenSSI)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODEexport.jl#L133-L137">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_COMBOS" href="#StructuralIdentifiability.print_for_COMBOS"><code>StructuralIdentifiability.print_for_COMBOS</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_COMBOS(ode)</code></pre><p>Prints the ODE in the format accepted by COMBOS (http://biocyb1.cs.ucla.edu/combos/)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODEexport.jl#L182-L186">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../utils/util/">« Other Utilities</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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href="../../utils/local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/global_identifiability/">Global Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/elimination/">Elimination</a></li><li><a class="tocitem" href="../../utils/ode/">ODE Tools</a></li><li><a class="tocitem" href="../../utils/power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../../utils/primality/">Primality Checks</a></li><li><a class="tocitem" href="../../utils/wronskian/">Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output Equation tools</a></li><li><a class="tocitem" href="../../utils/util/">Other Utilities</a></li></ul></li><li><span class="tocitem">Export</span><ul><li class="is-active"><a class="tocitem" href>Exporting to Other Systems</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Export</a></li><li class="is-active"><a href>Exporting to Other Systems</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Exporting to Other Systems</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/export/export.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Exporting-to-Other-Systems"><a class="docs-heading-anchor" href="#Exporting-to-Other-Systems">Exporting to Other Systems</a><a id="Exporting-to-Other-Systems-1"></a><a class="docs-heading-anchor-permalink" href="#Exporting-to-Other-Systems" title="Permalink"></a></h1><p>Here we put some helpful utilities to export your code to other identifiability software.</p><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_maple" href="#StructuralIdentifiability.print_for_maple"><code>StructuralIdentifiability.print_for_maple</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_maple(ode, package)</code></pre><p>Prints the ODE in the format accepted by maple packages</p><ul><li>SIAN (https://github.com/pogudingleb/SIAN) if package=:SIAN</li><li>DifferentialAlgebra if package=:DifferentialAlgebra</li><li>DifferentialThomas if package=:DifferentialThomas</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODEexport.jl#L1-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_DAISY" href="#StructuralIdentifiability.print_for_DAISY"><code>StructuralIdentifiability.print_for_DAISY</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_DAISY(ode)</code></pre><p>Prints the ODE in the format accepted by DAISY (https://daisy.dei.unipd.it/)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODEexport.jl#L90-L94">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_GenSSI" href="#StructuralIdentifiability.print_for_GenSSI"><code>StructuralIdentifiability.print_for_GenSSI</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_GenSSI(ode)</code></pre><p>Prints the ODE in the format accepted by GenSSI 2.0 (https://github.com/genssi-developer/GenSSI)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODEexport.jl#L133-L137">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.print_for_COMBOS" href="#StructuralIdentifiability.print_for_COMBOS"><code>StructuralIdentifiability.print_for_COMBOS</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">print_for_COMBOS(ode)</code></pre><p>Prints the ODE in the format accepted by COMBOS (http://biocyb1.cs.ucla.edu/combos/)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODEexport.jl#L182-L186">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../utils/util/">« Other Utilities</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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All Types of Identifiability</span></a></li><li><a class="tocitem" href="#Assessing-Local-Identifiability"><span>Assessing Local Identifiability</span></a></li><li><a class="tocitem" href="#Finding-Identifiable-Functions"><span>Finding Identifiable Functions</span></a></li></ul></li></ul></li><li><span class="tocitem">Library</span><ul><li><a class="tocitem" href="../../utils/local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/global_identifiability/">Global Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/elimination/">Elimination</a></li><li><a class="tocitem" href="../../utils/ode/">ODE Tools</a></li><li><a class="tocitem" href="../../utils/power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../../utils/primality/">Primality Checks</a></li><li><a class="tocitem" href="../../utils/wronskian/">Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output Equation tools</a></li><li><a class="tocitem" href="../../utils/util/">Other Utilities</a></li></ul></li><li><span class="tocitem">Export</span><ul><li><a class="tocitem" href="../../export/export/">Exporting to Other Systems</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Basics</a></li><li class="is-active"><a href>Functions to Assess Identifiability</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Functions to Assess Identifiability</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/identifiability/identifiability.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Functions-to-Assess-Identifiability"><a class="docs-heading-anchor" href="#Functions-to-Assess-Identifiability">Functions to Assess Identifiability</a><a id="Functions-to-Assess-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Functions-to-Assess-Identifiability" title="Permalink"></a></h1><h2 id="Assessing-All-Types-of-Identifiability"><a class="docs-heading-anchor" href="#Assessing-All-Types-of-Identifiability">Assessing All Types of Identifiability</a><a id="Assessing-All-Types-of-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Assessing-All-Types-of-Identifiability" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.assess_identifiability" href="#StructuralIdentifiability.assess_identifiability"><code>StructuralIdentifiability.assess_identifiability</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">assess_identifiability(ode; funcs_to_check = [], prob_threshold=0.99, loglevel=Logging.Info)</code></pre><p>Input:</p><ul><li><code>ode</code> - the ODE model</li><li><code>funcs_to_check</code> - list of functions to check identifiability for; if empty, all parameters  and states are taken</li><li><code>known_ic</code>: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).</li><li><code>prob_threshold</code> - probability of correctness.</li><li><code>loglevel</code> - the minimal level of log messages to display (<code>Logging.Info</code> by default)</li></ul><p>Assesses identifiability of a given ODE model. The result is guaranteed to be correct with the probability at least <code>prob_threshold</code>. The function returns an (ordered) dictionary from the functions to check to their identifiability properties  (one of <code>:nonidentifiable</code>, <code>:locally</code>, <code>:globally</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/StructuralIdentifiability.jl#L86-L103">source</a></section></article><h2 id="Assessing-Local-Identifiability"><a class="docs-heading-anchor" href="#Assessing-Local-Identifiability">Assessing Local Identifiability</a><a id="Assessing-Local-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Assessing-Local-Identifiability" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.assess_local_identifiability" href="#StructuralIdentifiability.assess_local_identifiability"><code>StructuralIdentifiability.assess_local_identifiability</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{&lt;: Any, 1}, prob_threshold::Float64=0.99, type=:SE, loglevel=Logging.Info) where P &lt;: MPolyRingElem{Nemo.QQFieldElem}</code></pre><p>Checks the local identifiability/observability of the functions in <code>funcs_to_check</code>. The result is correct with probability at least <code>prob_threshold</code>.</p><p>Call this function if you have a specific collection of parameters of which you would like to check local identifiability.</p><p><code>type</code> can be either <code>:SE</code> (single-experiment identifiability) or <code>:ME</code> (multi-experiment identifiability). If the type is <code>:ME</code>, states are not allowed to appear in the <code>funcs_to_check</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/local_identifiability.jl#L148-L157">source</a></section><section><div><pre><code class="language-julia hljs">assess_local_identifiability(dds::DDS{P}; funcs_to_check::Array{&lt;: Any, 1}, known_ic, prob_threshold::Float64=0.99, loglevel=Logging.Info) where P &lt;: MPolyRingElem{Nemo.QQFieldElem}</code></pre><p>Checks the local identifiability/observability of the functions in <code>funcs_to_check</code>. The result is correct with probability at least <code>prob_threshold</code>. A list of quantities can be provided as <code>known_ic</code> for which the initial conditions can be assumed to be known and generic.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/discrete.jl#L378-L383">source</a></section></article><h2 id="Finding-Identifiable-Functions"><a class="docs-heading-anchor" href="#Finding-Identifiable-Functions">Finding Identifiable Functions</a><a id="Finding-Identifiable-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Finding-Identifiable-Functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_identifiable_functions" href="#StructuralIdentifiability.find_identifiable_functions"><code>StructuralIdentifiability.find_identifiable_functions</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">find_identifiable_functions(ode::ODE; options...)</code></pre><p>Finds all functions of parameters/states that are identifiable in the given ODE system.</p><p><strong>Options</strong></p><p>This functions takes the following optional arguments:</p><ul><li><code>with_states</code>: When <code>true</code>, also reports the identifiabile functions in the   ODE states. Default is <code>false</code>.</li><li><code>simplify</code>: The extent to which the output functions are simplified. Stronger simplification may require more time. Possible options are:<ul><li><code>:standard</code>: Default simplification.</li><li><code>:weak</code>: Weak simplification. This option is the fastest, but the output functions can be quite complex.</li><li><code>:strong</code>: Strong simplification. This option is the slowest, but the output</li></ul>functions are nice and simple.<ul><li><code>:absent</code>: No simplification.</li></ul></li><li><code>known_ic</code>: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).</li><li><code>prob_threshold</code>: A float in the range from 0 to 1, the probability of correctness. Default is <code>0.99</code>.</li><li><code>seed</code>: The rng seed. Default value is <code>42</code>.</li><li><code>loglevel</code> - the minimal level of log messages to display (<code>Logging.Info</code> by default)</li></ul><p><strong>Example</strong></p><pre><code class="language-julia hljs">using StructuralIdentifiability
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All Types of Identifiability</span></a></li><li><a class="tocitem" href="#Assessing-Local-Identifiability"><span>Assessing Local Identifiability</span></a></li><li><a class="tocitem" href="#Finding-Identifiable-Functions"><span>Finding Identifiable Functions</span></a></li></ul></li></ul></li><li><span class="tocitem">Library</span><ul><li><a class="tocitem" href="../../utils/local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/global_identifiability/">Global Identifiability Tools</a></li><li><a class="tocitem" href="../../utils/elimination/">Elimination</a></li><li><a class="tocitem" href="../../utils/ode/">ODE Tools</a></li><li><a class="tocitem" href="../../utils/power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../../utils/primality/">Primality Checks</a></li><li><a class="tocitem" href="../../utils/wronskian/">Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output 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Identifiability</a><a id="Functions-to-Assess-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Functions-to-Assess-Identifiability" title="Permalink"></a></h1><h2 id="Assessing-All-Types-of-Identifiability"><a class="docs-heading-anchor" href="#Assessing-All-Types-of-Identifiability">Assessing All Types of Identifiability</a><a id="Assessing-All-Types-of-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Assessing-All-Types-of-Identifiability" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.assess_identifiability" href="#StructuralIdentifiability.assess_identifiability"><code>StructuralIdentifiability.assess_identifiability</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">assess_identifiability(ode; funcs_to_check = [], prob_threshold=0.99, loglevel=Logging.Info)</code></pre><p>Input:</p><ul><li><code>ode</code> - the ODE model</li><li><code>funcs_to_check</code> - list of functions to check identifiability for; if empty, all parameters  and states are taken</li><li><code>known_ic</code>: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).</li><li><code>prob_threshold</code> - probability of correctness.</li><li><code>loglevel</code> - the minimal level of log messages to display (<code>Logging.Info</code> by default)</li></ul><p>Assesses identifiability of a given ODE model. The result is guaranteed to be correct with the probability at least <code>prob_threshold</code>. The function returns an (ordered) dictionary from the functions to check to their identifiability properties  (one of <code>:nonidentifiable</code>, <code>:locally</code>, <code>:globally</code>).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/StructuralIdentifiability.jl#L86-L103">source</a></section></article><h2 id="Assessing-Local-Identifiability"><a class="docs-heading-anchor" href="#Assessing-Local-Identifiability">Assessing Local Identifiability</a><a id="Assessing-Local-Identifiability-1"></a><a class="docs-heading-anchor-permalink" href="#Assessing-Local-Identifiability" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.assess_local_identifiability" href="#StructuralIdentifiability.assess_local_identifiability"><code>StructuralIdentifiability.assess_local_identifiability</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{&lt;: Any, 1}, prob_threshold::Float64=0.99, type=:SE, loglevel=Logging.Info) where P &lt;: MPolyRingElem{Nemo.QQFieldElem}</code></pre><p>Checks the local identifiability/observability of the functions in <code>funcs_to_check</code>. The result is correct with probability at least <code>prob_threshold</code>.</p><p>Call this function if you have a specific collection of parameters of which you would like to check local identifiability.</p><p><code>type</code> can be either <code>:SE</code> (single-experiment identifiability) or <code>:ME</code> (multi-experiment identifiability). If the type is <code>:ME</code>, states are not allowed to appear in the <code>funcs_to_check</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/local_identifiability.jl#L148-L157">source</a></section><section><div><pre><code class="language-julia hljs">assess_local_identifiability(dds::DDS{P}; funcs_to_check::Array{&lt;: Any, 1}, known_ic, prob_threshold::Float64=0.99, loglevel=Logging.Info) where P &lt;: MPolyRingElem{Nemo.QQFieldElem}</code></pre><p>Checks the local identifiability/observability of the functions in <code>funcs_to_check</code>. The result is correct with probability at least <code>prob_threshold</code>. A list of quantities can be provided as <code>known_ic</code> for which the initial conditions can be assumed to be known and generic.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/discrete.jl#L378-L383">source</a></section></article><h2 id="Finding-Identifiable-Functions"><a class="docs-heading-anchor" href="#Finding-Identifiable-Functions">Finding Identifiable Functions</a><a id="Finding-Identifiable-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Finding-Identifiable-Functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_identifiable_functions" href="#StructuralIdentifiability.find_identifiable_functions"><code>StructuralIdentifiability.find_identifiable_functions</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">find_identifiable_functions(ode::ODE; options...)</code></pre><p>Finds all functions of parameters/states that are identifiable in the given ODE system.</p><p><strong>Options</strong></p><p>This functions takes the following optional arguments:</p><ul><li><code>with_states</code>: When <code>true</code>, also reports the identifiabile functions in the   ODE states. Default is <code>false</code>.</li><li><code>simplify</code>: The extent to which the output functions are simplified. Stronger simplification may require more time. Possible options are:<ul><li><code>:standard</code>: Default simplification.</li><li><code>:weak</code>: Weak simplification. This option is the fastest, but the output functions can be quite complex.</li><li><code>:strong</code>: Strong simplification. This option is the slowest, but the output</li></ul>functions are nice and simple.<ul><li><code>:absent</code>: No simplification.</li></ul></li><li><code>known_ic</code>: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).</li><li><code>prob_threshold</code>: A float in the range from 0 to 1, the probability of correctness. Default is <code>0.99</code>.</li><li><code>seed</code>: The rng seed. Default value is <code>42</code>.</li><li><code>loglevel</code> - the minimal level of log messages to display (<code>Logging.Info</code> by default)</li></ul><p><strong>Example</strong></p><pre><code class="language-julia hljs">using StructuralIdentifiability
 
 ode = @ODEmodel(
     x0&#39;(t) = -(a01 + a21) * x0(t) + a12 * x1(t),
@@ -16,4 +16,4 @@
 # prints
 3-element Vector{AbstractAlgebra.Generic.FracFieldElem{Nemo.QQMPolyRingElem}}:
  a12 + a01 + a21
- a12*a01</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/identifiable_functions.jl#L2-L48">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../input/input/">« Parsing input system</a><a class="docs-footer-nextpage" href="../../utils/local_identifiability/">Local Identifiability Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ a12*a01</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/identifiable_functions.jl#L2-L48">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../input/input/">« Parsing input system</a><a class="docs-footer-nextpage" href="../../utils/local_identifiability/">Local Identifiability Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/index.html b/dev/index.html
index 6c51dc21..3186252c 100644
--- a/dev/index.html
+++ b/dev/index.html
@@ -15,9 +15,9 @@
   pages   = {194-235}
 }</code></pre><h2 id="Feature-Summary"><a class="docs-heading-anchor" href="#Feature-Summary">Feature Summary</a><a id="Feature-Summary-1"></a><a class="docs-heading-anchor-permalink" href="#Feature-Summary" title="Permalink"></a></h2><p><code>StructuralIdentifiability.jl</code> can assess local and global identifiability of ODE models. In addition to these straightforward identifiability queries on individual parameters, the package can distinguish between single- and multi-experiment identifiability.</p><h2 id="Feature-List"><a class="docs-heading-anchor" href="#Feature-List">Feature List</a><a id="Feature-List-1"></a><a class="docs-heading-anchor-permalink" href="#Feature-List" title="Permalink"></a></h2><ul><li>Local identifiability checks</li><li>Global identifiability checks</li><li>Assessment of identifiable functions of parameters and states</li><li>Model reparametrization (experimental)</li></ul><h2 id="Contributing"><a class="docs-heading-anchor" href="#Contributing">Contributing</a><a id="Contributing-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing" title="Permalink"></a></h2><ul><li><p>Please refer to the <a href="https://github.com/SciML/ColPrac/blob/master/README.md">SciML ColPrac: Contributor&#39;s Guide on Collaborative Practices for Community Packages</a> for guidance on PRs, issues, and other matters relating to contributing to StructuralIdentifiability.</p></li><li><p>There are a few community forums:</p><ul><li>The #diffeq-bridged channel in the <a href="https://julialang.org/slack/">Julia Slack</a></li><li><a href="https://gitter.im/JuliaDiffEq/Lobby">JuliaDiffEq</a> on Gitter</li><li>On the Julia Discourse forums</li><li>See also <a href="https://sciml.ai/community/">SciML Community page</a></li></ul></li></ul><h2 id="Reproducibility"><a class="docs-heading-anchor" href="#Reproducibility">Reproducibility</a><a id="Reproducibility-1"></a><a class="docs-heading-anchor-permalink" href="#Reproducibility" title="Permalink"></a></h2><details><summary>The documentation of this SciML package was built using these direct dependencies,</summary><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Status `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl/docs/Project.toml`
   [6e4b80f9] BenchmarkTools v1.5.0
-  [e30172f5] Documenter v1.3.0
-  [961ee093] ModelingToolkit v9.9.0
-  [220ca800] StructuralIdentifiability v0.5.6 `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl`</code></pre></details><details><summary>and using this machine and Julia version.</summary><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Julia Version 1.10.2
+  [e30172f5] Documenter v1.4.0
+  [961ee093] ModelingToolkit v9.12.0
+  [220ca800] StructuralIdentifiability v0.5.7 `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl`</code></pre></details><details><summary>and using this machine and Julia version.</summary><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Julia Version 1.10.2
 Commit bd47eca2c8a (2024-03-01 10:14 UTC)
 Build Info:
   Official https://julialang.org/ release
@@ -30,13 +30,13 @@
 Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)</code></pre></details><details><summary>A more complete overview of all dependencies and their versions is also provided.</summary><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Status `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl/docs/Manifest.toml`
   [47edcb42] ADTypes v0.2.7
   [a4c015fc] ANSIColoredPrinters v0.0.1
-  [c3fe647b] AbstractAlgebra v0.40.7
+  [c3fe647b] AbstractAlgebra v0.40.9
   [1520ce14] AbstractTrees v0.4.5
   [7d9f7c33] Accessors v0.1.36
   [79e6a3ab] Adapt v4.0.4
   [ec485272] ArnoldiMethod v0.4.0
   [4fba245c] ArrayInterface v7.9.0
-  [4c555306] ArrayLayouts v1.9.1
+  [4c555306] ArrayLayouts v1.9.2
   [a9b6321e] Atomix v0.1.0
   [6e4b80f9] BenchmarkTools v1.5.0
   [e2ed5e7c] Bijections v0.1.6
@@ -59,18 +59,18 @@
   [adafc99b] CpuId v0.3.1
   [a8cc5b0e] Crayons v4.1.1
   [9a962f9c] DataAPI v1.16.0
-  [864edb3b] DataStructures v0.18.18
+  [864edb3b] DataStructures v0.18.20
   [e2d170a0] DataValueInterfaces v1.0.0
-  [2b5f629d] DiffEqBase v6.149.0
-  [459566f4] DiffEqCallbacks v3.5.0
+  [2b5f629d] DiffEqBase v6.149.1
+  [459566f4] DiffEqCallbacks v3.6.1
   [163ba53b] DiffResults v1.1.0
   [b552c78f] DiffRules v1.15.1
   [31c24e10] Distributions v0.25.107
   [ffbed154] DocStringExtensions v0.9.3
-  [e30172f5] Documenter v1.3.0
-  [5b8099bc] DomainSets v0.7.11
+  [e30172f5] Documenter v1.4.0
+  [5b8099bc] DomainSets v0.7.12
   [fa6b7ba4] DualNumbers v0.6.8
-  [7c1d4256] DynamicPolynomials v0.5.5
+  [7c1d4256] DynamicPolynomials v0.5.6
   [06fc5a27] DynamicQuantities v0.13.2
   [4e289a0a] EnumX v1.0.4
 ⌃ [f151be2c] EnzymeCore v0.6.6
@@ -81,7 +81,7 @@
   [29a986be] FastLapackInterface v2.0.2
   [1a297f60] FillArrays v1.10.0
   [64ca27bc] FindFirstFunctions v1.2.0
-  [6a86dc24] FiniteDiff v2.23.0
+  [6a86dc24] FiniteDiff v2.23.1
   [1fa38f19] Format v1.3.7
   [f6369f11] ForwardDiff v0.10.36
   [069b7b12] FunctionWrappers v1.1.3
@@ -113,7 +113,7 @@
   [b964fa9f] LaTeXStrings v1.3.1
   [2ee39098] LabelledArrays v1.15.1
   [984bce1d] LambertW v0.4.6
-  [23fbe1c1] Latexify v0.16.2
+  [23fbe1c1] Latexify v0.16.3
   [10f19ff3] LayoutPointers v0.1.15
   [0e77f7df] LazilyInitializedFields v1.2.2
   [5078a376] LazyArrays v1.9.1
@@ -125,18 +125,18 @@
   [1914dd2f] MacroTools v0.5.13
   [d125e4d3] ManualMemory v0.1.8
   [d0879d2d] MarkdownAST v0.1.2
-  [a3b82374] MatrixFactorizations v2.1.2
+  [a3b82374] MatrixFactorizations v2.2.0
   [bb5d69b7] MaybeInplace v0.1.2
   [e1d29d7a] Missings v1.2.0
-  [961ee093] ModelingToolkit v9.9.0
+  [961ee093] ModelingToolkit v9.12.0
   [46d2c3a1] MuladdMacro v0.2.4
   [102ac46a] MultivariatePolynomials v0.5.4
-  [d8a4904e] MutableArithmetics v1.4.2
+  [d8a4904e] MutableArithmetics v1.4.3
   [d41bc354] NLSolversBase v7.8.3
   [77ba4419] NaNMath v1.0.2
   [2edaba10] Nemo v0.43.2
-  [8913a72c] NonlinearSolve v3.9.1
-  [6fe1bfb0] OffsetArrays v1.13.0
+  [8913a72c] NonlinearSolve v3.10.0
+  [6fe1bfb0] OffsetArrays v1.14.0
   [bac558e1] OrderedCollections v1.6.3
   [1dea7af3] OrdinaryDiffEq v6.74.1
   [90014a1f] PDMats v0.11.31
@@ -145,9 +145,9 @@
   [d96e819e] Parameters v0.12.3
   [69de0a69] Parsers v2.8.1
   [e409e4f3] PoissonRandom v0.4.4
-  [f517fe37] Polyester v0.7.12
+  [f517fe37] Polyester v0.7.13
   [1d0040c9] PolyesterWeave v0.2.1
-  [d236fae5] PreallocationTools v0.4.20
+  [d236fae5] PreallocationTools v0.4.21
   [aea7be01] PrecompileTools v1.2.1
   [21216c6a] Preferences v1.4.3
   [08abe8d2] PrettyTables v2.3.1
@@ -158,15 +158,15 @@
   [e6cf234a] RandomNumbers v1.5.3
   [3cdcf5f2] RecipesBase v1.3.4
   [731186ca] RecursiveArrayTools v3.13.0
-  [f2c3362d] RecursiveFactorization v0.2.21
+  [f2c3362d] RecursiveFactorization v0.2.23
   [189a3867] Reexport v1.2.2
   [2792f1a3] RegistryInstances v0.1.0
   [ae029012] Requires v1.3.0
   [79098fc4] Rmath v0.7.1
-  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
+  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
   [94e857df] SIMDTypes v0.1.0
   [476501e8] SLEEFPirates v0.6.42
-  [0bca4576] SciMLBase v2.31.0
+  [0bca4576] SciMLBase v2.33.1
   [c0aeaf25] SciMLOperators v0.3.8
   [53ae85a6] SciMLStructures v1.1.0
   [efcf1570] Setfield v1.1.1
@@ -174,7 +174,7 @@
   [699a6c99] SimpleTraits v0.9.4
   [ce78b400] SimpleUnPack v1.1.0
   [a2af1166] SortingAlgorithms v1.2.1
-  [47a9eef4] SparseDiffTools v2.17.0
+  [47a9eef4] SparseDiffTools v2.17.1
   [e56a9233] Sparspak v0.3.9
   [276daf66] SpecialFunctions v2.3.1
   [aedffcd0] Static v0.8.10
@@ -184,20 +184,20 @@
   [82ae8749] StatsAPI v1.7.0
   [2913bbd2] StatsBase v0.34.3
   [4c63d2b9] StatsFuns v1.3.1
-  [7792a7ef] StrideArraysCore v0.5.3
+  [7792a7ef] StrideArraysCore v0.5.5
   [892a3eda] StringManipulation v0.3.4
-  [220ca800] StructuralIdentifiability v0.5.6 `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl`
-  [2efcf032] SymbolicIndexingInterface v0.3.15
+  [220ca800] StructuralIdentifiability v0.5.7 `~/work/StructuralIdentifiability.jl/StructuralIdentifiability.jl`
+  [2efcf032] SymbolicIndexingInterface v0.3.16
   [19f23fe9] SymbolicLimits v0.2.0
   [d1185830] SymbolicUtils v1.5.1
-  [0c5d862f] Symbolics v5.27.1
+  [0c5d862f] Symbolics v5.28.0
   [3783bdb8] TableTraits v1.0.1
   [bd369af6] Tables v1.11.1
   [8290d209] ThreadingUtilities v0.5.2
   [a759f4b9] TimerOutputs v0.5.23
   [0796e94c] Tokenize v0.5.28
   [3bb67fe8] TranscodingStreams v0.10.7
-  [d5829a12] TriangularSolve v0.1.21
+  [d5829a12] TriangularSolve v0.2.0
   [410a4b4d] Tricks v0.1.8
   [781d530d] TruncatedStacktraces v1.4.0
   [5c2747f8] URIs v1.5.1
@@ -205,7 +205,7 @@
   [1986cc42] Unitful v1.19.0
   [a7c27f48] Unityper v0.1.6
   [013be700] UnsafeAtomics v0.2.1
-  [3d5dd08c] VectorizationBase v0.21.65
+  [3d5dd08c] VectorizationBase v0.21.66
   [19fa3120] VertexSafeGraphs v0.2.0
   [e21ec000] Antic_jll v0.201.500+0
   [d9960996] Arb_jll v200.2300.0+0
@@ -273,4 +273,4 @@
   [3f19e933] p7zip_jll v17.4.0+2
 Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`</code></pre></details>You can also download the 
 <a href="">manifest</a> file and the
-<a href="">project</a> file.</article><nav class="docs-footer"><a class="docs-footer-nextpage" href="tutorials/creating_ode/">Creating ODE System »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<a href="">project</a> file.</article><nav class="docs-footer"><a class="docs-footer-nextpage" href="tutorials/creating_ode/">Creating ODE System »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/input/input/index.html b/dev/input/input/index.html
index 23e320b6..e1f20fbc 100644
--- a/dev/input/input/index.html
+++ b/dev/input/input/index.html
@@ -9,10 +9,10 @@
     x1&#39;(t) = a * x1(t) + u(t),
     x2&#39;(t) = b * x2(t) + c*x1(t)*x2(t),
     y(t) = x1(t)
-)</code></pre><p>Here,</p><ul><li><code>x1</code>, <code>x2</code> are state variables</li><li><code>y</code> is an output variable</li><li><code>u</code> is an input variable</li><li><code>a</code>, <code>b</code>, <code>c</code> are time-independent parameters</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/input_macro.jl#L242-L268">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ODE" href="#StructuralIdentifiability.ODE"><code>StructuralIdentifiability.ODE</code></a> — <span class="docstring-category">Type</span></header><section><div><p>The main structure that represents input ODE system.</p><p>Stores information about states (<code>x_vars</code>), outputs (<code>y_vars</code>), inputs (<code>u_vars</code>), parameters (<code>parameters</code>) and the equations.</p><p>This structure is constructed via <code>@ODEmodel</code> macro.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.set_parameter_values" href="#StructuralIdentifiability.set_parameter_values"><code>StructuralIdentifiability.set_parameter_values</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">set_parameter_values(ode, param_values)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ODE as above</li><li><code>param_values</code> - values for (possibly, some of) the parameters as dictionary <code>parameter</code> =&gt; <code>value</code></li></ul><p>Output:</p><ul><li>new ode with the parameters in param_values plugged with the given numbers</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L87-L96">source</a></section></article><h2 id="Create-Compartmental-Model"><a class="docs-heading-anchor" href="#Create-Compartmental-Model">Create Compartmental Model</a><a id="Create-Compartmental-Model-1"></a><a class="docs-heading-anchor-permalink" href="#Create-Compartmental-Model" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.linear_compartment_model" href="#StructuralIdentifiability.linear_compartment_model"><code>StructuralIdentifiability.linear_compartment_model</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">linear_compartment_model(graph, inputs, outputs, leaks)</code></pre><p>Input: defines a linear compartment model with nodes numbered from 1 to <code>n</code> by</p><ul><li><code>graph</code> - and array of integer arrays representing the adjacency lists of the graph</li><li><code>inputs</code> - array of input nodes</li><li><code>outputs</code> - array of output nodes</li><li><code>leaks</code> - array of sink nodes</li></ul><p>Output:</p><ul><li>the corresponding ODE system in the notation of https://doi.org/10.1007/s11538-015-0098-0</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/lincomp.jl#L16-L27">source</a></section></article><h2 id="Discrete-time-systems"><a class="docs-heading-anchor" href="#Discrete-time-systems">Discrete-time systems</a><a id="Discrete-time-systems-1"></a><a class="docs-heading-anchor-permalink" href="#Discrete-time-systems" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.@DDSmodel" href="#StructuralIdentifiability.@DDSmodel"><code>StructuralIdentifiability.@DDSmodel</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">macro DDSmodel</code></pre><p>Macro for creating a DDS (discrete dynamical system)  from a list of equations. It also injects all variables into the global scope.</p><p><strong>Example</strong></p><p>Creating a simple <code>DDS</code>:</p><pre><code class="language-julia hljs">using StructuralIdentifiability
+)</code></pre><p>Here,</p><ul><li><code>x1</code>, <code>x2</code> are state variables</li><li><code>y</code> is an output variable</li><li><code>u</code> is an input variable</li><li><code>a</code>, <code>b</code>, <code>c</code> are time-independent parameters</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/input_macro.jl#L242-L268">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ODE" href="#StructuralIdentifiability.ODE"><code>StructuralIdentifiability.ODE</code></a> — <span class="docstring-category">Type</span></header><section><div><p>The main structure that represents input ODE system.</p><p>Stores information about states (<code>x_vars</code>), outputs (<code>y_vars</code>), inputs (<code>u_vars</code>), parameters (<code>parameters</code>) and the equations.</p><p>This structure is constructed via <code>@ODEmodel</code> macro.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.set_parameter_values" href="#StructuralIdentifiability.set_parameter_values"><code>StructuralIdentifiability.set_parameter_values</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">set_parameter_values(ode, param_values)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ODE as above</li><li><code>param_values</code> - values for (possibly, some of) the parameters as dictionary <code>parameter</code> =&gt; <code>value</code></li></ul><p>Output:</p><ul><li>new ode with the parameters in param_values plugged with the given numbers</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L87-L96">source</a></section></article><h2 id="Create-Compartmental-Model"><a class="docs-heading-anchor" href="#Create-Compartmental-Model">Create Compartmental Model</a><a id="Create-Compartmental-Model-1"></a><a class="docs-heading-anchor-permalink" href="#Create-Compartmental-Model" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.linear_compartment_model" href="#StructuralIdentifiability.linear_compartment_model"><code>StructuralIdentifiability.linear_compartment_model</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">linear_compartment_model(graph, inputs, outputs, leaks)</code></pre><p>Input: defines a linear compartment model with nodes numbered from 1 to <code>n</code> by</p><ul><li><code>graph</code> - and array of integer arrays representing the adjacency lists of the graph</li><li><code>inputs</code> - array of input nodes</li><li><code>outputs</code> - array of output nodes</li><li><code>leaks</code> - array of sink nodes</li></ul><p>Output:</p><ul><li>the corresponding ODE system in the notation of https://doi.org/10.1007/s11538-015-0098-0</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/lincomp.jl#L16-L27">source</a></section></article><h2 id="Discrete-time-systems"><a class="docs-heading-anchor" href="#Discrete-time-systems">Discrete-time systems</a><a id="Discrete-time-systems-1"></a><a class="docs-heading-anchor-permalink" href="#Discrete-time-systems" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.@DDSmodel" href="#StructuralIdentifiability.@DDSmodel"><code>StructuralIdentifiability.@DDSmodel</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">macro DDSmodel</code></pre><p>Macro for creating a DDS (discrete dynamical system)  from a list of equations. It also injects all variables into the global scope.</p><p><strong>Example</strong></p><p>Creating a simple <code>DDS</code>:</p><pre><code class="language-julia hljs">using StructuralIdentifiability
 
 dds = @DDSmodel(
     x1(t + 1) = a * x1(t) + u(t),
     x2(t + 1) = b * x2(t) + c*x1(t)*x2(t),
     y(t) = x1(t)
-)</code></pre><p>Here,</p><ul><li><code>x1</code>, <code>x2</code> are state variables</li><li><code>y</code> is an output variable</li><li><code>u</code> is an input variable</li><li><code>a</code>, <code>b</code>, <code>c</code> are time-independent parameters</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/input_macro.jl#L275-L302">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/reparametrization/">« Reparametrizations</a><a class="docs-footer-nextpage" href="../../identifiability/identifiability/">Functions to Assess Identifiability »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre><p>Here,</p><ul><li><code>x1</code>, <code>x2</code> are state variables</li><li><code>y</code> is an output variable</li><li><code>u</code> is an input variable</li><li><code>a</code>, <code>b</code>, <code>c</code> are time-independent parameters</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/input_macro.jl#L275-L302">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/reparametrization/">« Reparametrizations</a><a class="docs-footer-nextpage" href="../../identifiability/identifiability/">Functions to Assess Identifiability »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/ioequations/ioequations.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Finding-Input-Output-Equations"><a class="docs-heading-anchor" href="#Finding-Input-Output-Equations">Finding Input-Output Equations</a><a id="Finding-Input-Output-Equations-1"></a><a class="docs-heading-anchor-permalink" href="#Finding-Input-Output-Equations" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_ioequations" href="#StructuralIdentifiability.find_ioequations"><code>StructuralIdentifiability.find_ioequations</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">find_ioequations(ode, [var_change_policy=:default])</code></pre><p>Finds the input-output equations of an ODE system Input:</p><ul><li><code>ode</code> - the ODE system</li><li><code>var_change_policy</code> - whether to perform automatic variable change, can be one of <code>:default</code>, <code>:yes</code>, <code>:no</code></li><li><code>loglevel</code> - logging level (default: Logging.Info)</li></ul><p>Output:</p><ul><li>a dictionary from “leaders” to the corresponding input-output equations; if an extra projection is needed, it will be the value corresponding to <code>rand_proj_var</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/io_equation.jl#L332-L344">source</a></section></article><h1 id="Reducing-with-respect-to-Input-Output-Equations"><a class="docs-heading-anchor" href="#Reducing-with-respect-to-Input-Output-Equations">Reducing with respect to Input-Output Equations</a><a id="Reducing-with-respect-to-Input-Output-Equations-1"></a><a class="docs-heading-anchor-permalink" href="#Reducing-with-respect-to-Input-Output-Equations" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.PBRepresentation" href="#StructuralIdentifiability.PBRepresentation"><code>StructuralIdentifiability.PBRepresentation</code></a> — <span class="docstring-category">Type</span></header><section><div><p>The structure for storing a projection-based representation of differential ideal (see Section 2.3 https://arxiv.org/abs/2111.00991). Contains the following fields:</p><ul><li><code>y_names</code> - the names of the variables with finite order in the profile (typically, outputs)</li><li><code>u_names</code> - the names of the variables with infinite order in the profile (typically, inputs)</li><li><code>param_names</code> - the names of the parameters</li><li><code>profile</code> - the profile of the PB-representation (see Definition 2.13) as a dict from <code>y_names</code> with finite orders to the orders</li><li><code>projections</code> - the corresponding projections (see Definition 2.15) as a dict from <code>y_names</code> to the projections</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/pb_representation.jl#L1-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.pseudodivision" href="#StructuralIdentifiability.pseudodivision"><code>StructuralIdentifiability.pseudodivision</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">pseudodivision(f, g, x)</code></pre><p>Computes the result of pseudodivision of <code>f</code> by <code>g</code> as univariate polynomials in <code>x</code> Input:</p><ul><li><code>f</code> - the polynomial to be divided</li><li><code>g</code> - the polynomial to divide by</li><li><code>x</code> - the variable for the division</li></ul><p>Output: the pseudoremainder of <code>f</code> divided by <code>g</code> w.r.t. <code>x</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/pb_representation.jl#L166-L176">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.diffreduce" href="#StructuralIdentifiability.diffreduce"><code>StructuralIdentifiability.diffreduce</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">diffreduce(diffpoly, pbr)</code></pre><p>Computes the result of differential reduction of a differential polynomial <code>diffpoly</code> with respect to the charset defined by a PB-representation <code>pbr</code> Input:</p><ul><li><code>diffpoly</code> - a polynomial representing a differential polynomial to be reduced</li><li><code>pbr</code> - a projection-based representation</li></ul><p>Output: the result of differential reduction of <code>diffpoly</code> by <code>pbr</code> considered as a characteristic set (see Remark 2.20 in the paper)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/pb_representation.jl#L205-L215">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.io_switch!" href="#StructuralIdentifiability.io_switch!"><code>StructuralIdentifiability.io_switch!</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">io_switch(pbr)</code></pre><p>In a single-output pb-representation <code>pbr</code> makes the leading variable to be the first of the inputs</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/pb_representation.jl#L242-L246">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../utils/wronskian/">« Wronskian Tools</a><a class="docs-footer-nextpage" href="../../utils/util/">Other Utilities »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/ioequations/ioequations.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Finding-Input-Output-Equations"><a class="docs-heading-anchor" href="#Finding-Input-Output-Equations">Finding Input-Output Equations</a><a id="Finding-Input-Output-Equations-1"></a><a class="docs-heading-anchor-permalink" href="#Finding-Input-Output-Equations" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_ioequations" href="#StructuralIdentifiability.find_ioequations"><code>StructuralIdentifiability.find_ioequations</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">find_ioequations(ode, [var_change_policy=:default])</code></pre><p>Finds the input-output equations of an ODE system Input:</p><ul><li><code>ode</code> - the ODE system</li><li><code>var_change_policy</code> - whether to perform automatic variable change, can be one of <code>:default</code>, <code>:yes</code>, <code>:no</code></li><li><code>loglevel</code> - logging level (default: Logging.Info)</li></ul><p>Output:</p><ul><li>a dictionary from “leaders” to the corresponding input-output equations; if an extra projection is needed, it will be the value corresponding to <code>rand_proj_var</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/io_equation.jl#L332-L344">source</a></section></article><h1 id="Reducing-with-respect-to-Input-Output-Equations"><a class="docs-heading-anchor" href="#Reducing-with-respect-to-Input-Output-Equations">Reducing with respect to Input-Output Equations</a><a id="Reducing-with-respect-to-Input-Output-Equations-1"></a><a class="docs-heading-anchor-permalink" href="#Reducing-with-respect-to-Input-Output-Equations" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.PBRepresentation" href="#StructuralIdentifiability.PBRepresentation"><code>StructuralIdentifiability.PBRepresentation</code></a> — <span class="docstring-category">Type</span></header><section><div><p>The structure for storing a projection-based representation of differential ideal (see Section 2.3 https://arxiv.org/abs/2111.00991). Contains the following fields:</p><ul><li><code>y_names</code> - the names of the variables with finite order in the profile (typically, outputs)</li><li><code>u_names</code> - the names of the variables with infinite order in the profile (typically, inputs)</li><li><code>param_names</code> - the names of the parameters</li><li><code>profile</code> - the profile of the PB-representation (see Definition 2.13) as a dict from <code>y_names</code> with finite orders to the orders</li><li><code>projections</code> - the corresponding projections (see Definition 2.15) as a dict from <code>y_names</code> to the projections</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/pb_representation.jl#L1-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.pseudodivision" href="#StructuralIdentifiability.pseudodivision"><code>StructuralIdentifiability.pseudodivision</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">pseudodivision(f, g, x)</code></pre><p>Computes the result of pseudodivision of <code>f</code> by <code>g</code> as univariate polynomials in <code>x</code> Input:</p><ul><li><code>f</code> - the polynomial to be divided</li><li><code>g</code> - the polynomial to divide by</li><li><code>x</code> - the variable for the division</li></ul><p>Output: the pseudoremainder of <code>f</code> divided by <code>g</code> w.r.t. <code>x</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/pb_representation.jl#L166-L176">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.diffreduce" href="#StructuralIdentifiability.diffreduce"><code>StructuralIdentifiability.diffreduce</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">diffreduce(diffpoly, pbr)</code></pre><p>Computes the result of differential reduction of a differential polynomial <code>diffpoly</code> with respect to the charset defined by a PB-representation <code>pbr</code> Input:</p><ul><li><code>diffpoly</code> - a polynomial representing a differential polynomial to be reduced</li><li><code>pbr</code> - a projection-based representation</li></ul><p>Output: the result of differential reduction of <code>diffpoly</code> by <code>pbr</code> considered as a characteristic set (see Remark 2.20 in the paper)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/pb_representation.jl#L205-L215">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.io_switch!" href="#StructuralIdentifiability.io_switch!"><code>StructuralIdentifiability.io_switch!</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">io_switch(pbr)</code></pre><p>In a single-output pb-representation <code>pbr</code> makes the leading variable to be the first of the inputs</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/pb_representation.jl#L242-L246">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../utils/wronskian/">« Wronskian Tools</a><a class="docs-footer-nextpage" href="../../utils/util/">Other Utilities »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/objects.inv b/dev/objects.inv
index ba2459ee..c19fb115 100644
Binary files a/dev/objects.inv and b/dev/objects.inv differ
diff --git a/dev/tutorials/creating_ode/index.html b/dev/tutorials/creating_ode/index.html
index 6c642463..1b3a316c 100644
--- a/dev/tutorials/creating_ode/index.html
+++ b/dev/tutorials/creating_ode/index.html
@@ -57,4 +57,4 @@
   c2    =&gt; :nonidentifiable
   chi2  =&gt; :globally
   r2    =&gt; :globally
-  beta2 =&gt; :globally</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>D. H. Wright, <a href="https://doi.org/10.1086/285003"><em>A Simple, Stable Model of Mutualism Incorporating Handling Time</em></a>, The American Naturalist, 1989, 134(4).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../identifiability/">Identifiability of Differential Models (Local and Global) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+  beta2 =&gt; :globally</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>D. H. Wright, <a href="https://doi.org/10.1086/285003"><em>A Simple, Stable Model of Mutualism Incorporating Handling Time</em></a>, The American Naturalist, 1989, 134(4).</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../identifiability/">Identifiability of Differential Models (Local and Global) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/discrete_time/index.html b/dev/tutorials/discrete_time/index.html
index 19e279a4..c0e74b6d 100644
--- a/dev/tutorials/discrete_time/index.html
+++ b/dev/tutorials/discrete_time/index.html
@@ -40,4 +40,4 @@
   S(t) =&gt; 1
   I(t) =&gt; 1
   R(t) =&gt; 0</code></pre><p>For each parameter or state, the value in the returned dictionary is <code>true</code> (<code>1</code>) if the parameter is locally identifiable and <code>false</code> (<code>0</code>) otherwise. We see that <code>R(t)</code> is not identifiable, which makes sense: it does not affect the dynamics of the observable in any way.</p><p>The <code>assess_local_identifiability</code> function has three important keyword arguments:</p><ul><li><code>funcs_to_check</code> is a list of functions for which one want to assess identifiability, for example, the following code will check if <code>β * S</code> is locally identifiable.</li></ul><pre><code class="language-julia hljs">assess_local_identifiability(dds; funcs_to_check = [β * S])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">OrderedCollections.OrderedDict{Any, Bool} with 1 entry:
-  S(t)*β =&gt; 1</code></pre><ul><li><p><code>prob_threshold</code> is the probability of correctness (default value <code>0.99</code>, i.e., 99%). The underlying algorithm is a Monte-Carlo algorithm, so in principle it may produce incorrect result but the probability of correctness of the returned result is guaranteed to be at least <code>prob_threshold</code> (in fact, the employed bounds are quite conservative, so in practice incorrect result is almost never produced).</p></li><li><p><code>known_ic</code> is a list of the states for which initial conditions are known. In this case, the identifiability results will be valid not at any time point <code>t</code> but only at <code>t = 0</code>.</p></li></ul><p>As other main functions in the package, <code>assess_local_identifiability</code> accepts an optional parameter <code>loglevel</code> (default: <code>Logging.Info</code>) to adjust the verbosity of logging.</p><p>The implementation is based on a version of the observability rank criterion and will be described in a forthcoming paper.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>S. Nõmm, C. Moog, <a href="https://doi.org/10.1016/S1474-6670(17)31245-4"><em>Identifiability of discrete-time nonlinear systems</em></a>, IFAC Proceedings Volumes, 2004.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../identifiable_functions/">« Globally Identifiable Functions</a><a class="docs-footer-nextpage" href="../reparametrization/">Reparametrizations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+  S(t)*β =&gt; 1</code></pre><ul><li><p><code>prob_threshold</code> is the probability of correctness (default value <code>0.99</code>, i.e., 99%). The underlying algorithm is a Monte-Carlo algorithm, so in principle it may produce incorrect result but the probability of correctness of the returned result is guaranteed to be at least <code>prob_threshold</code> (in fact, the employed bounds are quite conservative, so in practice incorrect result is almost never produced).</p></li><li><p><code>known_ic</code> is a list of the states for which initial conditions are known. In this case, the identifiability results will be valid not at any time point <code>t</code> but only at <code>t = 0</code>.</p></li></ul><p>As other main functions in the package, <code>assess_local_identifiability</code> accepts an optional parameter <code>loglevel</code> (default: <code>Logging.Info</code>) to adjust the verbosity of logging.</p><p>The implementation is based on a version of the observability rank criterion and will be described in a forthcoming paper.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>S. Nõmm, C. Moog, <a href="https://doi.org/10.1016/S1474-6670(17)31245-4"><em>Identifiability of discrete-time nonlinear systems</em></a>, IFAC Proceedings Volumes, 2004.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../identifiable_functions/">« Globally Identifiable Functions</a><a class="docs-footer-nextpage" href="../reparametrization/">Reparametrizations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/identifiability/index.html b/dev/tutorials/identifiability/index.html
index e00a9aba..366bc140 100644
--- a/dev/tutorials/identifiability/index.html
+++ b/dev/tutorials/identifiability/index.html
@@ -59,4 +59,4 @@
   c     =&gt; :globally
   delta =&gt; :locally
   gama  =&gt; :locally
-  sigma =&gt; :globally</code></pre><p>And we see that now <code>alpha</code> and <code>gama</code> become locally identifiable.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>A. Sedoglavic, <a href="https://doi.org/10.1006/jsco.2002.0532"><em>A probabilistic algorithm to test local algebraic observability in polynomial time</em></a>, Journal of Symbolic Computation, 2002.</p></blockquote></li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a><blockquote><p>A. Ovchinnikov, A. Pillay, G. Pogudin, T. Scanlon, <a href="https://doi.org/10.1137/21M1389845"><em>Multi-experiment Parameter Identifiability of ODEs and Model Theory</em></a>, SIAM Journal on Applied Algebra and Geometry, 2022.</p></blockquote></li><li class="footnote" id="footnote-3"><a class="tag is-link" href="#citeref-3">3</a><blockquote><p>D. Gonze, P. Ruoff, <a href="https://doi.org/10.1007/s10441-020-09379-8"><em>The Goodwin Oscillator and its Legacy</em></a>, Acta Biotheoretica, 2020.</p></blockquote></li><li class="footnote" id="footnote-4"><a class="tag is-link" href="#citeref-4">4</a><blockquote><p>R. Dong, C. Goodbrake, H. Harrington, G. Pogudin, <a href="https://doi.org/10.1137/22M1469067"><em>Differential elimination for dynamical models via projections with applications to structural identifiability</em></a>, SIAM Journal on Applied Algebra and Geometry, 2023.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../creating_ode/">« Creating ODE System</a><a class="docs-footer-nextpage" href="../identifiable_functions/">Globally Identifiable Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+  sigma =&gt; :globally</code></pre><p>And we see that now <code>alpha</code> and <code>gama</code> become locally identifiable.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>A. Sedoglavic, <a href="https://doi.org/10.1006/jsco.2002.0532"><em>A probabilistic algorithm to test local algebraic observability in polynomial time</em></a>, Journal of Symbolic Computation, 2002.</p></blockquote></li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a><blockquote><p>A. Ovchinnikov, A. Pillay, G. Pogudin, T. Scanlon, <a href="https://doi.org/10.1137/21M1389845"><em>Multi-experiment Parameter Identifiability of ODEs and Model Theory</em></a>, SIAM Journal on Applied Algebra and Geometry, 2022.</p></blockquote></li><li class="footnote" id="footnote-3"><a class="tag is-link" href="#citeref-3">3</a><blockquote><p>D. Gonze, P. Ruoff, <a href="https://doi.org/10.1007/s10441-020-09379-8"><em>The Goodwin Oscillator and its Legacy</em></a>, Acta Biotheoretica, 2020.</p></blockquote></li><li class="footnote" id="footnote-4"><a class="tag is-link" href="#citeref-4">4</a><blockquote><p>R. Dong, C. Goodbrake, H. Harrington, G. Pogudin, <a href="https://doi.org/10.1137/22M1469067"><em>Differential elimination for dynamical models via projections with applications to structural identifiability</em></a>, SIAM Journal on Applied Algebra and Geometry, 2023.</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../creating_ode/">« Creating ODE System</a><a class="docs-footer-nextpage" href="../identifiable_functions/">Globally Identifiable Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/identifiable_functions/index.html b/dev/tutorials/identifiable_functions/index.html
index a5ba3bfa..2ad72d17 100644
--- a/dev/tutorials/identifiable_functions/index.html
+++ b/dev/tutorials/identifiable_functions/index.html
@@ -30,4 +30,4 @@
  p1*p3
  p1 + p3
  p2*x2(0) + p4*x1(0)
- (-p1*x2(0) + p3*x2(0))//(p2*x2(0) - p4*x1(0))</code></pre><p>We see that <code>x2(0)</code> becomes an identifiable function as well, which is natural since <code>x1(t) * x2(t)</code> was an identifiable function before.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>Y. Lecourtier, F. Lamnabhi-Lagarrigue, and E. Walter, <a href="https://doi.org/10.1109/CDC.1987.272467"><em>A method to prove that nonlinear models can be unidentifiable</em></a>, Proceedings of the 26th Conference on Decision and Control, December 1987, 2144-2145;</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../identifiability/">« Identifiability of Differential Models (Local and Global)</a><a class="docs-footer-nextpage" href="../discrete_time/">Identifiability of Discrete-Time Models (Local) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ (-p1*x2(0) + p3*x2(0))//(p2*x2(0) - p4*x1(0))</code></pre><p>We see that <code>x2(0)</code> becomes an identifiable function as well, which is natural since <code>x1(t) * x2(t)</code> was an identifiable function before.</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>Y. Lecourtier, F. Lamnabhi-Lagarrigue, and E. Walter, <a href="https://doi.org/10.1109/CDC.1987.272467"><em>A method to prove that nonlinear models can be unidentifiable</em></a>, Proceedings of the 26th Conference on Decision and Control, December 1987, 2144-2145;</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../identifiability/">« Identifiability of Differential Models (Local and Global)</a><a class="docs-footer-nextpage" href="../discrete_time/">Identifiability of Discrete-Time Models (Local) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/tutorials/reparametrization/index.html b/dev/tutorials/reparametrization/index.html
index f447ccc5..c0a15169 100644
--- a/dev/tutorials/reparametrization/index.html
+++ b/dev/tutorials/reparametrization/index.html
@@ -60,4 +60,4 @@
   X4(t) =&gt; :globally
   a1    =&gt; :globally
   a2    =&gt; :globally
-  a3    =&gt; :globally</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>T. Sauer, T. Berry, D. Ebeigbe, M. Norton, A. Whalen, S. Schiff, <a href="https://doi.org/10.1137/20m1353289"><em>Identifiability of infection model parameters early in an epidemic</em></a>, SIAM Journal on Control and Optimization, 2022;</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../discrete_time/">« Identifiability of Discrete-Time Models (Local)</a><a class="docs-footer-nextpage" href="../../input/input/">Parsing input system »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+  a3    =&gt; :globally</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a><blockquote><p>T. Sauer, T. Berry, D. Ebeigbe, M. Norton, A. Whalen, S. Schiff, <a href="https://doi.org/10.1137/20m1353289"><em>Identifiability of infection model parameters early in an epidemic</em></a>, SIAM Journal on Control and Optimization, 2022;</p></blockquote></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../discrete_time/">« Identifiability of Discrete-Time Models (Local)</a><a class="docs-footer-nextpage" href="../../input/input/">Parsing input system »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/elimination/index.html b/dev/utils/elimination/index.html
index bb6fe629..a7a4bb67 100644
--- a/dev/utils/elimination/index.html
+++ b/dev/utils/elimination/index.html
@@ -3,4 +3,4 @@
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href="../local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../global_identifiability/">Global Identifiability Tools</a></li><li class="is-active"><a class="tocitem" href>Elimination</a></li><li><a class="tocitem" href="../ode/">ODE Tools</a></li><li><a class="tocitem" href="../power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../primality/">Primality Checks</a></li><li><a class="tocitem" href="../wronskian/">Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output Equation tools</a></li><li><a class="tocitem" href="../util/">Other Utilities</a></li></ul></li><li><span class="tocitem">Export</span><ul><li><a class="tocitem" href="../../export/export/">Exporting to Other Systems</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control 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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Elimination"><a class="docs-heading-anchor" href="#Elimination">Elimination</a><a id="Elimination-1"></a><a class="docs-heading-anchor-permalink" href="#Elimination" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Bezout_matrix</code></a></li><li><a href="#StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Sylvester_matrix</code></a></li><li><a href="#StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.choose</code></a></li><li><a href="#StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.eliminate_var</code></a></li><li><a href="#StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.simplify_matrix</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Bezout_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">Bezout_matrix(f, g, var_elim)</code></pre><p>Compute the Bezout matrix of two polynomials f, g with respect to var_elim</p><p>Inputs:</p><ul><li><code>f</code> - first polynomial</li><li><code>g</code> - second polynomial</li><li><code>var_elim</code> - variable, of which f and g are considered as polynomials</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - The Bezout matrix</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/elimination.jl#L48-L60">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Sylvester_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">Sylvester_matrix(f, g, var_elim)</code></pre><p>Compute the Sylvester matrix of two polynomials f, g with respect to var_elim Inputs:</p><ul><li><code>f</code> - first polynomial</li><li><code>g</code> - second polynomial</li><li><code>var_elim</code> - variable, of which f and g are considered as polynomials</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - The Sylvester matrix</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/elimination.jl#L83-L93">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.choose</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">choose(polys, generic_point_generator)</code></pre><p>Input:</p><ul><li><code>polys</code> - an array of distinct irreducible polynomials in the same ring</li><li><code>generic_point_generator</code> - a generic point generator as described above for one of polys</li></ul><p>Output:</p><ul><li>the polynomial that vanishes at the <code>generic_point_generator</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/elimination.jl#L266-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.eliminate_var</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">eliminate_var(f, g, var_elim, generic_point_generator)</code></pre><p>Eliminate a variable from a pair of polynomials</p><p>Input:</p><ul><li><code>f</code> and <code>g</code> - polynomials</li><li><code>var_elim</code> - variable to be eliminated</li><li><code>generic_point_generator</code> - a generic point generator object for the factor     of the resultant of <code>f</code> and <code>g</code> of interest</li></ul><p>Output:</p><ul><li><code>polynomial</code> - the desired factor of the resultant of <code>f</code> and <code>g</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/elimination.jl#L294-L307">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.simplify_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">simplify_matrix(M)</code></pre><p>Eliminate GCD of entries of every row and column</p><p>Input:</p><ul><li><code>M::MatrixElem</code> - matrix to be simplified</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - Simplified matrix</li><li><code>extra_factors::Vector{AbstractAlgebra.MPolyRingElem}</code> - array of GCDs eliminated from <code>M</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/elimination.jl#L117-L128">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../global_identifiability/">« Global Identifiability Tools</a><a class="docs-footer-nextpage" href="../ode/">ODE Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Elimination"><a class="docs-heading-anchor" href="#Elimination">Elimination</a><a id="Elimination-1"></a><a class="docs-heading-anchor-permalink" href="#Elimination" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Bezout_matrix</code></a></li><li><a href="#StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Sylvester_matrix</code></a></li><li><a href="#StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.choose</code></a></li><li><a href="#StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.eliminate_var</code></a></li><li><a href="#StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.simplify_matrix</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.Bezout_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Bezout_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">Bezout_matrix(f, g, var_elim)</code></pre><p>Compute the Bezout matrix of two polynomials f, g with respect to var_elim</p><p>Inputs:</p><ul><li><code>f</code> - first polynomial</li><li><code>g</code> - second polynomial</li><li><code>var_elim</code> - variable, of which f and g are considered as polynomials</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - The Bezout matrix</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/elimination.jl#L48-L60">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.Sylvester_matrix-Union{Tuple{P}, Tuple{P, P, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.Sylvester_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">Sylvester_matrix(f, g, var_elim)</code></pre><p>Compute the Sylvester matrix of two polynomials f, g with respect to var_elim Inputs:</p><ul><li><code>f</code> - first polynomial</li><li><code>g</code> - second polynomial</li><li><code>var_elim</code> - variable, of which f and g are considered as polynomials</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - The Sylvester matrix</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/elimination.jl#L83-L93">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability.choose-Union{Tuple{P}, Tuple{Vector{P}, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.choose</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">choose(polys, generic_point_generator)</code></pre><p>Input:</p><ul><li><code>polys</code> - an array of distinct irreducible polynomials in the same ring</li><li><code>generic_point_generator</code> - a generic point generator as described above for one of polys</li></ul><p>Output:</p><ul><li>the polynomial that vanishes at the <code>generic_point_generator</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/elimination.jl#L266-L275">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability.eliminate_var-Union{Tuple{P}, Tuple{P, P, P, Any}} where P&lt;:(AbstractAlgebra.MPolyRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability.eliminate_var</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">eliminate_var(f, g, var_elim, generic_point_generator)</code></pre><p>Eliminate a variable from a pair of polynomials</p><p>Input:</p><ul><li><code>f</code> and <code>g</code> - polynomials</li><li><code>var_elim</code> - variable to be eliminated</li><li><code>generic_point_generator</code> - a generic point generator object for the factor     of the resultant of <code>f</code> and <code>g</code> of interest</li></ul><p>Output:</p><ul><li><code>polynomial</code> - the desired factor of the resultant of <code>f</code> and <code>g</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/elimination.jl#L294-L307">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.simplify_matrix-Union{Tuple{AbstractAlgebra.MatElem{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.simplify_matrix</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">simplify_matrix(M)</code></pre><p>Eliminate GCD of entries of every row and column</p><p>Input:</p><ul><li><code>M::MatrixElem</code> - matrix to be simplified</li></ul><p>Output:</p><ul><li><code>M::MatrixElem</code> - Simplified matrix</li><li><code>extra_factors::Vector{AbstractAlgebra.MPolyRingElem}</code> - array of GCDs eliminated from <code>M</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/elimination.jl#L117-L128">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../global_identifiability/">« Global Identifiability Tools</a><a class="docs-footer-nextpage" href="../ode/">ODE Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/global_identifiability/index.html b/dev/utils/global_identifiability/index.html
index 8ffdfb2b..861e0ff6 100644
--- a/dev/utils/global_identifiability/index.html
+++ b/dev/utils/global_identifiability/index.html
@@ -12,4 +12,4 @@
 rff = RationalFunctionField([x // y, y // z])
 
 # Constructs a subfield generated by y / x, 1 / x, z / y
-rff = RationalFunctionField([[x, y, R(1)], [y, z]])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/RationalFunctionFields/RationalFunctionField.jl#L2-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.field_contains" href="#StructuralIdentifiability.field_contains"><code>StructuralIdentifiability.field_contains</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">field_contains(field, ratfuncs, prob_threshold)</code></pre><p>Checks whether given rational function field <code>field</code> contains given rational functions <code>ratfuncs</code> (represented as a list of lists). The result is correct with probability at least <code>prob_threshold</code></p><p>Inputs:</p><ul><li><code>field</code> - a rational function field</li><li><code>ratfuncs</code> - a list of lists of polynomials. Each of the lists, say, <code>[f1, ..., fn]</code>, defines generators <code>f2/f1, ..., fn/f1</code>.</li><li><code>prob_threshold</code> real number from (0, 1)</li></ul><p>Output:</p><ul><li>a list <code>L[i]</code> of bools of length <code>length(rat_funcs)</code> such that <code>L[i]</code> is true iff  the i-th function belongs to <code>field</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/RationalFunctionFields/RationalFunctionField.jl#L82-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.get_degree_and_coeffsize" href="#StructuralIdentifiability.get_degree_and_coeffsize"><code>StructuralIdentifiability.get_degree_and_coeffsize</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">get_degree_and_coeffsize(f)</code></pre><p>for <code>f</code> being a polynomial/rational function over rationals (<code>QQ</code>) returns a tuple <code>(degree, max_coef_size)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/local_identifiability.jl#L121-L126">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../local_identifiability/">« Local Identifiability Tools</a><a class="docs-footer-nextpage" href="../elimination/">Elimination »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+rff = RationalFunctionField([[x, y, R(1)], [y, z]])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/RationalFunctionFields/RationalFunctionField.jl#L2-L21">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.field_contains" href="#StructuralIdentifiability.field_contains"><code>StructuralIdentifiability.field_contains</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">field_contains(field, ratfuncs, prob_threshold)</code></pre><p>Checks whether given rational function field <code>field</code> contains given rational functions <code>ratfuncs</code> (represented as a list of lists). The result is correct with probability at least <code>prob_threshold</code></p><p>Inputs:</p><ul><li><code>field</code> - a rational function field</li><li><code>ratfuncs</code> - a list of lists of polynomials. Each of the lists, say, <code>[f1, ..., fn]</code>, defines generators <code>f2/f1, ..., fn/f1</code>.</li><li><code>prob_threshold</code> real number from (0, 1)</li></ul><p>Output:</p><ul><li>a list <code>L[i]</code> of bools of length <code>length(rat_funcs)</code> such that <code>L[i]</code> is true iff  the i-th function belongs to <code>field</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/RationalFunctionFields/RationalFunctionField.jl#L82-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.get_degree_and_coeffsize" href="#StructuralIdentifiability.get_degree_and_coeffsize"><code>StructuralIdentifiability.get_degree_and_coeffsize</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">get_degree_and_coeffsize(f)</code></pre><p>for <code>f</code> being a polynomial/rational function over rationals (<code>QQ</code>) returns a tuple <code>(degree, max_coef_size)</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/local_identifiability.jl#L121-L126">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../local_identifiability/">« Local Identifiability Tools</a><a class="docs-footer-nextpage" href="../elimination/">Elimination »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/local_identifiability/index.html b/dev/utils/local_identifiability/index.html
index d2a6715d..8e20f765 100644
--- a/dev/utils/local_identifiability/index.html
+++ b/dev/utils/local_identifiability/index.html
@@ -3,4 +3,4 @@
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class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Local-Identifiability-Tools"><a class="docs-heading-anchor" href="#Local-Identifiability-Tools">Local Identifiability Tools</a><a id="Local-Identifiability-Tools-1"></a><a class="docs-heading-anchor-permalink" href="#Local-Identifiability-Tools" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.differentiate_output"><code>StructuralIdentifiability.differentiate_output</code></a></li><li><a href="#StructuralIdentifiability.differentiate_solution"><code>StructuralIdentifiability.differentiate_solution</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.differentiate_solution" href="#StructuralIdentifiability.differentiate_solution"><code>StructuralIdentifiability.differentiate_solution</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">differentiate_solution(ode, params, ic, inputs, prec)</code></pre><p>Input:</p><ul><li>the same as for <code>power_series_solutions</code></li></ul><p>Output:</p><ul><li>a tuple consisting of the power series solution and a dictionary of the form <code>(u, v) =&gt; power series</code>, where <code>u</code> is a state variable <code>v</code> is a state or parameter, and the power series is the partial derivative of the function <code>u</code> w.r.t. <code>v</code> evaluated at the solution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/local_identifiability.jl#L16-L26">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.differentiate_output" href="#StructuralIdentifiability.differentiate_output"><code>StructuralIdentifiability.differentiate_output</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">differentiate_output(ode, params, ic, inputs, prec)</code></pre><p>Similar to <code>differentiate_solution</code> but computes partial derivatives of prescribed outputs returns a dictionary of the form <code>y_function =&gt; Dict(var =&gt; dy/dvar)</code> where <code>dy/dvar</code> is the derivative of <code>y_function</code> with respect to <code>var</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/local_identifiability.jl#L76-L82">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../identifiability/identifiability/">« Functions to Assess Identifiability</a><a class="docs-footer-nextpage" href="../global_identifiability/">Global Identifiability Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label 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class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Local-Identifiability-Tools"><a class="docs-heading-anchor" href="#Local-Identifiability-Tools">Local Identifiability Tools</a><a id="Local-Identifiability-Tools-1"></a><a class="docs-heading-anchor-permalink" href="#Local-Identifiability-Tools" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.differentiate_output"><code>StructuralIdentifiability.differentiate_output</code></a></li><li><a href="#StructuralIdentifiability.differentiate_solution"><code>StructuralIdentifiability.differentiate_solution</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.differentiate_solution" href="#StructuralIdentifiability.differentiate_solution"><code>StructuralIdentifiability.differentiate_solution</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">differentiate_solution(ode, params, ic, inputs, prec)</code></pre><p>Input:</p><ul><li>the same as for <code>power_series_solutions</code></li></ul><p>Output:</p><ul><li>a tuple consisting of the power series solution and a dictionary of the form <code>(u, v) =&gt; power series</code>, where <code>u</code> is a state variable <code>v</code> is a state or parameter, and the power series is the partial derivative of the function <code>u</code> w.r.t. <code>v</code> evaluated at the solution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/local_identifiability.jl#L16-L26">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.differentiate_output" href="#StructuralIdentifiability.differentiate_output"><code>StructuralIdentifiability.differentiate_output</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">differentiate_output(ode, params, ic, inputs, prec)</code></pre><p>Similar to <code>differentiate_solution</code> but computes partial derivatives of prescribed outputs returns a dictionary of the form <code>y_function =&gt; Dict(var =&gt; dy/dvar)</code> where <code>dy/dvar</code> is the derivative of <code>y_function</code> with respect to <code>var</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/local_identifiability.jl#L76-L82">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../identifiability/identifiability/">« Functions to Assess Identifiability</a><a class="docs-footer-nextpage" href="../global_identifiability/">Global Identifiability Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label 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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Functions-to-work-with-the-ODE-structure"><a class="docs-heading-anchor" href="#Functions-to-work-with-the-ODE-structure">Functions to work with the ODE structure</a><a id="Functions-to-work-with-the-ODE-structure-1"></a><a class="docs-heading-anchor-permalink" href="#Functions-to-work-with-the-ODE-structure" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability._reduce_mod_p-Tuple{Nemo.QQMPolyRingElem, Int64}" href="#StructuralIdentifiability._reduce_mod_p-Tuple{Nemo.QQMPolyRingElem, Int64}"><code>StructuralIdentifiability._reduce_mod_p</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_reduce_mod_p(f, p)</code></pre><p>Reduces a polynomial/rational function over Q modulo p</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L214-L218">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.power_series_solution-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.power_series_solution-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.power_series_solution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">power_series_solution(ode, param_values, initial_conditions, input_values, prec)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ode to solve</li><li><code>param_values</code> - parameter values, must be a dictionary mapping parameter to a value</li><li><code>initial_conditions</code> - initial conditions of <code>ode</code>, must be a dictionary mapping state variable to a value</li><li><code>input_values</code> - power series for the inputs presented as a dictionary variable =&gt; list of coefficients</li><li><code>prec</code> - the precision of solutions</li></ul><p>Output:</p><ul><li>computes a power series solution with precision prec presented as a dictionary variable =&gt; corresponding coordinate of the solution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L143-L155">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.reduce_ode_mod_p-Tuple{ODE{&lt;:AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}, Int64}" href="#StructuralIdentifiability.reduce_ode_mod_p-Tuple{ODE{&lt;:AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}, Int64}"><code>StructuralIdentifiability.reduce_ode_mod_p</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">reduce_ode_mod_p(ode, p)</code></pre><p>Input: ode is an ODE over QQ, p is a prime number Output: the reduction mod p, throws an exception if p divides one of the denominators</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L238-L243">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.set_parameter_values-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.set_parameter_values-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.set_parameter_values</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">set_parameter_values(ode, param_values)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ODE as above</li><li><code>param_values</code> - values for (possibly, some of) the parameters as dictionary <code>parameter</code> =&gt; <code>value</code></li></ul><p>Output:</p><ul><li>new ode with the parameters in param_values plugged with the given numbers</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/ODE.jl#L87-L96">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_submodels-Union{Tuple{ODE{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.find_submodels-Union{Tuple{ODE{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.find_submodels</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">find_submodels(ode)</code></pre><p>The function calculates and returns all valid submodels given a system of ODEs.</p><p>Input:</p><ul><li><code>ode</code> - an ODEs system to be studied</li></ul><p>Output: </p><ul><li>A list of submodels represented as <code>ode</code> objects</li></ul><p>Example:</p><pre><code class="nohighlight hljs">&gt;ode = @ODEmodel(x1&#39;(t) = x1(t)^2, 
+</script><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script 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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Functions-to-work-with-the-ODE-structure"><a class="docs-heading-anchor" href="#Functions-to-work-with-the-ODE-structure">Functions to work with the ODE structure</a><a id="Functions-to-work-with-the-ODE-structure-1"></a><a class="docs-heading-anchor-permalink" href="#Functions-to-work-with-the-ODE-structure" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability._reduce_mod_p-Tuple{Nemo.QQMPolyRingElem, Int64}" href="#StructuralIdentifiability._reduce_mod_p-Tuple{Nemo.QQMPolyRingElem, Int64}"><code>StructuralIdentifiability._reduce_mod_p</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_reduce_mod_p(f, p)</code></pre><p>Reduces a polynomial/rational function over Q modulo p</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L214-L218">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.power_series_solution-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.power_series_solution-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.power_series_solution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">power_series_solution(ode, param_values, initial_conditions, input_values, prec)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ode to solve</li><li><code>param_values</code> - parameter values, must be a dictionary mapping parameter to a value</li><li><code>initial_conditions</code> - initial conditions of <code>ode</code>, must be a dictionary mapping state variable to a value</li><li><code>input_values</code> - power series for the inputs presented as a dictionary variable =&gt; list of coefficients</li><li><code>prec</code> - the precision of solutions</li></ul><p>Output:</p><ul><li>computes a power series solution with precision prec presented as a dictionary variable =&gt; corresponding coordinate of the solution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L143-L155">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.reduce_ode_mod_p-Tuple{ODE{&lt;:AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}, Int64}" href="#StructuralIdentifiability.reduce_ode_mod_p-Tuple{ODE{&lt;:AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}, Int64}"><code>StructuralIdentifiability.reduce_ode_mod_p</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">reduce_ode_mod_p(ode, p)</code></pre><p>Input: ode is an ODE over QQ, p is a prime number Output: the reduction mod p, throws an exception if p divides one of the denominators</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L238-L243">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.set_parameter_values-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.set_parameter_values-Union{Tuple{P}, Tuple{T}, Tuple{ODE{P}, Dict{P, T}}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.set_parameter_values</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">set_parameter_values(ode, param_values)</code></pre><p>Input:</p><ul><li><code>ode</code> - an ODE as above</li><li><code>param_values</code> - values for (possibly, some of) the parameters as dictionary <code>parameter</code> =&gt; <code>value</code></li></ul><p>Output:</p><ul><li>new ode with the parameters in param_values plugged with the given numbers</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/ODE.jl#L87-L96">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.find_submodels-Union{Tuple{ODE{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.find_submodels-Union{Tuple{ODE{P}}, Tuple{P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.find_submodels</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">find_submodels(ode)</code></pre><p>The function calculates and returns all valid submodels given a system of ODEs.</p><p>Input:</p><ul><li><code>ode</code> - an ODEs system to be studied</li></ul><p>Output: </p><ul><li>A list of submodels represented as <code>ode</code> objects</li></ul><p>Example:</p><pre><code class="nohighlight hljs">&gt;ode = @ODEmodel(x1&#39;(t) = x1(t)^2, 
                  x2&#39;(t) = x1(t) * x2(t), 
                  y1(t) = x1(t), 
                  y2(t) = x2(t))
@@ -12,4 +12,4 @@
         
         x1&#39;(t) = a(t)*x2(t)^2 + x1(t)
         y1(t) = x1(t)
-    ]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/submodels.jl#L173-L196">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../elimination/">« Elimination</a><a class="docs-footer-nextpage" href="../power_series_utils/">Power Series Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+    ]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/submodels.jl#L173-L196">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../elimination/">« Elimination</a><a class="docs-footer-nextpage" href="../power_series_utils/">Power Series Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/power_series_utils/index.html b/dev/utils/power_series_utils/index.html
index c03a5f3c..60da2f4e 100644
--- a/dev/utils/power_series_utils/index.html
+++ b/dev/utils/power_series_utils/index.html
@@ -3,4 +3,4 @@
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class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Power-Series-Utilities"><a class="docs-heading-anchor" href="#Power-Series-Utilities">Power Series Utilities</a><a id="Power-Series-Utilities-1"></a><a class="docs-heading-anchor-permalink" href="#Power-Series-Utilities" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability._matrix_inv_newton_iteration</code></a></li><li><a href="#StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}"><code>StructuralIdentifiability.ps_diff</code></a></li><li><a href="#StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}"><code>StructuralIdentifiability.ps_integrate</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_homlinear_de</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_inv"><code>StructuralIdentifiability.ps_matrix_inv</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_linear_de</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}"><code>StructuralIdentifiability.ps_matrix_log</code></a></li><li><a href="#StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.ps_ode_solution</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability._matrix_inv_newton_iteration</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_matrix_inv_newton_iteration(M, Minv)</code></pre><p>Performs a single step of Newton iteration for inverting <code>M</code> with <code>Minv</code> being a partial result</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L21-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}" href="#StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}"><code>StructuralIdentifiability.ps_diff</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_diff(ps)</code></pre><p>Input:</p><ul><li><code>ps</code> - (absolute capped) univariate power series</li></ul><p>Output:</p><ul><li>the derivative of <code>ps</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L64-L72">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}" href="#StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}"><code>StructuralIdentifiability.ps_integrate</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_integrate(ps)</code></pre><p>Input:</p><ul><li><code>ps</code> - (absolute capped) univariate power series</li></ul><p>Output:</p><ul><li>the integral of <code>ps</code> without constant term</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L84-L91">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem" href="#StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_homlinear_de</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_homlinear_de(A, Y0, prec)</code></pre><p>Input:</p><ul><li><code>A</code> - a square matrix with entries in a univariate power series ring</li><li><code>Y0</code> - a square invertible matrix over the base field</li></ul><p>Output:</p><ul><li>matrix <code>Y</code> such that <code>Y&#39; = AY</code> up to precision of <code>A - 1</code> and <code>Y(0) = Y0</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L143-L151">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_inv" href="#StructuralIdentifiability.ps_matrix_inv"><code>StructuralIdentifiability.ps_matrix_inv</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_inv(M, prec)</code></pre><p>Input:</p><ul><li><code>M</code> - a square matrix with entries in a univariate power series ring     it is assumed that M(0) is invertible and all entries having the same precision</li><li><code>prec</code> - an integer, precision, if <code>-1</code> then defaults to precision of <code>M</code></li></ul><p>Output:</p><ul><li>the inverse of <code>M</code> computed up to <code>prec</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L35-L45">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem" href="#StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_linear_de</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_linear_de(A, B, Y0, prec)</code></pre><p>Input:</p><ul><li><code>A</code>, <code>B</code> - square matrices with entries in a univariate power series ring</li><li><code>Y0</code> - a matrix over the base field with the rows number the same as <code>A</code></li></ul><p>Output:</p><ul><li>matrix <code>Y</code> such that <code>Y&#39; = AY + B</code> up to precision of <code>A - 1</code> and <code>Y(0) = Y0</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L190-L199">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}" href="#StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}"><code>StructuralIdentifiability.ps_matrix_log</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_log(M)</code></pre><p>Input:</p><ul><li>M - a square matrix with entries in a univariate power series ring     it is assumed that <code>M(0)</code> is the identity</li></ul><p>Output:</p><ul><li>the natural log of <code>M</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L103-L111">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.ps_ode_solution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_ode_solution(equations, ic, inputs, prec)</code></pre><p>Input:</p><ul><li><code>equations</code> - a system of the form <span>$A(x, u, mu)x&#39; - B(x, u, mu) = 0$</span>,               where A is a generically nonsingular square matrix. <em>Assumption</em>: <code>A</code> is nonzero at zero</li><li><code>ic</code> - initial conditions for x&#39;s (dictionary)</li><li><code>inputs</code> - power series for inputs represented as arrays (dictionary)</li><li><code>prec</code> - precision of the solution</li></ul><p>Output:</p><ul><li>power series solution of the system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/power_series_utils.jl#L216-L228">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ode/">« ODE 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class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Power-Series-Utilities"><a class="docs-heading-anchor" href="#Power-Series-Utilities">Power Series Utilities</a><a id="Power-Series-Utilities-1"></a><a class="docs-heading-anchor-permalink" href="#Power-Series-Utilities" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability._matrix_inv_newton_iteration</code></a></li><li><a href="#StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}"><code>StructuralIdentifiability.ps_diff</code></a></li><li><a href="#StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}"><code>StructuralIdentifiability.ps_integrate</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_homlinear_de</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_inv"><code>StructuralIdentifiability.ps_matrix_inv</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_linear_de</code></a></li><li><a href="#StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}"><code>StructuralIdentifiability.ps_matrix_log</code></a></li><li><a href="#StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.ps_ode_solution</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})" href="#StructuralIdentifiability._matrix_inv_newton_iteration-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{T}, AbstractAlgebra.MatElem{T}}} where T&lt;:(AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem})"><code>StructuralIdentifiability._matrix_inv_newton_iteration</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_matrix_inv_newton_iteration(M, Minv)</code></pre><p>Performs a single step of Newton iteration for inverting <code>M</code> with <code>Minv</code> being a partial result</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L21-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}" href="#StructuralIdentifiability.ps_diff-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.RingElem}}"><code>StructuralIdentifiability.ps_diff</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_diff(ps)</code></pre><p>Input:</p><ul><li><code>ps</code> - (absolute capped) univariate power series</li></ul><p>Output:</p><ul><li>the derivative of <code>ps</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L64-L72">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}" href="#StructuralIdentifiability.ps_integrate-Tuple{AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}"><code>StructuralIdentifiability.ps_integrate</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_integrate(ps)</code></pre><p>Input:</p><ul><li><code>ps</code> - (absolute capped) univariate power series</li></ul><p>Output:</p><ul><li>the integral of <code>ps</code> without constant term</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L84-L91">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem" href="#StructuralIdentifiability.ps_matrix_homlinear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_homlinear_de</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_homlinear_de(A, Y0, prec)</code></pre><p>Input:</p><ul><li><code>A</code> - a square matrix with entries in a univariate power series ring</li><li><code>Y0</code> - a square invertible matrix over the base field</li></ul><p>Output:</p><ul><li>matrix <code>Y</code> such that <code>Y&#39; = AY</code> up to precision of <code>A - 1</code> and <code>Y(0) = Y0</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L143-L151">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_inv" href="#StructuralIdentifiability.ps_matrix_inv"><code>StructuralIdentifiability.ps_matrix_inv</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_inv(M, prec)</code></pre><p>Input:</p><ul><li><code>M</code> - a square matrix with entries in a univariate power series ring     it is assumed that M(0) is invertible and all entries having the same precision</li><li><code>prec</code> - an integer, precision, if <code>-1</code> then defaults to precision of <code>M</code></li></ul><p>Output:</p><ul><li>the inverse of <code>M</code> computed up to <code>prec</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L35-L45">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem" href="#StructuralIdentifiability.ps_matrix_linear_de-Union{Tuple{T}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}}, Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{T}}, AbstractAlgebra.MatElem{&lt;:T}, Int64}} where T&lt;:AbstractAlgebra.FieldElem"><code>StructuralIdentifiability.ps_matrix_linear_de</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_linear_de(A, B, Y0, prec)</code></pre><p>Input:</p><ul><li><code>A</code>, <code>B</code> - square matrices with entries in a univariate power series ring</li><li><code>Y0</code> - a matrix over the base field with the rows number the same as <code>A</code></li></ul><p>Output:</p><ul><li>matrix <code>Y</code> such that <code>Y&#39; = AY + B</code> up to precision of <code>A - 1</code> and <code>Y(0) = Y0</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L190-L199">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}" href="#StructuralIdentifiability.ps_matrix_log-Tuple{AbstractAlgebra.MatElem{&lt;:AbstractAlgebra.AbsPowerSeriesRingElem{&lt;:AbstractAlgebra.FieldElem}}}"><code>StructuralIdentifiability.ps_matrix_log</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_matrix_log(M)</code></pre><p>Input:</p><ul><li>M - a square matrix with entries in a univariate power series ring     it is assumed that <code>M(0)</code> is the identity</li></ul><p>Output:</p><ul><li>the natural log of <code>M</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L103-L111">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}" href="#StructuralIdentifiability.ps_ode_solution-Union{Tuple{P}, Tuple{T}, Tuple{Vector{P}, Dict{P, T}, Dict{P, Vector{T}}, Int64}} where {T&lt;:AbstractAlgebra.FieldElem, P&lt;:AbstractAlgebra.MPolyRingElem{T}}"><code>StructuralIdentifiability.ps_ode_solution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">ps_ode_solution(equations, ic, inputs, prec)</code></pre><p>Input:</p><ul><li><code>equations</code> - a system of the form <span>$A(x, u, mu)x&#39; - B(x, u, mu) = 0$</span>,               where A is a generically nonsingular square matrix. <em>Assumption</em>: <code>A</code> is nonzero at zero</li><li><code>ic</code> - initial conditions for x&#39;s (dictionary)</li><li><code>inputs</code> - power series for inputs represented as arrays (dictionary)</li><li><code>prec</code> - precision of the solution</li></ul><p>Output:</p><ul><li>power series solution of the system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/power_series_utils.jl#L216-L228">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ode/">« ODE 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title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/primality/index.html b/dev/utils/primality/index.html
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--- a/dev/utils/primality/index.html
+++ b/dev/utils/primality/index.html
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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Primality-Checks"><a class="docs-heading-anchor" href="#Primality-Checks">Primality Checks</a><a id="Primality-Checks-1"></a><a class="docs-heading-anchor-permalink" href="#Primality-Checks" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.check_primality"><code>StructuralIdentifiability.check_primality</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.check_primality" href="#StructuralIdentifiability.check_primality"><code>StructuralIdentifiability.check_primality</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">check_primality(polys::Dict{QQMPolyRingElem, QQMPolyRingElem}, extra_relations::Array{QQMPolyRingElem, 1})</code></pre><p>The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.</p><p>The <code>extra_relations</code> allows adding more polynomials to the generators (not affecting the saturation).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/primality_check.jl#L32-L40">source</a></section><section><div><pre><code class="language-julia hljs">check_primality(polys::Dict{QQMPolyRingElem, QQMPolyRingElem})</code></pre><p>The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/primality_check.jl#L58-L64">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../power_series_utils/">« Power Series Tools</a><a class="docs-footer-nextpage" href="../wronskian/">Wronskian Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button 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Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Primality-Checks"><a class="docs-heading-anchor" href="#Primality-Checks">Primality Checks</a><a id="Primality-Checks-1"></a><a class="docs-heading-anchor-permalink" href="#Primality-Checks" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.check_primality"><code>StructuralIdentifiability.check_primality</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.check_primality" href="#StructuralIdentifiability.check_primality"><code>StructuralIdentifiability.check_primality</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">check_primality(polys::Dict{QQMPolyRingElem, QQMPolyRingElem}, extra_relations::Array{QQMPolyRingElem, 1})</code></pre><p>The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.</p><p>The <code>extra_relations</code> allows adding more polynomials to the generators (not affecting the saturation).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/primality_check.jl#L32-L40">source</a></section><section><div><pre><code class="language-julia hljs">check_primality(polys::Dict{QQMPolyRingElem, QQMPolyRingElem})</code></pre><p>The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/primality_check.jl#L58-L64">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../power_series_utils/">« Power Series Tools</a><a class="docs-footer-nextpage" href="../wronskian/">Wronskian Tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button 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Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/utils/reparametrization/index.html b/dev/utils/reparametrization/index.html
index 782c1c34..269d4916 100644
--- a/dev/utils/reparametrization/index.html
+++ b/dev/utils/reparametrization/index.html
@@ -23,4 +23,4 @@
   X1 =&gt; x1
   a2 =&gt; d
   a3 =&gt; a
-  a1 =&gt; c</code></pre><p>Notice that the <code>new_ode</code> is fully identifiabile, and has <code>1</code> less parameter compared to the original one.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/parametrizations.jl#L439-L491">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+  a1 =&gt; c</code></pre><p>Notice that the <code>new_ode</code> is fully identifiabile, and has <code>1</code> less parameter compared to the original one.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/parametrizations.jl#L439-L491">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Other-Helpful-Functions"><a class="docs-heading-anchor" href="#Other-Helpful-Functions">Other Helpful Functions</a><a id="Other-Helpful-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Other-Helpful-Functions" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By"><code>StructuralIdentifiability.compare_rational_func_by</code></a></li><li><a href="#StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}"><code>StructuralIdentifiability.decompose_derivative</code></a></li><li><a href="#StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T"><code>StructuralIdentifiability.dennums_to_fractions</code></a></li><li><a href="#StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.eval_at_dict</code></a></li><li><a href="#StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.extract_coefficients</code></a></li><li><a href="#StructuralIdentifiability.fractions_to_dennums-Tuple{Any}"><code>StructuralIdentifiability.fractions_to_dennums</code></a></li><li><a href="#StructuralIdentifiability.gen_tag_name"><code>StructuralIdentifiability.gen_tag_name</code></a></li><li><a href="#StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.make_substitution</code></a></li><li><a href="#StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.parent_ring_change</code></a></li><li><a href="#StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}"><code>StructuralIdentifiability.replace_with_ic</code></a></li><li><a href="#StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.switch_ring</code></a></li><li><a href="#StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}"><code>StructuralIdentifiability.uncertain_factorization</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By" href="#StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By"><code>StructuralIdentifiability.compare_rational_func_by</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">compare_rational_func_by(f, g, by)</code></pre><p>Returns </p><ul><li><code>-1</code> if <code>f &lt; g</code>,</li><li><code>0</code> if <code>f = g</code>, and </li><li><code>1</code> if <code>f &gt; g</code>.</li></ul><p>Functions&#39; numerators and denominators are compared using <code>by</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L113-L122">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}" href="#StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}"><code>StructuralIdentifiability.decompose_derivative</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">decompose_derivative(varname, prefixes)</code></pre><p>Determines if it is possible to represent the <code>varname</code> as <code>a_number</code> where <code>a</code> is an element of <code>prefixes</code> If yes, returns a pair (a, number), otherwise nothing</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L485-L490">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T" href="#StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T"><code>StructuralIdentifiability.dennums_to_fractions</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">dennums_to_fractions(dennums)</code></pre><p>Returns the field generators represented by fractions.</p><p>Input: an array of arrays of polynomials, as in  <code>[[f1, f2, f3, ...], [g1, g2, g3, ...], ...]</code></p><p>Output: an array of fractions <code>[f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/RationalFunctionFields/util.jl#L2-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.eval_at_dict</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">eval_at_dict(f, d)</code></pre><p>Evaluates a polynomial/rational function on a dictionary of type <code>var =&gt; val</code> and missing values are replaced with zeroes</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L34-L38">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.extract_coefficients</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">extract_coefficients(poly, variables)</code></pre><p>Input:</p><ul><li><code>poly</code> - multivariate polynomial</li><li><code>variables</code> - a list of variables from the generators of the ring of p</li></ul><p>Output:</p><ul><li>dictionary with keys being tuples of length <code>length(variables)</code> and values being polynomials in the variables other than those which are the coefficients at the corresponding monomials (in a smaller polynomial ring)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L373-L381">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.fractions_to_dennums-Tuple{Any}" href="#StructuralIdentifiability.fractions_to_dennums-Tuple{Any}"><code>StructuralIdentifiability.fractions_to_dennums</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fractions_to_dennums(fractions)</code></pre><p>Returns the field generators represented by lists of denominators and numerators.</p><p>Input: an array of fractions, as in <code>[f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]</code></p><p>Output: an array of arrays of polynomials, <code>[[f1, f2, f3, ...], [g1, g2, g3, ...], ...]</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/RationalFunctionFields/util.jl#L25-L36">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.gen_tag_name" href="#StructuralIdentifiability.gen_tag_name"><code>StructuralIdentifiability.gen_tag_name</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">gen_tag_name(base; stop_words)
-gen_tag_names(n, base; stop_words)</code></pre><p>Generates a string which will not collide with the words in <code>stop_words</code>.</p><p><strong>Arguments</strong></p><ul><li><code>n</code>: Generates a sequence of unique strings of length <code>n</code></li><li><code>base</code>: A string or a vector of strings, the base for the generated sequence</li><li><code>stop_words</code>: A vector of strings, stop words</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L436-L447">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.make_substitution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">make_substitution(f, var_sub, val_numer, val_denom)</code></pre><p>Substitute a variable in a polynomial with an expression</p><p>Input:</p><ul><li><code>f</code> - the polynomial</li><li><code>var_sub</code> - the variable to be substituted</li><li><code>var_numer</code> - numerator of the substitution expression</li><li><code>var_denom</code> - denominator of the substitution expression</li></ul><p>Output:</p><ul><li><code>polynomial</code> - result of substitution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L150-L163">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}" href="#StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.parent_ring_change</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">parent_ring_change(poly, new_ring)</code></pre><p>Converts a polynomial to a different polynomial ring Input</p><ul><li><code>poly</code> - a polynomial to be converted</li><li><code>new_ring</code> - a polynomial ring such that every variable name appearing in poly appears among the generators</li></ul><p>Output:</p><ul><li>a polynomial in <code>new_ring</code> “equal” to <code>poly</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L224-L234">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}" href="#StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}"><code>StructuralIdentifiability.replace_with_ic</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">replace_with_ic(ode::ODE, funcs)</code></pre><p>Takes an ode and a list of functions in the states and parameters and makes a change of variable names <code>x(t) -&gt; x(0)</code>. Function is used to prepare the output for the case of known initial conditions</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L524-L529">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}" href="#StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.switch_ring</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">switch_ring(v, ring)</code></pre><p>For a variable <code>v</code>, returns a variable in <code>ring</code> with the same name</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L472-L476">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}" href="#StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}"><code>StructuralIdentifiability.uncertain_factorization</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">uncertain_factorization(f)</code></pre><p>Input:</p><ul><li><code>f</code> - polynomial with rational coefficients</li></ul><p>Output:</p><ul><li>list of pairs <code>(div, certainty)</code> where<ul><li><code>div</code>&#39;s are divisors of <code>f</code> such that <code>f</code> is their product with certain powers</li><li>if <code>certainty</code> is true, <code>div</code> is <span>$Q$</span>-irreducible</li></ul></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/util.jl#L297-L307">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../ioequations/ioequations/">« Input-Output Equation tools</a><a class="docs-footer-nextpage" href="../../export/export/">Exporting to Other Systems »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. 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fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Other-Helpful-Functions"><a class="docs-heading-anchor" href="#Other-Helpful-Functions">Other Helpful Functions</a><a id="Other-Helpful-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Other-Helpful-Functions" title="Permalink"></a></h1><ul><li><a href="#StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By"><code>StructuralIdentifiability.compare_rational_func_by</code></a></li><li><a href="#StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}"><code>StructuralIdentifiability.decompose_derivative</code></a></li><li><a href="#StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T"><code>StructuralIdentifiability.dennums_to_fractions</code></a></li><li><a href="#StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.eval_at_dict</code></a></li><li><a href="#StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.extract_coefficients</code></a></li><li><a href="#StructuralIdentifiability.fractions_to_dennums-Tuple{Any}"><code>StructuralIdentifiability.fractions_to_dennums</code></a></li><li><a href="#StructuralIdentifiability.gen_tag_name"><code>StructuralIdentifiability.gen_tag_name</code></a></li><li><a href="#StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.make_substitution</code></a></li><li><a href="#StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.parent_ring_change</code></a></li><li><a href="#StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}"><code>StructuralIdentifiability.replace_with_ic</code></a></li><li><a href="#StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.switch_ring</code></a></li><li><a href="#StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}"><code>StructuralIdentifiability.uncertain_factorization</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By" href="#StructuralIdentifiability.compare_rational_func_by-Union{Tuple{By}, Tuple{Any, Any, By}, Tuple{Any, Any, By, Any}} where By"><code>StructuralIdentifiability.compare_rational_func_by</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">compare_rational_func_by(f, g, by)</code></pre><p>Returns </p><ul><li><code>-1</code> if <code>f &lt; g</code>,</li><li><code>0</code> if <code>f = g</code>, and </li><li><code>1</code> if <code>f &gt; g</code>.</li></ul><p>Functions&#39; numerators and denominators are compared using <code>by</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L113-L122">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}" href="#StructuralIdentifiability.decompose_derivative-Tuple{String, Array{String}}"><code>StructuralIdentifiability.decompose_derivative</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">decompose_derivative(varname, prefixes)</code></pre><p>Determines if it is possible to represent the <code>varname</code> as <code>a_number</code> where <code>a</code> is an element of <code>prefixes</code> If yes, returns a pair (a, number), otherwise nothing</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L485-L490">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T" href="#StructuralIdentifiability.dennums_to_fractions-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T"><code>StructuralIdentifiability.dennums_to_fractions</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">dennums_to_fractions(dennums)</code></pre><p>Returns the field generators represented by fractions.</p><p>Input: an array of arrays of polynomials, as in  <code>[[f1, f2, f3, ...], [g1, g2, g3, ...], ...]</code></p><p>Output: an array of fractions <code>[f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/RationalFunctionFields/util.jl#L2-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.eval_at_dict-Union{Tuple{P}, Tuple{P, Dict{P, &lt;:AbstractAlgebra.RingElem}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.eval_at_dict</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">eval_at_dict(f, d)</code></pre><p>Evaluates a polynomial/rational function on a dictionary of type <code>var =&gt; val</code> and missing values are replaced with zeroes</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L34-L38">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.extract_coefficients-Union{Tuple{P}, Tuple{P, Vector{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.extract_coefficients</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">extract_coefficients(poly, variables)</code></pre><p>Input:</p><ul><li><code>poly</code> - multivariate polynomial</li><li><code>variables</code> - a list of variables from the generators of the ring of p</li></ul><p>Output:</p><ul><li>dictionary with keys being tuples of length <code>length(variables)</code> and values being polynomials in the variables other than those which are the coefficients at the corresponding monomials (in a smaller polynomial ring)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L373-L381">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.fractions_to_dennums-Tuple{Any}" href="#StructuralIdentifiability.fractions_to_dennums-Tuple{Any}"><code>StructuralIdentifiability.fractions_to_dennums</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fractions_to_dennums(fractions)</code></pre><p>Returns the field generators represented by lists of denominators and numerators.</p><p>Input: an array of fractions, as in <code>[f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]</code></p><p>Output: an array of arrays of polynomials, <code>[[f1, f2, f3, ...], [g1, g2, g3, ...], ...]</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/RationalFunctionFields/util.jl#L25-L36">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.gen_tag_name" href="#StructuralIdentifiability.gen_tag_name"><code>StructuralIdentifiability.gen_tag_name</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">gen_tag_name(base; stop_words)
+gen_tag_names(n, base; stop_words)</code></pre><p>Generates a string which will not collide with the words in <code>stop_words</code>.</p><p><strong>Arguments</strong></p><ul><li><code>n</code>: Generates a sequence of unique strings of length <code>n</code></li><li><code>base</code>: A string or a vector of strings, the base for the generated sequence</li><li><code>stop_words</code>: A vector of strings, stop words</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L436-L447">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.make_substitution-Union{Tuple{P}, NTuple{4, P}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.make_substitution</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">make_substitution(f, var_sub, val_numer, val_denom)</code></pre><p>Substitute a variable in a polynomial with an expression</p><p>Input:</p><ul><li><code>f</code> - the polynomial</li><li><code>var_sub</code> - the variable to be substituted</li><li><code>var_numer</code> - numerator of the substitution expression</li><li><code>var_denom</code> - denominator of the substitution expression</li></ul><p>Output:</p><ul><li><code>polynomial</code> - result of substitution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L150-L163">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}" href="#StructuralIdentifiability.parent_ring_change-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.parent_ring_change</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">parent_ring_change(poly, new_ring)</code></pre><p>Converts a polynomial to a different polynomial ring Input</p><ul><li><code>poly</code> - a polynomial to be converted</li><li><code>new_ring</code> - a polynomial ring such that every variable name appearing in poly appears among the generators</li></ul><p>Output:</p><ul><li>a polynomial in <code>new_ring</code> “equal” to <code>poly</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L224-L234">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}" href="#StructuralIdentifiability.replace_with_ic-Tuple{Any, Any}"><code>StructuralIdentifiability.replace_with_ic</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">replace_with_ic(ode::ODE, funcs)</code></pre><p>Takes an ode and a list of functions in the states and parameters and makes a change of variable names <code>x(t) -&gt; x(0)</code>. Function is used to prepare the output for the case of known initial conditions</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L524-L529">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}" href="#StructuralIdentifiability.switch_ring-Tuple{AbstractAlgebra.MPolyRingElem, AbstractAlgebra.MPolyRing}"><code>StructuralIdentifiability.switch_ring</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">switch_ring(v, ring)</code></pre><p>For a variable <code>v</code>, returns a variable in <code>ring</code> with the same name</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L472-L476">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}" href="#StructuralIdentifiability.uncertain_factorization-Tuple{AbstractAlgebra.MPolyRingElem{Nemo.QQFieldElem}}"><code>StructuralIdentifiability.uncertain_factorization</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">uncertain_factorization(f)</code></pre><p>Input:</p><ul><li><code>f</code> - polynomial with rational coefficients</li></ul><p>Output:</p><ul><li>list of pairs <code>(div, certainty)</code> where<ul><li><code>div</code>&#39;s are divisors of <code>f</code> such that <code>f</code> is their product with certain powers</li><li>if <code>certainty</code> is true, <code>div</code> is <span>$Q$</span>-irreducible</li></ul></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/util.jl#L297-L307">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../ioequations/ioequations/">« Input-Output Equation tools</a><a class="docs-footer-nextpage" href="../../export/export/">Exporting to Other Systems »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. 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href="../local_identifiability/">Local Identifiability Tools</a></li><li><a class="tocitem" href="../global_identifiability/">Global Identifiability Tools</a></li><li><a class="tocitem" href="../elimination/">Elimination</a></li><li><a class="tocitem" href="../ode/">ODE Tools</a></li><li><a class="tocitem" href="../power_series_utils/">Power Series Tools</a></li><li><a class="tocitem" href="../primality/">Primality Checks</a></li><li class="is-active"><a class="tocitem" href>Wronskian Tools</a></li><li><a class="tocitem" href="../../ioequations/ioequations/">Input-Output Equation tools</a></li><li><a class="tocitem" href="../util/">Other Utilities</a></li></ul></li><li><span class="tocitem">Export</span><ul><li><a class="tocitem" href="../../export/export/">Exporting to Other Systems</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Library</a></li><li class="is-active"><a href>Wronskian Tools</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Wronskian Tools</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/utils/wronskian.md" title="Edit source on GitHub"><span class="docs-icon 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Vector{Int64}}"><code>StructuralIdentifiability.get_max_below</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">get_max_below(t, vect)</code></pre><p>Input:</p><ul><li><code>t</code> - a trie with exponent vectors</li><li><code>vect</code> - yet another exponent vector</li></ul><p>Output:</p><ul><li>a pair <code>(d, v)</code> where <code>v</code> is a vector in the trie which is componentwise ≤ <code>vect</code> and the difference <code>d</code> is as small as possible</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/wronskian.jl#L90-L99">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.massive_eval-Tuple{Any, Any}" href="#StructuralIdentifiability.massive_eval-Tuple{Any, Any}"><code>StructuralIdentifiability.massive_eval</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">massive_eval(polys, eval_dict)</code></pre><p>Input:</p><ul><li><code>polys</code> - a list of polynomials</li><li><code>eval_dict</code> - dictionary from variables to the values. Missing values are treated as zeroes</li></ul><p>Output:</p><ul><li>a list of values of the polynomials</li></ul><p>Evaluates a list of polynomials at a point. Assumes that multiplications are relatively expensive (like in truncated power series) so all the monomials are precomputed first and the values of monomials of lower degree are cached and used to compute the values of the monomials of higher degree</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/wronskian.jl#L123-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.monomial_compress-Tuple{Any, ODE}" href="#StructuralIdentifiability.monomial_compress-Tuple{Any, ODE}"><code>StructuralIdentifiability.monomial_compress</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">monomial_compress(io_equation, ode)</code></pre><p>Compresses an input-output equation for the rank computation Input:</p><ul><li><code>io_equation</code> - input-output equation</li><li><code>ode</code> - the corresponding ODE model</li></ul><p>Output:</p><ul><li>pair (coeffs, terms) such that:<ul><li>sum of <code>coeffs[i] * terms[i] = io_equation</code></li><li><code>coeffs</code> involve only parameters, <code>terms</code> involve only inputs and outputs</li><li>length of the representation is the smallest possible</li></ul></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/wronskian.jl#L5-L18">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.wronskian-Union{Tuple{P}, Tuple{Dict{P, P}, ODE{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.wronskian-Union{Tuple{P}, Tuple{Dict{P, P}, ODE{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.wronskian</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">wronskian(io_equations, ode)</code></pre><p>Input:</p><ul><li><code>io_equations</code> - a set of io-equations in the form of the <code>Dict</code> as returned by <code>find_ioequations</code></li><li><code>ode</code> - the <code>ODE</code> object</li></ul><p>Output:</p><ul><li>a list of Wronskians evaluated at a point modulo prime</li></ul><p>Computes the Wronskians of io_equations</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/91869e96fb6d281c614990804cd43d545316fbf3/src/wronskian.jl#L188-L199">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../primality/">« Primality Checks</a><a class="docs-footer-nextpage" href="../../ioequations/ioequations/">Input-Output Equation tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Tuesday 9 April 2024 22:11">Tuesday 9 April 2024</span>. 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is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Library</a></li><li class="is-active"><a href>Wronskian Tools</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Wronskian Tools</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/master/docs/src/utils/wronskian.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Wronskian-Tools"><a class="docs-heading-anchor" href="#Wronskian-Tools">Wronskian Tools</a><a id="Wronskian-Tools-1"></a><a class="docs-heading-anchor-permalink" href="#Wronskian-Tools" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.get_max_below-Tuple{StructuralIdentifiability.ExpVectTrie, Vector{Int64}}" href="#StructuralIdentifiability.get_max_below-Tuple{StructuralIdentifiability.ExpVectTrie, Vector{Int64}}"><code>StructuralIdentifiability.get_max_below</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">get_max_below(t, vect)</code></pre><p>Input:</p><ul><li><code>t</code> - a trie with exponent vectors</li><li><code>vect</code> - yet another exponent vector</li></ul><p>Output:</p><ul><li>a pair <code>(d, v)</code> where <code>v</code> is a vector in the trie which is componentwise ≤ <code>vect</code> and the difference <code>d</code> is as small as possible</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/wronskian.jl#L90-L99">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.massive_eval-Tuple{Any, Any}" href="#StructuralIdentifiability.massive_eval-Tuple{Any, Any}"><code>StructuralIdentifiability.massive_eval</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">massive_eval(polys, eval_dict)</code></pre><p>Input:</p><ul><li><code>polys</code> - a list of polynomials</li><li><code>eval_dict</code> - dictionary from variables to the values. Missing values are treated as zeroes</li></ul><p>Output:</p><ul><li>a list of values of the polynomials</li></ul><p>Evaluates a list of polynomials at a point. Assumes that multiplications are relatively expensive (like in truncated power series) so all the monomials are precomputed first and the values of monomials of lower degree are cached and used to compute the values of the monomials of higher degree</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/wronskian.jl#L123-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.monomial_compress-Tuple{Any, ODE}" href="#StructuralIdentifiability.monomial_compress-Tuple{Any, ODE}"><code>StructuralIdentifiability.monomial_compress</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">monomial_compress(io_equation, ode)</code></pre><p>Compresses an input-output equation for the rank computation Input:</p><ul><li><code>io_equation</code> - input-output equation</li><li><code>ode</code> - the corresponding ODE model</li></ul><p>Output:</p><ul><li>pair (coeffs, terms) such that:<ul><li>sum of <code>coeffs[i] * terms[i] = io_equation</code></li><li><code>coeffs</code> involve only parameters, <code>terms</code> involve only inputs and outputs</li><li>length of the representation is the smallest possible</li></ul></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/wronskian.jl#L5-L18">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StructuralIdentifiability.wronskian-Union{Tuple{P}, Tuple{Dict{P, P}, ODE{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem" href="#StructuralIdentifiability.wronskian-Union{Tuple{P}, Tuple{Dict{P, P}, ODE{P}}} where P&lt;:AbstractAlgebra.MPolyRingElem"><code>StructuralIdentifiability.wronskian</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">wronskian(io_equations, ode)</code></pre><p>Input:</p><ul><li><code>io_equations</code> - a set of io-equations in the form of the <code>Dict</code> as returned by <code>find_ioequations</code></li><li><code>ode</code> - the <code>ODE</code> object</li></ul><p>Output:</p><ul><li>a list of Wronskians evaluated at a point modulo prime</li></ul><p>Computes the Wronskians of io_equations</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/StructuralIdentifiability.jl/blob/b7e6d9924cb90734f8cb5d99e5641bc3d9f02d1f/src/wronskian.jl#L188-L199">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../primality/">« Primality Checks</a><a class="docs-footer-nextpage" href="../../ioequations/ioequations/">Input-Output Equation tools »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Thursday 18 April 2024 22:36">Thursday 18 April 2024</span>. 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