High Level example 2 error: ExtraVariablesSystemException: The system is unbalanced

[f0nzie]

Example 2 in the home page of this repo produces error.

The error appears on the line @mtkbuild connected = ODESystem(connections, t, [a], [γ], systems = [lorenz1, lorenz2])

Expected behavior
Should produce a plot like in the demo.

Minimal Reproducible Example 👇

Without MRE, we would only be able to help you to a limited extent, and attention to the issue would be limited. to know more about MRE refer to wikipedia and stackoverflow.

using DifferentialEquations, ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

@parameters σ ρ β
@variables x(t) y(t) z(t)

eqs = [D(D(x)) ~ σ * (y - x),
    D(y) ~ x * (ρ - z) - y,
    D(z) ~ x * y - β * z]

@mtkbuild lorenz1 = ODESystem(eqs, t)
@mtkbuild lorenz2 = ODESystem(eqs, t)

@variables a(t)
@parameters γ
connections = [0 ~ lorenz1.x + lorenz2.y + a * γ]
@mtkbuild connected = ODESystem(connections, t, [a], [γ], systems = [lorenz1, lorenz2])

u0 = [lorenz1.x => 1.0,
    lorenz1.y => 0.0,
    lorenz1.z => 0.0,
    lorenz2.x => 0.0,
    lorenz2.y => 1.0,
    lorenz2.z => 0.0,
    a => 2.0]

p = [lorenz1.σ => 10.0,
    lorenz1.ρ => 28.0,
    lorenz1.β => 8 / 3,
    lorenz2.σ => 10.0,
    lorenz2.ρ => 28.0,
    lorenz2.β => 8 / 3,
    γ => 2.0]

tspan = (0.0, 100.0)
prob = ODEProblem(connected, u0, tspan, p)
sol = solve(prob) 

using Plots
plot(sol, idxs = (a, lorenz1.x, lorenz2.z))

Error & Stacktrace ⚠️

ERROR: LoadError: ModelingToolkit.ExtraVariablesSystemException("The system is unbalanced. There are 11 highest order derivative variables and 9 equations.\nMore variables than equations, here are the potential extra variable(s):\n lorenz1₊xˍt(t)\n lorenz1₊y(t)\n lorenz1₊z(t)\n lorenz1₊x(t)\n lorenz2₊xˍt(t)\n lorenz2₊y(t)\n lorenz2₊z(t)\n lorenz2₊x(t)\n y(t)\n a(t)")
Stacktrace:
  [1] error_reporting(state::TearingState{ODESystem}, bad_idxs::Vector{Int64}, n_highest_vars::Int64, iseqs::Bool, orig_inputs::Set{Any})
    @ ModelingToolkit.StructuralTransformations ~/.julia/packages/ModelingToolkit/cAhZr/src/structural_transformation/utils.jl:50
  [2] check_consistency(state::TearingState{ODESystem}, orig_inputs::Set{Any})
    @ ModelingToolkit.StructuralTransformations ~/.julia/packages/ModelingToolkit/cAhZr/src/structural_transformation/utils.jl:85
  [3] _structural_simplify!(state::TearingState{ODESystem}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Bool, warn_initialize_determined::Bool, dummy_derivative::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systemstructure.jl:689
  [4] structural_simplify!(state::TearingState{ODESystem}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Bool, warn_initialize_determined::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systemstructure.jl:635
  [5] __structural_simplify(sys::ODESystem, io::Nothing; simplify::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systems.jl:74
  [6] __structural_simplify
    @ ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systems.jl:55 [inlined]
  [7] structural_simplify(sys::ODESystem, io::Nothing; simplify::Bool, split::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systems.jl:22
  [8] structural_simplify
    @ ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systems.jl:19 [inlined]
  [9] structural_simplify(sys::ODESystem)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/systems.jl:19
 [10] top-level scope
    @ ~/.julia/packages/ModelingToolkit/cAhZr/src/systems/abstractsystem.jl:1643
 [11] include(fname::String)
    @ Base.MainInclude ./client.jl:489
 [12] run(debug_session::VSCodeDebugger.DebugAdapter.DebugSession, error_handler::VSCodeDebugger.var"#3#4"{String})
    @ VSCodeDebugger.DebugAdapter ~/.vscode-server/extensions/julialang.language-julia-1.105.2/scripts/packages/DebugAdapter/src/packagedef.jl:126
 [13] startdebugger()
    @ VSCodeDebugger ~/.vscode-server/extensions/julialang.language-julia-1.105.2/scripts/packages/VSCodeDebugger/src/VSCodeDebugger.jl:45
 [14] top-level scope
    @ ~/.vscode-server/extensions/julialang.language-julia-1.105.2/scripts/debugger/run_debugger.jl:12
 [15] include(mod::Module, _path::String)
    @ Base ./Base.jl:495
 [16] exec_options(opts::Base.JLOptions)
    @ Base ./client.jl:318
 [17] _start()
    @ Base ./client.jl:552
in expression starting at /workspaces/julia-quarto-diffeq-2020/github-modelingtoolkit-example2.jl:18

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/.julia/environments/v1.10/Project.toml`
  [b0b7db55] ComponentArrays v0.15.16
  [a6e380b2] ControlSystems v1.10.3
  [2445eb08] DataDrivenDiffEq v1.4.1
  [5b588203] DataDrivenSparse v0.1.2
  [1130ab10] DiffEqParamEstim v2.2.0
  [0c46a032] DifferentialEquations v7.13.0
  [f6369f11] ForwardDiff v0.10.36
  [7073ff75] IJulia v1.25.0
  [2b0e0bc5] LanguageServer v4.5.1
  [d3d80556] LineSearches v7.2.0
  [b2108857] Lux v0.5.62
⌃ [961ee093] ModelingToolkit v9.15.0
  [16a59e39] ModelingToolkitStandardLibrary v2.10.0
  [15e1cf62] NPZ v0.4.3
  [8913a72c] NonlinearSolve v3.13.1
⌃ [7f7a1694] Optimization v3.26.3
  [4e6fcdb7] OptimizationNLopt v0.2.2
  [36348300] OptimizationOptimJL v0.3.2
  [42dfb2eb] OptimizationOptimisers v0.2.1
  [500b13db] OptimizationPolyalgorithms v0.2.1
  [1dea7af3] OrdinaryDiffEq v6.87.0
  [91a5bcdd] Plots v1.40.5
  [438e738f] PyCall v1.96.4
  [1ed8b502] SciMLSensitivity v7.64.0
  [860ef19b] StableRNGs v1.0.2
  [90137ffa] StaticArrays v1.9.7
⌃ [24249f21] SymPy v2.1.1
  [b8865327] UnicodePlots v3.6.4
  [e88e6eb3] Zygote v0.6.70
  [37e2e46d] LinearAlgebra
  [10745b16] Statistics v1.10.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/environments/v1.10/Manifest.toml`
  [47edcb42] ADTypes v1.6.2
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.37
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.15.0
  [4c555306] ArrayLayouts v1.10.2
  [a9b6321e] Atomix v0.1.0
  [aae01518] BandedMatrices v1.7.2
⌅ [198e06fe] BangBang v0.3.40
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.7
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.9.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [49dc2e85] Calculus v0.5.1
  [7057c7e9] Cassette v0.3.13
  [082447d4] ChainRules v1.69.0
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.5
  [35d6a980] ColorSchemes v3.26.0
  [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [3709ef60] CommonEq v0.2.1
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
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  [34da2185] Compat v4.15.0
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  [8f4d0f93] Conda v1.10.2
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  [a6e380b2] ControlSystems v1.10.3
  [aaaaaaaa] ControlSystemsBase v1.10.3
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  [9a962f9c] DataAPI v1.16.0
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  [5b588203] DataDrivenSparse v0.1.2
⌅ [82cc6244] DataInterpolations v5.0.0
  [864edb3b] DataStructures v0.18.20
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  [8bb1440f] DelimitedFiles v1.9.1
  [39dd38d3] Dierckx v0.5.3
  [2b5f629d] DiffEqBase v6.152.2
  [459566f4] DiffEqCallbacks v3.7.0
  [77a26b50] DiffEqNoiseProcess v5.22.0
  [1130ab10] DiffEqParamEstim v2.2.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.13.0
  [a0c0ee7d] DifferentiationInterface v0.5.11
  [8d63f2c5] DispatchDoctor v0.4.12
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⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
  [da5c29d0] EllipsisNotation v1.8.0
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  [7da242da] Enzyme v0.12.27
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⌅ [6b7a57c9] Expronicon v0.8.5
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  [6a86dc24] FiniteDiff v2.23.1
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  [1fa38f19] Format v1.3.7
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  [0c68f7d7] GPUArrays v10.3.0
  [46192b85] GPUArraysCore v0.1.6
  [61eb1bfa] GPUCompiler v0.26.7
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  [b2108857] Lux v0.5.62
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  [34f89e08] LuxDeviceUtils v0.1.26
⌃ [82251201] LuxLib v0.3.39
  [7e8f7934] MLDataDevices v1.0.0
  [d8e11817] MLStyle v0.4.17
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  [99c1a7ee] MatrixEquations v2.4.2
  [a3b82374] MatrixFactorizations v3.0.0
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  [bb5d69b7] MaybeInplace v0.1.3
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
⌅ [128add7d] MicroCollections v0.1.4
  [e1d29d7a] Missings v1.2.0
⌃ [961ee093] ModelingToolkit v9.15.0
  [16a59e39] ModelingToolkitStandardLibrary v2.10.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [d8a4904e] MutableArithmetics v1.4.6
  [d41bc354] NLSolversBase v7.8.3
  [76087f3c] NLopt v1.0.2
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.21
  [15e1cf62] NPZ v0.4.3
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  [71a1bf82] NameResolution v0.1.5
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  [6fd5a793] Octavian v0.3.28
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  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [3bd65402] Optimisers v0.3.3
⌃ [7f7a1694] Optimization v3.26.3
⌃ [bca83a33] OptimizationBase v1.2.0
  [4e6fcdb7] OptimizationNLopt v0.2.2
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⌅ [76b0de8b] TestItemDetection v0.2.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
  [9f7883ad] Tracker v0.2.34
  [3bb67fe8] TranscodingStreams v0.11.1
⌃ [28d57a85] Transducers v0.4.80
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [b8865327] UnicodePlots v3.6.4
  [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [0fe1646c] UnrolledUtilities v0.1.2
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.1.5
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.70
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [d49dbf32] WeightInitializers v1.0.0
  [c2297ded] ZMQ v1.3.0
  [a5390f91] ZipFile v0.10.1
  [e88e6eb3] Zygote v0.6.70
  [700de1a5] ZygoteRules v0.2.5
  [6e34b625] Bzip2_jll v1.0.8+1
  [83423d85] Cairo_jll v1.18.0+2
  [ee1fde0b] Dbus_jll v1.14.10+0
  [cd4c43a9] Dierckx_jll v0.1.0+0
  [7cc45869] Enzyme_jll v0.0.141+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+0
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [d2c73de3] GR_jll v0.73.7+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
  [dad2f222] LLVMExtra_jll v0.0.31+0
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [dd4b983a] LZO_jll v2.10.2+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [079eb43e] NLopt_jll v2.7.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [36c8627f] Pango_jll v1.52.2+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.4.2+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.1+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [8f1865be] ZeroMQ_jll v4.3.5+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2

• Output of versioninfo()

julia> versioninfo()
Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 11th Gen Intel(R) Core(TM) i9-11980HK @ 2.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)

Additional context

Add any other context about the problem here.