Nelson Work-Precision Diagrams
using OrdinaryDiffEq
using OrdinaryDiffEqBDF, OrdinaryDiffEqExtrapolation, OrdinaryDiffEqFIRK, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK
using DiffEqDevTools, Plots
using Sundials, LSODA
using ODEInterface, ODEInterfaceDiffEq
using RecursiveFactorizationThe ODE function defined below models the reduced carbon-oxygen chemistry network of Nelson & Langer (1999, ApJ, 524, 923).
This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner. The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013) a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds. DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper, so the initial conditions and parameters were meant to mimic those from DESPOTIC.
Note: The composite hydrocarbon radical CHx represents both CH and CH2, the composite oxygen species OHx represents OH, H2O, O2 and their ions, and M represents the low ionization potential metals Mg, Fe, Ca, and Na.
Parameter definitions:
T = 10 --> Temperature (Kelvin)
Av = 2 --> V-Band Extinction
G₀ = 1.7 --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)."
n_H = 611 --> Hydrogen Number Density
shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)"function Nelson!(du, u, p, t)
T, Av, Go, n_H, shield = p
# 1: H2
du[1] = -1.2e-17 * u[1] +
n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) -
n_H * 4e-16 * u[1] * u[12] -
n_H * 7e-15 * u[1] * u[5] +
n_H * 1.7e-9 * u[10] * u[2] +
n_H * 2e-9 * u[2] * u[6] +
n_H * 2e-9 * u[2] * u[14] +
n_H * 8e-10 * u[2] * u[8]
# 2: H3+
du[2] = 1.2e-17 * u[1] +
n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) -
n_H * 1.7e-9 * u[10] * u[2] -
n_H * 2e-9 * u[2] * u[6] -
n_H * 2e-9 * u[2] * u[14] -
n_H * 8e-10 * u[2] * u[8]
# 3: e
du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) -
n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) -
n_H * (3.3e-5 * u[11] * u[3]) / T +
1.2e-17 * u[1] -
n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) +
6.8e-18 * u[4] -
n_H * (9e-11 * u[3] * u[5]) / (T^0.64) +
3e-10 * Go * exp(-3 * Av) * u[6] +
n_H * 2e-9 * u[2] * u[13]
+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14]
# 4: He
du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) -
6.8e-18 * u[4] +
n_H * 7e-15 * u[1] * u[5] +
n_H * 1.6e-9 * u[10] * u[5]
# 5: He+
du[5] = 6.8e-18 * u[4] -
n_H * (9e-11 * u[3] * u[5]) / (T^0.64) -
n_H * 7e-15 * u[1] * u[5] -
n_H * 1.6e-9 * u[10] * u[5]
# 6: C
du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) -
n_H * 2e-9 * u[2] * u[6] -
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] +
1e-9 * Go * exp(-1.5 * Av) * u[7] -
3e-10 * Go * exp(-3 * Av) * u[6] +
1e-10 * Go * exp(-3 * Av) * u[10] * shield
# 7: CHx
du[7] = n_H * (-2e-10) * u[7] * u[8] +
n_H * 4e-16 * u[1] * u[12] +
n_H * 2e-9 * u[2] * u[6] -
1e-9 * Go * u[7] * exp(-1.5 * Av)
# 8: O
du[8] = n_H * (-2e-10) * u[7] * u[8] +
n_H * 1.6e-9 * u[10] * u[5] -
n_H * 8e-10 * u[2] * u[8] +
5e-10 * Go * exp(-1.7 * Av) * u[9] +
1e-10 * Go * exp(-3 * Av) * u[10] * shield
# 9: OHx
du[9] = n_H * (-1e-9) * u[9] * u[12] +
n_H * 8e-10 * u[2] * u[8] -
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] -
5e-10 * Go * exp(-1.7 * Av) * u[9]
# 10: CO
du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T +
n_H * 2e-10 * u[7] * u[8] -
n_H * 1.7e-9 * u[10] * u[2] -
n_H * 1.6e-9 * u[10] * u[5] +
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] -
1e-10 * Go * exp(-3 * Av) * u[10] +
1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield
# 11: HCO+
du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T +
n_H * 1e-9 * u[9] * u[12] +
n_H * 1.7e-9 * u[10] * u[2] -
1.5e-10 * Go * exp(-2.5 * Av) * u[11]
# 12: C+
du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) -
n_H * 4e-16 * u[1] * u[12] -
n_H * 1e-9 * u[9] * u[12] +
n_H * 1.6e-9 * u[10] * u[5] +
3e-10 * Go * exp(-3 * Av) * u[6]
# 13: M+
du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) +
n_H * 2e-9 * u[2] * u[14] +
2.0e-10 * Go * exp(-1.9 * Av) * u[14]
# 14: M
du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) -
n_H * 2e-9 * u[2] * u[14] -
2.0e-10 * Go * exp(-1.9 * Av) * u[14]
end
# Set the Timespan, Parameters, and Initial Conditions
seconds_per_year = 3600 * 24 * 365
tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs
params = (10, # T
2, # Av
1.7, # Go
611, # n_H
1) # shield
u0 = [0.5, # 1: H2
9.059e-9, # 2: H3+
2.0e-4, # 3: e
0.1, # 4: He
7.866e-7, # 5: He+
0.0, # 6: C
0.0, # 7: CHx
0.0004, # 8: O
0.0, # 9: OHx
0.0, # 10: CO
0.0, # 11: HCO+
0.0002, # 12: C+
2.0e-7, # 13: M+
2.0e-7] # 14: M
prob = ODEProblem(Nelson!, u0, tspan, params)
refsol = solve(prob, Vern9(), abstol = 1e-14, reltol = 1e-14)
sol1 = solve(prob, Rodas5P())
sol2 = solve(prob, FBDF())
sol3 = solve(prob, lsoda())
sol4 = solve(prob, lsoda(), saveat = 1e10)retcode: Success
Interpolation: 1st order linear
t: 95-element Vector{Float64}:
0.0
1.0e10
2.0e10
3.0e10
4.0e10
5.0e10
6.0e10
7.0e10
8.0e10
9.0e10
⋮
8.6e11
8.7e11
8.8e11
8.9e11
9.0e11
9.1e11
9.2e11
9.3e11
9.4608e11
u: 95-element Vector{Vector{Float64}}:
[0.5, 9.059e-9, 0.0002, 0.1, 7.866e-7, 0.0, 0.0, 0.0004, 0.0, 0.0, 0.0, 0.
0002, 2.0e-7, 2.0e-7]
[0.4999997535369704, 8.193154457455469e-11, 0.00019197303336682174, 0.1000
0002886487377, 7.577351262491076e-7, 8.042342992821525e-6, 1.49925186263626
43e-7, 0.0003999674879715404, 1.1067638304100775e-10, 3.240131896517983e-8,
3.3451545560423566e-14, 0.00019177533041679414, 1.9528726921075105e-7, 2.0
471273078924893e-7]
[0.4999995075210584, 9.090316158336153e-11, 0.00018461935387378958, 0.1000
000562601198, 7.30339880209255e-7, 1.5480572363863645e-5, 2.000300361171384
6e-7, 0.00039990233527387485, 1.4466321223018468e-10, 9.752001980587566e-8,
4.373263586424432e-14, 0.00018422187752626965, 1.9189712227776098e-7, 2.08
102877722239e-7]
[0.4999992706516111, 1.0268278666266992e-10, 0.00017788865255185306, 0.100
0000823101555, 7.042898445209926e-7, 2.232067746875479e-5, 2.06208656840273
3e-7, 0.0003998249793482805, 1.5825894683323741e-10, 1.7486234569318328e-7,
4.7887781766364776e-14, 0.0001772982515858309, 1.8962171847126598e-7, 2.10
378281528734e-7]
[0.4999990426328743, 1.1047944310386002e-10, 0.0001717521353885941, 0.1000
0010708540578, 6.795145942383737e-7, 2.8580379834976427e-5, 1.8605427132856
04e-7, 0.00039974177445524555, 1.6055330761123543e-10, 2.580649437390939e-7
, 4.863811929077203e-14, 0.0001709755011738776, 1.8836261411409688e-7, 2.11
6373858859031e-7]
[0.4999988222961169, 1.1214512825014892e-10, 0.00016610214932054722, 0.100
00013079566746, 6.558043325632626e-7, 3.4346695009489656e-5, 1.726072821034
1615e-7, 0.00039966441024142784, 1.6471463276936157e-10, 3.3542499509755626
e-7, 4.985815571219808e-14, 0.00016514527304999023, 1.877725577159864e-7, 2
.122274422840136e-7]
[0.4999986089645403, 1.1301312452696201e-10, 0.00016088117474842152, 0.100
00015350341433, 6.33096585679416e-7, 3.968155815686876e-5, 1.59196819816350
05e-7, 0.0003995901104830985, 1.6886141974491672e-10, 4.0972060551075024e-7
, 5.104610902246676e-14, 0.00015974952484161368, 1.8771391474671e-7, 2.1228
608525328997e-7]
[0.4999984016924124, 1.1593684877979178e-10, 0.00015600611460040258, 0.100
00017532890296, 6.112710970559566e-7, 4.466487283056087e-5, 1.5126630795563
186e-7, 0.00039952045363073296, 1.7631004132599739e-10, 4.793700071205165e-
7, 5.32344989749965e-14, 0.00015470449133458915, 1.8796065523144963e-7, 2.1
203934476855036e-7]
[0.4999982013001409, 1.184410067837422e-10, 0.00015154905427904665, 0.1000
0019616781267, 5.904321873416034e-7, 4.922732395495452e-5, 1.44093662278483
6e-7, 0.0003994540704033752, 1.8418359629049677e-10, 5.457453586602043e-7,
5.5527630926796366e-14, 0.0001500828375344457, 1.887088566175661e-7, 2.1129
11433824339e-7]
[0.499998007202718, 1.2074897464625312e-10, 0.0001474639659320232, 0.10000
021608152558, 5.705184744292179e-7, 5.341504816290257e-5, 1.377880132974742
2e-7, 0.0003993907296694579, 1.9240989134703122e-10, 6.090778639087468e-7,
5.791432631570454e-14, 0.00014583808648206922, 1.8985069087087307e-7, 2.101
493091291269e-7]
⋮
[0.4999886971720987, 1.9795827809365797e-10, 8.950887024276836e-5, 0.10000
06600683044, 1.2653169561225698e-7, 0.00011707676413720376, 7.3788674819905
76e-8, 0.0003970478736288078, 4.892836316442913e-10, 2.95163695291137e-6, 1
.356984339173129e-13, 7.989781065115055e-5, 2.478036176330643e-7, 1.5219638
236693576e-7]
[0.4999885970930578, 1.9793342063952315e-10, 8.948878095668965e-5, 0.10000
066096407667, 1.2563592333740452e-7, 0.00011716555190079074, 7.361062500753
714e-8, 0.0003970280592975852, 4.894657459356276e-10, 2.971451102091994e-6,
1.356323361880553e-13, 7.97893867859006e-5, 2.478492488443751e-7, 1.521507
5115562496e-7]
[0.4999884972140397, 1.9791929065652404e-10, 8.947430636422426e-5, 0.10000
066181954592, 1.2478045408581226e-7, 0.00011724870322575066, 7.345727745258
005e-8, 0.00039700840539103006, 4.896846004578493e-10, 2.9911047898569364e-
6, 1.3557309797706945e-13, 7.96867351188127e-5, 2.4788900714769123e-7, 1.52
1109928523088e-7]
[0.4999883975359282, 1.979177458878945e-10, 8.946553362185228e-5, 0.100000
66263521029, 1.2396478970728907e-7, 0.00011732612905423649, 7.3330552042521
3e-8, 0.0003969889131988451, 4.899477157942837e-10, 3.0105967189810325e-6,
1.3552250374409033e-13, 7.958994408510943e-5, 2.4792310665125997e-7, 1.5207
689334874006e-7]
[0.49998829793856614, 1.9792446507578876e-10, 8.945767765481339e-5, 0.1000
0066343872818, 1.2316127181539434e-7, 0.00011740267214118327, 7.32118303907
7428e-8, 0.0003969695347916554, 4.902350223911299e-10, 3.029974838912789e-6
, 1.3547711665516858e-13, 7.949414159854762e-5, 2.479548615290058e-7, 1.520
451384709942e-7]
[0.49998819842252995, 1.979412902637886e-10, 8.945081324018611e-5, 0.10000
066423066675, 1.2236933325100569e-7, 0.00011747825595953078, 7.310298020102
55e-8, 0.00039695027133410766, 4.905539707304883e-10, 3.0492379775533577e-6
, 1.3543870790373717e-13, 7.93994034906198e-5, 2.479844937658461e-7, 1.5201
55062341539e-7]
[0.499988098988396, 1.9797006349547566e-10, 8.944501515504896e-5, 0.100000
66501159315, 1.2158840685500065e-7, 0.00011755280398221879, 7.3005869176961
49e-8, 0.0003969311239908482, 4.909120112944597e-10, 3.0683849628038885e-6,
1.3540904868322912e-13, 7.930580559281851e-5, 2.4801222534669814e-7, 1.519
8777465330185e-7]
[0.49998799963674095, 1.9801262681443172e-10, 8.94403581764805e-5, 0.10000
066578207453, 1.2081792546825682e-7, 0.00011762623968218706, 7.292236502226
876e-8, 0.00039691209392652354, 4.913165945651447e-10, 3.0874146225655315e-
6, 1.353899101870775e-13, 7.921342373663633e-5, 2.480382782564793e-7, 1.519
6172174352072e-7]
[0.4999878400536776, 1.9811462937457688e-10, 8.943545103579628e-5, 0.10000
066700053743, 1.1959946257185592e-7, 0.00011774179894869144, 7.282133161703
036e-8, 0.00039688174243430677, 4.920835452521089e-10, 3.1177653478356363e-
6, 1.3538566225456173e-13, 7.90676147779716e-5, 2.4807721124352237e-7, 1.51
92278875647764e-7]Validation Plot
using Plots
colors = palette(:acton, 5)
p1 = plot(sol1, vars = (0, 11), lc = colors[1], legend = false,
titlefontsize = 12, lw = 3, title = "Rodas5")
p2 = plot(sol2, vars = (0, 11), lc = colors[2], legend = false,
titlefontsize = 12, lw = 3, title = "FBDF")
p3 = plot(sol3, vars = (0, 11), lc = colors[3], legend = false,
titlefontsize = 12, lw = 3, title = "lsoda")
p4 = plot(sol4, vars = (0, 11), lc = colors[4], legend = false,
titlefontsize = 12, lw = 3, title = "lsoda with saveat")
combined_plot = plot(p1, p2, p3, p4, layout = (4, 1), dpi = 600, palette = :acton)
Run Benchmark
abstols = 1.0 ./ 10.0 .^ (8:10)
reltols = 1.0 ./ 10.0 .^ (8:10)
setups = [
Dict(:alg=>FBDF()),
Dict(:alg=>QNDF()),
Dict(:alg=>NordsieckBDF()),
#Dict(:alg=>Rodas4P()),
Dict(:alg=>CVODE_BDF()),
#Dict(:alg=>ddebdf()),
#Dict(:alg=>Rodas4()),
Dict(:alg=>Rodas5P()),
Dict(:alg=>KenCarp4()),
Dict(:alg=>KenCarp47()),
Dict(:alg=>RadauIIA9()),
Dict(:alg=>lsoda())
#Dict(:alg=>rodas()),
#Dict(:alg=>radau()),
#Dict(:alg=>lsoda()),
#Dict(:alg=>ImplicitEulerExtrapolation(min_order = 5, init_order = 3,threading = OrdinaryDiffEqCore.PolyesterThreads())),
#Dict(:alg=>ImplicitEulerExtrapolation(min_order = 5, init_order = 3,threading = false)),
#Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 5, threading = OrdinaryDiffEqCore.PolyesterThreads())),
#Dict(:alg=>ImplicitEulerBarycentricExtrapolation(min_order = 5, threading = false)),
]
wp = WorkPrecisionSet(prob, abstols, reltols, setups; appxsol = refsol,
save_everystep = false, print_names = true)
plot(wp)FBDF
QNDF
NordsieckBDF
CVODE_BDF
Rodas5P
KenCarp4
KenCarp47
RadauIIA9
lsoda
Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/AstroChem","nelson.jmd")Computer Information:
Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
JULIA_NUM_THREADS = auto
Package Information:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AstroChem/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
[479239e8] Catalyst v16.4.3
[f3b72e0c] DiffEqDevTools v3.6.3
[7f56f5a3] LSODA v1.2.0
⌃ [7ed4a6bd] LinearSolve v5.17.3
[77ba4419] NaNMath v1.1.4
[54ca160b] ODEInterface v0.5.2
⌅ [09606e27] ODEInterfaceDiffEq v4.1.0
[1dea7af3] OrdinaryDiffEq v7.8.1
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.9
⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.2
[becaefa8] OrdinaryDiffEqExtrapolation v2.6.3
[5960d6e9] OrdinaryDiffEqFIRK v2.8.7
[43230ef6] OrdinaryDiffEqRosenbrock v2.7.3
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.3
[91a5bcdd] Plots v1.41.7
[f2c3362d] RecursiveFactorization v0.2.30
[31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
[a6db7da4] SciMLLogging v2.1.0
[c3572dad] Sundials v6.7.1
[0c5d862f] Symbolics v7.39.2
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`And the full manifest:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AstroChem/Manifest.toml`
[47edcb42] ADTypes v1.24.0
[14f7f29c] AMD v0.5.4
[6e696c72] AbstractPlutoDingetjes v1.4.1
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.45
[79e6a3ab] Adapt v4.7.0
[66dad0bd] AliasTables v1.1.3
[ec485272] ArnoldiMethod v0.4.0
⌃ [4fba245c] ArrayInterface v7.30.1
[4c555306] ArrayLayouts v1.12.2
[aae01518] BandedMatrices v1.12.0
[6e4b80f9] BenchmarkTools v1.8.0
[e2ed5e7c] Bijections v0.2.2
[b2a6c25c] BinaryHeaps v1.1.0
[caf10ac8] BipartiteGraphs v0.1.14
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[8e7c35d0] BlockArrays v1.10.0
[70df07ce] BracketingNonlinearSolve v1.12.7
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.7
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⌅ [eafb193a] Highlights v0.5.3
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⌃ [7ed4a6bd] LinearSolve v5.17.3
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⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.3
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[19f34311] SciMLJacobianOperators v0.1.19
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⌃ [c0aeaf25] SciMLOperators v1.30.0
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[0c0c59c1] StarAlgebras v0.3.0
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[ed4db957] TaskLocalValues v0.1.3
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⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
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⌅ [e9f186c6] Libffi_jll v3.4.7+0
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[6de9746b] Qt6Svg_jll v6.10.2+0
[e99dba38] Qt6Wayland_jll v6.10.2+1
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[a51aa0fd] Xorg_libXi_jll v1.8.4+0
[d1454406] Xorg_libXinerama_jll v1.1.7+0
[ec84b674] Xorg_libXrandr_jll v1.5.6+0
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[a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
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[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
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[a4ae2306] libaom_jll v3.14.1+0
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[d8fb68d0] xkbcommon_jll v1.13.0+0
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[b27032c2] LibCURL v0.6.4
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[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
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[3fa0cd96] REPL v1.11.0
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[ea8e919c] SHA v0.7.0
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[2f01184e] SparseArrays v1.12.0
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[fa267f1f] TOML v1.0.3
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[e66e0078] CompilerSupportLibraries_jll v1.3.1+2
[deac9b47] LibCURL_jll v8.15.0+0
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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`