ModelingToolkit Integration

This is a quick intro based on the lotka volterra fishing problem. It is similar to the classical fishing example, but we will use ModelingToolkit.jl to model it.

Setup

We will use Corleone to define our optimal control problem.

using Corleone
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEqTsit5
using ComponentArrays, ForwardDiff
using Optimization
using OptimizationMOI, Ipopt
using LuxCore, Random
using CairoMakie

We start by defining our system

@variables begin
    x(..) = 0.5, [tunable = false]
    y(..) = 0.7, [tunable = false]
    u(..) = 0.0, [bounds = (0.0, 1.0), input = true]
end
@constants begin
    c₁ = 0.4
    c₂ = 0.2
end
eqs = [
    D(x(t)) ~ x(t) - x(t) * y(t) - c₁ * u(t) * x(t)
    D(y(t)) ~ -y(t) + x(t) * y(t) - c₂ * u(t) * y(t)
]
costs = [
    Symbolics.Integral(t in (0.0, 12.0))(
        (x(t) - 1.0)^2 + (y(t) - 1.0)^2
    ),
]
@named lotka_volterra = System(eqs, t, costs = costs)

function plot_lotka(sol)
    f = Figure()
    ax = CairoMakie.Axis(f[1, 1])
    scatterlines!(ax, sol, vars = [1, 2, 3])
    f[1, 2] = Legend(f, ax, "States", framevisible = false)
    ax1 = CairoMakie.Axis(f[2, 1])
    stairs!(ax1, sol, vars = [4])
    f[2, 2] = Legend(f, ax1, "Controls", framevisible = false)
    return f
end
plot_lotka (generic function with 1 method)

Single Shooting

dynopt = CorleoneDynamicOptProblem(
    lotka_volterra, [],
    u(t) => 0.0:0.1:11.9,
    algorithm = Tsit5(),
)

optprob = OptimizationProblem(dynopt, AutoForwardDiff(), Val(:ComponentArrays))

sol = solve(
    optprob, Ipopt.Optimizer(), max_iter = 1000, tol = 5.0e-6,
    hessian_approximation = "limited-memory"
)


u_opt = ComponentVector(sol.u, optprob.f.f.ax)
opt_traj, _ = dynopt.layer(nothing, u_opt, LuxCore.initialstates(Random.default_rng(), dynopt.layer))

plot_lotka(opt_traj)

Multiple Shooting

dynopt = CorleoneDynamicOptProblem(
    lotka_volterra, [],
    u(t) => 0.0:0.1:11.9,
    algorithm = Tsit5(),
    shooting = [0.0, 3.0, 6.0, 9.0]
)

optprob = OptimizationProblem(dynopt, AutoForwardDiff(), Val(:ComponentArrays))

sol = solve(
    optprob, Ipopt.Optimizer(), max_iter = 1000, tol = 5.0e-6,
    hessian_approximation = "limited-memory"
)

u_opt = ComponentVector(sol.u, optprob.f.f.ax)
opt_traj, _ = dynopt.layer(nothing, u_opt, LuxCore.initialstates(Random.default_rng(), dynopt.layer))

plot_lotka(opt_traj)

Appendix

This example was built using these direct dependencies,
        using Pkg
        Pkg.status()
Status `~/work/Corleone.jl/Corleone.jl/docs/Project.toml`
  [13f3f980] CairoMakie v0.15.8
  [b0b7db55] ComponentArrays v0.15.32
  [2751e0db] Corleone v0.0.3 `~/work/Corleone.jl/Corleone.jl`
  [6590a4b1] CorleoneOED v0.0.2
  [e30172f5] Documenter v1.17.0
  [daee34ce] DocumenterCitations v1.4.1
  [d12716ef] DocumenterInterLinks v1.1.0
  [f6369f11] ForwardDiff v1.3.2
  [b6b21f68] Ipopt v1.14.1
  [682c06a0] JSON v1.4.0
  [98b081ad] Literate v2.21.0
  [bb33d45b] LuxCore v1.5.3
  [961ee093] ModelingToolkit v11.13.0
  [7f7a1694] Optimization v5.5.0
  [22f7324a] OptimizationLBFGSB v1.4.0
  [fd9f6733] OptimizationMOI v1.2.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.9.0
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [ddb6d928] YAML v0.4.16
  [9a3f8284] Random v1.11.0
and using this machine and Julia version.
        using InteractiveUtils
        InteractiveUtils.versioninfo()
Julia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 9V74 80-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver4)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
        using Pkg
        Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/work/Corleone.jl/Corleone.jl/docs/Manifest.toml`
  [47edcb42] ADTypes v1.21.0
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [621f4979] AbstractFFTs v1.5.0
  [6e696c72] AbstractPlutoDingetjes v1.3.2
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.43
  [79e6a3ab] Adapt v4.5.0
  [35492f91] AdaptivePredicates v1.2.0
  [66dad0bd] AliasTables v1.1.3
  [27a7e980] Animations v0.4.2
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.22.0
  [4c555306] ArrayLayouts v1.12.2
  [67c07d97] Automa v1.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.8
  [198e06fe] BangBang v0.4.8
  [18cc8868] BaseDirs v1.3.2
  [6e4b80f9] BenchmarkTools v1.6.3
  [2027ae74] BibInternal v0.3.7
  [13533e5b] BibParser v0.2.3
  [f1be7e48] Bibliography v0.3.1
  [e2ed5e7c] Bijections v0.2.2
  [caf10ac8] BipartiteGraphs v0.1.7
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.9.3
  [70df07ce] BracketingNonlinearSolve v1.11.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.7
  [96374032] CRlibm v1.0.2
  [159f3aea] Cairo v1.1.1
  [13f3f980] CairoMakie v0.15.8
  [d360d2e6] ChainRulesCore v1.26.0
  [ae650224] ChunkSplitters v3.2.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [a2cac450] ColorBrewer v0.4.2
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [b0b7db55] ComponentArrays v0.15.32
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [95dc2771] ComputePipeline v0.1.6
  [2569d6c7] ConcreteStructs v0.2.3
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
  [2751e0db] Corleone v0.0.3 `~/work/Corleone.jl/Corleone.jl`
  [6590a4b1] CorleoneOED v0.0.2
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [927a84f5] DelaunayTriangulation v1.6.6
  [2b5f629d] DiffEqBase v6.210.1
  [459566f4] DiffEqCallbacks v4.12.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.16
  [8d63f2c5] DispatchDoctor v0.4.28
  [31c24e10] Distributions v0.25.123
  [43dc2714] DocInventories v1.0.0
  [ffbed154] DocStringExtensions v0.9.5
  [e30172f5] Documenter v1.17.0
  [daee34ce] DocumenterCitations v1.4.1
  [d12716ef] DocumenterInterLinks v1.1.0
  [5b8099bc] DomainSets v0.7.16
  [7c1d4256] DynamicPolynomials v0.6.4
  [4e289a0a] EnumX v1.0.7
  [f151be2c] EnzymeCore v0.8.18
  [429591f6] ExactPredicates v2.2.9
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [411431e0] Extents v0.1.6
  [b86e33f2] FFTA v0.3.1
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.3.1
  [5789e2e9] FileIO v1.18.0
  [8fc22ac5] FilePaths v0.9.0
  [48062228] FilePathsBase v0.9.24
  [1a297f60] FillArrays v1.16.0
  [64ca27bc] FindFirstFunctions v1.8.0
  [6a86dc24] FiniteDiff v2.29.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.2
  [b38be410] FreeType v4.1.1
  [663a7486] FreeTypeAbstraction v0.10.8
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [5c1252a2] GeometryBasics v0.5.10
  [d7ba0133] Git v1.5.0
  [a2bd30eb] Graphics v1.1.3
  [86223c79] Graphs v1.14.0
  [3955a311] GridLayoutBase v0.11.2
  [42e2da0e] Grisu v1.0.2
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [b5f81e59] IOCapture v1.0.0
  [615f187c] IfElse v0.1.1
  [2803e5a7] ImageAxes v0.6.12
  [c817782e] ImageBase v0.1.7
  [a09fc81d] ImageCore v0.10.5
  [82e4d734] ImageIO v0.6.9
  [bc367c6b] ImageMetadata v0.9.10
  [3263718b] ImplicitDiscreteSolve v1.8.0
  [9b13fd28] IndirectArrays v1.0.0
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [18e54dd8] IntegerMathUtils v0.1.3
  [a98d9a8b] Interpolations v0.16.2
  [d1acc4aa] IntervalArithmetic v1.0.2
  [8197267c] IntervalSets v0.7.13
  [3587e190] InverseFunctions v0.1.17
  [b6b21f68] Ipopt v1.14.1
  [92d709cd] IrrationalConstants v0.2.6
  [f1662d9f] Isoband v0.1.1
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.4.0
  [7d188eb4] JSONSchema v1.5.0
  [ae98c720] Jieko v0.2.1
  [b835a17e] JpegTurbo v0.1.6
  [ccbc3e58] JumpProcesses v9.23.1
  [5ab0869b] KernelDensity v0.6.11
  [ba0b0d4f] Krylov v0.10.5
  [5be7bae1] LBFGSB v0.4.1
  [b964fa9f] LaTeXStrings v1.4.0
  [10f19ff3] LayoutPointers v0.1.17
  [0e77f7df] LazilyInitializedFields v1.3.0
  [8cdb02fc] LazyModules v0.3.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.1
  [87fe0de2] LineSearch v0.1.6
  [7ed4a6bd] LinearSolve v3.63.0
  [98b081ad] Literate v2.21.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [bb33d45b] LuxCore v1.5.3
  [1914dd2f] MacroTools v0.5.16
  [ee78f7c6] Makie v0.24.8
  [d125e4d3] ManualMemory v0.1.8
  [dbb5928d] MappedArrays v0.4.3
  [d0879d2d] MarkdownAST v0.1.3
  [b8f27783] MathOptInterface v1.49.0
  [0a4f8689] MathTeXEngine v0.6.7
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v11.13.0
  [7771a370] ModelingToolkitBase v1.20.0
  [6bb917b9] ModelingToolkitTearing v1.5.0
  [e94cdb99] MosaicViews v0.3.4
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.13
  [d8a4904e] MutableArithmetics v1.6.7
  [77ba4419] NaNMath v1.1.3
  [f09324ee] Netpbm v1.1.1
  [be0214bd] NonlinearSolveBase v2.15.0
  [5959db7a] NonlinearSolveFirstOrder v2.0.0
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.17.0
  [67456a42] OhMyThreads v0.8.5
  [52e1d378] OpenEXR v0.3.3
  [7f7a1694] Optimization v5.5.0
  [bca83a33] OptimizationBase v5.0.0
  [22f7324a] OptimizationLBFGSB v1.4.0
  [fd9f6733] OptimizationMOI v1.2.0
  [bac558e1] OrderedCollections v1.8.1
  [bbf590c4] OrdinaryDiffEqCore v3.16.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.9.0
  [90014a1f] PDMats v0.11.37
  [f57f5aa1] PNGFiles v0.4.4
  [19eb6ba3] Packing v0.5.1
  [5432bcbf] PaddedViews v0.5.12
  [69de0a69] Parsers v2.8.3
  [eebad327] PkgVersion v0.3.3
  [995b91a9] PlotUtils v1.4.4
  [e409e4f3] PoissonRandom v0.4.7
  [f517fe37] Polyester v0.7.19
  [1d0040c9] PolyesterWeave v0.2.2
  [647866c9] PolygonOps v0.1.2
  [d236fae5] PreallocationTools v1.1.2
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.2
  [27ebfcd6] Primes v0.5.7
  [33c8b6b6] ProgressLogging v0.1.6
  [92933f4c] ProgressMeter v1.11.0
  [43287f4e] PtrArrays v1.4.0
  [4b34888f] QOI v1.0.2
  [1fd47b50] QuadGK v2.11.2
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.48.0
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [79098fc4] Rmath v0.9.0
  [5eaf0fd0] RoundingEmulator v0.2.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.17
  [9dfe8606] SCCNonlinearSolve v1.11.0
  [fdea26ae] SIMD v3.7.2
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.148.0
  [19f34311] SciMLJacobianOperators v0.1.12
  [a6db7da4] SciMLLogging v1.9.1
  [c0aeaf25] SciMLOperators v1.15.1
  [431bcebd] SciMLPublic v1.0.1
  [53ae85a6] SciMLStructures v1.10.0
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [65257c39] ShaderAbstractions v0.5.0
  [992d4aef] Showoff v1.0.3
  [73760f76] SignedDistanceFields v0.4.1
  [727e6d20] SimpleNonlinearSolve v2.11.0
  [699a6c99] SimpleTraits v0.9.5
  [45858cf5] Sixel v0.1.5
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.2.1
  [0a514795] SparseMatrixColorings v0.4.24
  [276daf66] SpecialFunctions v2.7.1
  [860ef19b] StableRNGs v1.0.4
  [91464d47] StableTasks v0.1.7
  [cae243ae] StackViews v0.1.2
  [64909d44] StateSelection v1.3.0
  [aedffcd0] Static v1.3.1
  [0d7ed370] StaticArrayInterface v1.9.0
  [90137ffa] StaticArrays v1.9.17
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.10
  [4c63d2b9] StatsFuns v1.5.2
  [7792a7ef] StrideArraysCore v0.5.8
  [69024149] StringEncodings v0.3.7
  [09ab397b] StructArrays v0.7.2
  [ec057cc2] StructUtils v2.6.3
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [19f23fe9] SymbolicLimits v1.1.0
  [d1185830] SymbolicUtils v4.19.0
  [0c5d862f] Symbolics v7.15.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [5d786b92] TerminalLoggers v0.1.7
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.5
  [731e570b] TiffImages v0.11.6
  [a759f4b9] TimerOutputs v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.3
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.6.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.28.0
  [d30d5f5c] WeakCacheSets v0.1.0
  [e3aaa7dc] WebP v0.1.3
  [efce3f68] WoodburyMatrices v1.1.0
  [ddb6d928] YAML v0.4.16
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.5+1
  [5ae413db] EarCut_jll v2.2.4+0
  [2e619515] Expat_jll v2.7.3+0
  [b22a6f82] FFMPEG_jll v8.0.1+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [59f7168a] Giflib_jll v5.2.3+0
  [020c3dae] Git_LFS_jll v3.7.0+0
  [f8c6e375] Git_jll v2.53.0+0
  [7746bdde] Glib_jll v2.86.3+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [e33a78d0] Hwloc_jll v2.13.0+0
  [905a6f67] Imath_jll v3.2.2+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1901+0
  [aacddb02] JpegTurbo_jll v3.1.4+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.3+0
  [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.41.3+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.200+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.30+0
  [6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.30+0
  [18a262bb] OpenEXR_jll v3.4.4+0
  [9bd350c2] OpenSSH_jll v10.2.1+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [319450e9] SPRAL_jll v2025.9.18+0
⌅ [02c8fc9c] XML2_jll v2.13.9+0
  [ffd25f8a] XZ_jll v5.8.2+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.18.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.13.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [b53b4c65] libpng_jll v1.6.55+0
  [075b6546] libsixel_jll v1.10.5+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [c5f90fcd] libwebp_jll v1.6.0+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

This page was generated using Literate.jl.