Pluto notebook for the analysis of dynamical systems in the course CED 1

CED1-ds-analysis.jl

### A Pluto.jl notebook ###
# v0.20.3

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
    #! format: on
end

# ╔═╡ 6617f488-a294-11ef-0527-fb2e425d0102
using PlutoUI # Interactive utilities

# ╔═╡ 1fdeeec2-9df5-44b1-9956-4ece3ed3247b
using Plots, LaTeXStrings

# ╔═╡ a527d075-e8c8-4604-8dae-33c460d6af99
using Roots

# ╔═╡ 6a77d7bf-d28f-4cdc-a54e-a451f7bb7564
default(size = 500 .* (√2, 1), dpi = 180, linewidth = 3, label = false)

# ╔═╡ 58b1c9b5-c834-48fe-a82b-a3c8fdb11e2c
TableOfContents()

# ╔═╡ 76d1d1d7-6a14-4194-8b1f-e4d31ce2700f
md"# One dimensional dynamical systems"

# ╔═╡ 4d7b4c58-99eb-432c-b710-c135baeb213a
md"
## Continuous time - One parameter $\mu$

First, we define two functions ``f(x; \mu)`` and ``\partial f \big/ \partial x``.

*Side note:* To write greek letters such as $\alpha$, $\beta$, $\mu$ etc. in `Julia` just write `\alpha` and press `tab`!

"

# ╔═╡ 600ff102-362c-492b-9c53-2205ced7382c
f(x; μ) = μ + x - x^3;

# ╔═╡ 689e8c58-9556-4836-9f3d-df6291ebbc23
f′(x; μ) = 1 - 3x^2;

# ╔═╡ 49ff1ce3-ff67-428b-8298-36709b8b227e
md"Let's define a set ``M`` from which we can pick parameters, ``\mu \in M``."

# ╔═╡ 0901c9b1-47a9-49f0-ba7e-2857f0be0f49
M = -1.5:0.05:1.5; # Values between -1 and 1, with step 0.01

# ╔═╡ b8945136-e199-4ceb-b9b1-66d9386d5b8f
md"Let's pick a default value for the paramter ``\mu =`` $(@bind μ Slider(M, default = 0, show_value = true))"

# ╔═╡ 721261ec-61e5-4f64-ab30-557a0b8e5eba
md"Using the `Roots.jl` we find the steady states 

$\bar{x} \in \{ a \leq x \leq b: \; f(x; \mu) = 0 \}$

for $μ =$ $μ.
"

# ╔═╡ c7034c9d-dbfe-40a9-8a79-7f2d98456e7a
begin
	a = -2
	b = 2

	steadystates = find_zeros(x -> f(x; μ), (a, b))

	"Steady states: $steadystates"
end

# ╔═╡ 92b81957-72cf-4a94-b336-65ecf388a321
md"
Let's now plot $\dot{x} = f(x; \mu)$. At the steady states $\bar{x}$ we plot a marker which is full if the steady state is **stable** $f'(\bar{x}; \mu) < 0$ and white if it is **unstable** $f'(\bar{x}; \mu) > 0$.


"

# ╔═╡ 91485276-96ac-43bd-b5a0-a71043b59306
let
	xs = a:0.01:b

	fig = plot(xlabel = L"x", ylabel = L"\dot{x}", ylims = (-4, 4)) # Creates the figure
	hline!(fig, [0.]; c = :black, linewidth = 1.5)

	for x in a:(1/3):b # Draws the arrows
		x′ = x + sign(f(x; μ)) * 0.01
		
		plot!(fig, [x, x′], [0, 0]; arrow=(:closed, 2.0), c = :black)
	end
	
	plot!(fig, xs, x -> f(x; μ); c = :darkred, label = L"$f(x; \mu = %$μ)$")

	for x̄ in steadystates # Draws the steady state
		isstable = f′(x̄; μ) < 0
		color = isstable ? :darkred : :white
		
		scatter!(fig, [x̄], [0.]; color = color, markerstrokecolor = :darkred, markersize = 7)
	end

	fig
end

# ╔═╡ 916f3ed1-29ae-451f-97ac-163cf82346bd
md"
We can now create the bifurcation plot. For parameter $\mu$ we plot the steady states $\overline{x}$. Here we do it simply using `Roots.jl` and the derivative that we provide. A more complete analysis could be done with `BifurcationKit.jl` ([see here](https://bifurcationkit.github.io/BifurcationKitDocs.jl/stable/)). 
"

# ╔═╡ a541a17b-6f81-4a61-995d-118de8ac8862
let
	fig = plot(xlabel = L"\mu", ylabel = L"\bar{x}")

	for μcrit in M, x̄ in find_zeros(x -> f(x; μ = μcrit), (a, b))
		isstable = f′(x̄; μ = μcrit) < 0
		color = isstable ? :darkred : :white
		
		scatter!(fig, [μcrit], [x̄]; color = color, markerstrokecolor = :darkred, markersize = 3)
	end

	fig
end

# ╔═╡ 63122a90-04ac-4a3e-870b-ab99d326aa8b
md"## Discrete time - One parameter $\mu$"

# ╔═╡ 5339d701-b274-4cc1-a3c0-a2d420a422b5
md"
We now move to discrete time systems of the form

$x_{t + 1} = \varphi_{\varepsilon}(x_t).$

As before, we define $\varphi_{\varepsilon}$ and $\varphi'_{\varepsilon}$.

*Note:* I am using $\varepsilon$ as a parameter instead of $\mu$ just to avoid confusion between variables!
"

# ╔═╡ c8b3eebd-9656-498a-87fb-05b2a9359e41
φ(x; ε) = x^3 + ε;

# ╔═╡ 54423830-803d-4da5-b250-f120a727aa12
φ′(x; ε) = 3x^2;

# ╔═╡ 204f0f22-b315-4b77-aef1-700d2756fcac
md"Pick a new default value for the paramter ``\varepsilon =`` $(@bind ε Slider(M, default = 0, show_value = true))"

# ╔═╡ 047f3fb2-93ca-486a-beae-7823746e0759
md"
As before, we find steady states

$\bar{x} \in \{ c \leq x \leq d: \; \varphi(x; \varepsilon) = x \}$

for $\varepsilon =$ $ε.
"

# ╔═╡ 309fa02b-3f4d-4bc1-a377-efdc02fb865d
begin
	c = -2
	d = 2

	discsteadystates = find_zeros(x -> φ(x; ε) - x, (c, d))

	"Steady states: $discsteadystates"
end

# ╔═╡ 64dec03b-d1f5-4258-a121-b3e7e69a5a43
let
	xs = c:0.01:d

	fig = plot(xlabel = L"x_t", ylabel = L"x_{t + 1}", ylims = (c, d), xlims = (c, d)) # Creates the figure
	
	plot!(fig, xs, x -> x; c = :black, linewidth = 1.5, linestyle = :dash)
	plot!(fig, xs, x -> φ(x; ε); c = :darkblue, label = L"$\varphi(x; \varepsilon = %$ε)$")

	for x̄ in discsteadystates # Draws the steady state
		isstable = abs(φ′(x̄; ε)) < 1
		color = isstable ? :darkblue : :white
		
		scatter!(fig, [x̄], [φ(x̄; ε)]; color = color, markerstrokecolor = :darkblue, markersize = 7)
	end

	fig
end


# ╔═╡ 0a1a5a04-2281-4a27-bed0-b8067b6ce6aa
md"
One common way to plot the dynamics $x_{t + 1} = \varphi_{\varepsilon}(x_t)$ is to do it in the figure above as follows

1. Plot the initial condition $x_0$ as a marker.
2. Projected onto the $x \mapsto x$ line and reflect back onto the graph of $\varphi_{\varepsilon}$ to get $x_{1}$
3. Continue for $t$ steps to get $x_{t}$.


Pick

- ``x_0 =`` $(@bind x₀ Slider(c:0.01:d, show_value = true, default = 0))
- ``t =`` $(@bind t Slider(0:20, default = 0, show_value = true)) 

to see in the graph below.
"

# ╔═╡ e334061a-2a7e-4344-b9ac-92edb65cf39e
let
	xs = c:0.01:d

	fig = plot(xlabel = L"x_t", ylabel = L"x_{t + 1}", ylims = (c, d), xlims = (c, d)) # Creates the figure
	
	plot!(fig, xs, x -> x; c = :black, linewidth = 1.5, linestyle = :dash)
	plot!(fig, xs, x -> φ(x; ε); c = :darkblue, label = L"$\varphi(x; \varepsilon = %$ε)$")

	for x̄ in discsteadystates # Draws the steady state
		isstable = φ′(x̄; ε) < 1
		color = isstable ? :darkblue : :white
		
		scatter!(fig, [x̄], [φ(x̄; ε)]; color = color, markerstrokecolor = :darkblue, markersize = 7)
	end

	xₜ = x₀
	scatter!(fig, [xₜ], [φ(xₜ; ε)]; c = :black)
	
	for n in 1:t 
		plot!(fig, [xₜ, φ(xₜ; ε)], [φ(xₜ; ε), φ(xₜ; ε)]; c = :black, linewidth = 2)
		xₜ = φ(xₜ; ε)
		plot!(fig, [xₜ, xₜ], [xₜ, φ(xₜ; ε)]; c = :black, linewidth = 2)
		scatter!(fig, [xₜ], [φ(xₜ; ε)]; c = :black)
	end

	fig
end


# ╔═╡ f3d0ab96-3d4d-4485-adc1-b8deef661544
let
	fig = plot(xlabel = L"\varepsilon", ylabel = L"\bar{x}")

	for ε in M, x̄ in find_zeros(x -> φ(x; ε = ε) - x, (c, d))
		isstable = φ′(x̄; ε) < 1
		color = isstable ? :darkblue : :white
		
		scatter!(fig, [ε], [x̄]; color = color, markerstrokecolor = :darkblue, markersize = 3)
	end

	fig
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"

[compat]
LaTeXStrings = "~1.3.1"
Plots = "~1.40.8"
PlutoUI = "~0.7.60"
Roots = "~2.2.1"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.11.1"
manifest_format = "2.0"
project_hash = "128b0019b25338c7bb0b51ba03ec7812b5861cef"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.2"

[[deps.Accessors]]
deps = ["CompositionsBase", "ConstructionBase", "InverseFunctions", "LinearAlgebra", "MacroTools", "Markdown"]
git-tree-sha1 = "b392ede862e506d451fc1616e79aa6f4c673dab8"
uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
version = "0.1.38"

    [deps.Accessors.extensions]
    AccessorsAxisKeysExt = "AxisKeys"
    AccessorsDatesExt = "Dates"
    AccessorsIntervalSetsExt = "IntervalSets"
    AccessorsStaticArraysExt = "StaticArrays"
    AccessorsStructArraysExt = "StructArrays"
    AccessorsTestExt = "Test"
    AccessorsUnitfulExt = "Unitful"

    [deps.Accessors.weakdeps]
    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
    Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.2"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.11.0"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
version = "1.11.0"

[[deps.BitFlags]]
git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.9"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+1"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "009060c9a6168704143100f36ab08f06c2af4642"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.18.2+1"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.6"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "b5278586822443594ff615963b0c09755771b3e0"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.26.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.5"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

    [deps.ColorVectorSpace.weakdeps]
    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.11"

[[deps.CommonSolve]]
git-tree-sha1 = "0eee5eb66b1cf62cd6ad1b460238e60e4b09400c"
uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
version = "0.2.4"

[[deps.Compat]]
deps = ["TOML", "UUIDs"]
git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.16.0"
weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"

[[deps.CompositionsBase]]
git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
version = "0.1.2"
weakdeps = ["InverseFunctions"]

    [deps.CompositionsBase.extensions]
    CompositionsBaseInverseFunctionsExt = "InverseFunctions"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.4.2"

[[deps.ConstructionBase]]
git-tree-sha1 = "76219f1ed5771adbb096743bff43fb5fdd4c1157"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.5.8"

    [deps.ConstructionBase.extensions]
    ConstructionBaseIntervalSetsExt = "IntervalSets"
    ConstructionBaseLinearAlgebraExt = "LinearAlgebra"
    ConstructionBaseStaticArraysExt = "StaticArrays"

    [deps.ConstructionBase.weakdeps]
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[[deps.Contour]]
git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.3"

[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.16.0"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.20"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
version = "1.11.0"

[[deps.Dbus_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af"
uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab"
version = "1.14.10+0"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
version = "1.9.1"

[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
version = "0.0.20230411+0"

[[deps.ExceptionUnwrapping]]
deps = ["Test"]
git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
version = "0.1.10"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1c6317308b9dc757616f0b5cb379db10494443a7"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.6.2+0"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "53ebe7511fa11d33bec688a9178fac4e49eeee00"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.2"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.4+1"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
version = "1.11.0"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.5"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"]
git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.96+0"

[[deps.Format]]
git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
version = "1.3.7"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.13.2+0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.14+0"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"]
git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.4.0+1"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
git-tree-sha1 = "629693584cef594c3f6f99e76e7a7ad17e60e8d5"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.73.7"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "a8863b69c2a0859f2c2c87ebdc4c6712e88bdf0d"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.73.7+0"

[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
git-tree-sha1 = "674ff0db93fffcd11a3573986e550d66cd4fd71f"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.80.5+0"

[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "1336e07ba2eb75614c99496501a8f4b233e9fafe"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.10.10"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "401e4f3f30f43af2c8478fc008da50096ea5240f"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "8.3.1+0"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.5"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.5"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "b6d6bfdd7ce25b0f9b2f6b3dd56b2673a66c8770"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.5"

[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
version = "1.11.0"

[[deps.InverseFunctions]]
git-tree-sha1 = "a779299d77cd080bf77b97535acecd73e1c5e5cb"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.17"
weakdeps = ["Dates", "Test"]

    [deps.InverseFunctions.extensions]
    InverseFunctionsDatesExt = "Dates"
    InverseFunctionsTestExt = "Test"

[[deps.IrrationalConstants]]
git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.2.2"

[[deps.JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "39d64b09147620f5ffbf6b2d3255be3c901bec63"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.8"

[[deps.JLLWrappers]]
deps = ["Artifacts", "Preferences"]
git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.6.1"

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.4"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "3.0.4+0"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.2+0"

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"

[[deps.LLVMOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929"
uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
version = "18.1.7+0"

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.2+1"

[[deps.LaTeXStrings]]
git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.1"

[[deps.Latexify]]
deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.16.5"

    [deps.Latexify.extensions]
    DataFramesExt = "DataFrames"
    SparseArraysExt = "SparseArrays"
    SymEngineExt = "SymEngine"

    [deps.Latexify.weakdeps]
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.6.0+0"

[[deps.LibGit2]]
deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
version = "1.11.0"

[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.7.2+0"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.0+1"

[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
version = "1.11.0"

[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[deps.Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"]
git-tree-sha1 = "9fd170c4bbfd8b935fdc5f8b7aa33532c991a673"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.11+0"

[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.6.0+0"

[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "fbb1f2bef882392312feb1ede3615ddc1e9b99ed"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.49.0+0"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.17.0+0"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "0c4f9c4f1a50d8f35048fa0532dabbadf702f81e"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.40.1+0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.5.1+1"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "5ee6203157c120d79034c748a2acba45b82b8807"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.40.1+0"

[[deps.LinearAlgebra]]
deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
version = "1.11.0"

[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "a2d09619db4e765091ee5c6ffe8872849de0feea"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.28"

    [deps.LogExpFunctions.extensions]
    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

    [deps.LogExpFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
version = "1.11.0"

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "f02b56007b064fbfddb4c9cd60161b6dd0f40df3"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.1.0"

[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"

[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.13"

[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
version = "1.11.0"

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.9"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.6+0"

[[deps.Measures]]
git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.2"

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.2.0"

[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
version = "1.11.0"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2023.12.12"

[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.2"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.27+1"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+2"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "38cb508d080d21dc1128f7fb04f20387ed4c0af4"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.4.3"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "3.0.15+1"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.3+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.3"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.42.0+1"

[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.54.1+0"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.1"

[[deps.Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"

[[deps.Pixman_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
git-tree-sha1 = "35621f10a7531bc8fa58f74610b1bfb70a3cfc6b"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.43.4+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.11.0"
weakdeps = ["REPL"]

    [deps.Pkg.extensions]
    REPLExt = "REPL"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "6e55c6841ce3411ccb3457ee52fc48cb698d6fb0"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.2.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "7b1a9df27f072ac4c9c7cbe5efb198489258d1f5"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.4.1"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
git-tree-sha1 = "45470145863035bb124ca51b320ed35d071cc6c2"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.40.8"

    [deps.Plots.extensions]
    FileIOExt = "FileIO"
    GeometryBasicsExt = "GeometryBasics"
    IJuliaExt = "IJulia"
    ImageInTerminalExt = "ImageInTerminal"
    UnitfulExt = "Unitful"

    [deps.Plots.weakdeps]
    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "eba4810d5e6a01f612b948c9fa94f905b49087b0"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.60"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.3"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
version = "1.11.0"

[[deps.Qt6Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
git-tree-sha1 = "492601870742dcd38f233b23c3ec629628c1d724"
uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
version = "6.7.1+1"

[[deps.Qt6Declarative_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6ShaderTools_jll"]
git-tree-sha1 = "e5dd466bf2569fe08c91a2cc29c1003f4797ac3b"
uuid = "629bc702-f1f5-5709-abd5-49b8460ea067"
version = "6.7.1+2"

[[deps.Qt6ShaderTools_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"]
git-tree-sha1 = "1a180aeced866700d4bebc3120ea1451201f16bc"
uuid = "ce943373-25bb-56aa-8eca-768745ed7b5a"
version = "6.7.1+1"

[[deps.Qt6Wayland_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6Declarative_jll"]
git-tree-sha1 = "729927532d48cf79f49070341e1d918a65aba6b0"
uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3"
version = "6.7.1+1"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
version = "1.11.0"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
version = "1.11.0"

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.12"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.1"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[deps.Roots]]
deps = ["Accessors", "CommonSolve", "Printf"]
git-tree-sha1 = "3a7c7e5c3f015415637f5debdf8a674aa2c979c4"
uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
version = "2.2.1"

    [deps.Roots.extensions]
    RootsChainRulesCoreExt = "ChainRulesCore"
    RootsForwardDiffExt = "ForwardDiff"
    RootsIntervalRootFindingExt = "IntervalRootFinding"
    RootsSymPyExt = "SymPy"
    RootsSymPyPythonCallExt = "SymPyPythonCall"

    [deps.Roots.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    IntervalRootFinding = "d2bf35a9-74e0-55ec-b149-d360ff49b807"
    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
    SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.1"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
version = "1.11.0"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.2.0"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
version = "1.11.0"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.2.1"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.11.0"

[[deps.Statistics]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.11.1"
weakdeps = ["SparseArrays"]

    [deps.Statistics.extensions]
    SparseArraysExt = ["SparseArrays"]

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.7.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.3"

[[deps.StyledStrings]]
uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
version = "1.11.0"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.7.0+0"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
version = "1.11.0"

[[deps.TranscodingStreams]]
git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.11.3"

[[deps.Tricks]]
git-tree-sha1 = "7822b97e99a1672bfb1b49b668a6d46d58d8cbcb"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.9"

[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
version = "1.11.0"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
version = "1.11.0"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unitful]]
deps = ["Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.21.0"
weakdeps = ["ConstructionBase", "InverseFunctions"]

    [deps.Unitful.extensions]
    ConstructionBaseUnitfulExt = "ConstructionBase"
    InverseFunctionsUnitfulExt = "InverseFunctions"

[[deps.UnitfulLatexify]]
deps = ["LaTeXStrings", "Latexify", "Unitful"]
git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8"
uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
version = "1.6.4"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "1165b0443d0eca63ac1e32b8c0eb69ed2f4f8127"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.13.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.41+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.4.6+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "326b4fea307b0b39892b3e85fa451692eda8d46c"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.1+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "3796722887072218eabafb494a13c963209754ce"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.4+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.6+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.11+0"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.4+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.6+1"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "936081b536ae4aa65415d869287d43ef3cb576b2"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.53.0+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.9.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.3+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.44+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

# ╔═╡ Cell order:
# ╠═6617f488-a294-11ef-0527-fb2e425d0102
# ╠═1fdeeec2-9df5-44b1-9956-4ece3ed3247b
# ╠═6a77d7bf-d28f-4cdc-a54e-a451f7bb7564
# ╠═58b1c9b5-c834-48fe-a82b-a3c8fdb11e2c
# ╟─76d1d1d7-6a14-4194-8b1f-e4d31ce2700f
# ╟─4d7b4c58-99eb-432c-b710-c135baeb213a
# ╠═600ff102-362c-492b-9c53-2205ced7382c
# ╠═689e8c58-9556-4836-9f3d-df6291ebbc23
# ╟─49ff1ce3-ff67-428b-8298-36709b8b227e
# ╠═0901c9b1-47a9-49f0-ba7e-2857f0be0f49
# ╟─b8945136-e199-4ceb-b9b1-66d9386d5b8f
# ╠═a527d075-e8c8-4604-8dae-33c460d6af99
# ╟─721261ec-61e5-4f64-ab30-557a0b8e5eba
# ╟─c7034c9d-dbfe-40a9-8a79-7f2d98456e7a
# ╟─92b81957-72cf-4a94-b336-65ecf388a321
# ╟─91485276-96ac-43bd-b5a0-a71043b59306
# ╟─916f3ed1-29ae-451f-97ac-163cf82346bd
# ╟─a541a17b-6f81-4a61-995d-118de8ac8862
# ╟─63122a90-04ac-4a3e-870b-ab99d326aa8b
# ╟─5339d701-b274-4cc1-a3c0-a2d420a422b5
# ╠═c8b3eebd-9656-498a-87fb-05b2a9359e41
# ╠═54423830-803d-4da5-b250-f120a727aa12
# ╟─204f0f22-b315-4b77-aef1-700d2756fcac
# ╟─047f3fb2-93ca-486a-beae-7823746e0759
# ╠═309fa02b-3f4d-4bc1-a377-efdc02fb865d
# ╠═64dec03b-d1f5-4258-a121-b3e7e69a5a43
# ╟─0a1a5a04-2281-4a27-bed0-b8067b6ce6aa
# ╟─e334061a-2a7e-4344-b9ac-92edb65cf39e
# ╟─f3d0ab96-3d4d-4485-adc1-b8deef661544
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002