pluto_taylor_1.jl

### A Pluto.jl notebook ###
# v0.19.27

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)
    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
end

# ╔═╡ 581f8ff0-d1fc-11ec-3cab-5f335ec587ad
begin
	using PlutoUI 
	using Plots
	using Colors

	# Small patch to make images look more crisp:
	# https://github.com/JuliaImages/ImageShow.jl/pull/50
	Base.showable(::MIME"text/html", ::AbstractMatrix{<:Colorant}) = false
end

# ╔═╡ c299148e-4b85-4bf3-a514-20d1dff0dc59
md"""
## Taylor's Theorem and Taylor Expansion

Taylor's theorem says that if $f(x)$ is $C^\infty$ near $x=a$ then for any $N=1,2,3,\dotsc$

$f(x)
=
\sum_{n=0}^{N-1}
\frac{f^{(n)}(a)}{n!}
(x-a)^n
+
R_N(x),$

$R_N(x)
=
\frac{f^{(N)}\bigl(\theta{x}+(1-\theta)a)}{N!}(x-a)^N,$

$R_N(x)
=
\frac{(x-a)^N}{(N-1)!}
\int_0^1
(1-t)^{N-1}
f\bigl(tx+(1-t)a)
dt,$

where $\theta=\theta(x,a,N)\in(0,1)$ is a constant depending on $x$, $a$ and $N$. 
For **some** smooth function $f$ and **some** $x$, we have 

$f(x)
-
\sum_{n=0}^{N-1}
\frac{f^{(n)}(a)}{n!}
(x-a)^n
=
R_N(x) \rightarrow 0 \quad\text{as}\quad N\rightarrow\infty.$

In this case it is well-known that there exists $\rho\in(0,\infty]$ such that 

$f(x)=
\sum_{n=0}^\infty
\frac{f^{(n)}(a)}{n!}
(x-a)^n,
\quad
x\in(a-\rho,a+\rho).$

The right hand side of the above is said to be the Taylor series or the Taylor expansion of $f(x)$ at center $x=a$ with convergence radius $\rho$.
"""

# ╔═╡ 6f6479b6-265a-4474-8a90-3df0ff98cfac
md"""
##### Examples of Taylor Expansion #1

$(1+x)^\alpha=\sum_{n=0}^\infty\begin{pmatrix}\alpha \\ n\end{pmatrix}x^n, \quad x\in(-1,1), \quad \alpha\in\mathbb{C},$

$\begin{pmatrix}\alpha \\ n\end{pmatrix}=\frac{\alpha(\alpha-1)\dotsb(\alpha-n+1)}{n!}\quad(n=1,2,3,\dotsc), \quad \begin{pmatrix}\alpha \\ 0\end{pmatrix}=1,$

$\log(1+x)=\sum_{n=1}^\infty\frac{(-1)^{n-1}x^n}{n}, \quad x\in(-1,1].$

"""

# ╔═╡ fd9270b6-bcb1-444a-b2e8-bc07efee3a24
md"""
##### Observation #1
$\log(1+x)=\sum_{n=1}^\infty\frac{(-1)^{n-1}x^n}{n}, \quad x\in(-1,1].$

For any $\varepsilon\in(0,1)$, 

$\max_{x\in[-1+\varepsilon,1]}\left\lvert\log(1+x)-\sum_{n=1}^N\frac{(-1)^{n-1}x^n}{n}\right\rvert \rightarrow 0 \quad (N\rightarrow\infty).$


"""

# ╔═╡ 3edf319a-48e4-48f0-82ab-f81e5f2c581c
begin
	x = range(-1, 1.2, length = 221);
	f1=log.(ones(221)+x);
	N=30;
	# each term
    s1=zeros(N,221);
	for n=1:N
	    for l=1:221
	        s1[n,l]=(-1)^(n-1)*x[l]^n/n;
	    end
	end
	# sum
	S1=zeros(N,221);
	S1[1,:]=s1[1,:];
	for l=1:221
	    for n=2:N
		    S1[n,l]=S1[n-1,l]+s1[n,l];
	    end
    end
end

# ╔═╡ a1aa2ce7-db42-44d2-a9d8-4ae67976f76f
md"""
N= $(@bind l1 Slider(1:N, show_value=true))
"""

# ╔═╡ cceffb37-cb1f-4436-aab6-17f325504276
begin
	h1=S1[l1,:];
    plot([f1,h1],grid=false,linewidth=2,ylim=(-4,2),
         title="log(1+x) and its Taylor Series",
         xticks = ([0 101 201;], [-1 0 1]),xlabel="x",
         label=["log(1+x)" "Taylor Polynomial"],
	     legend=:topleft,legendfont=font(12))
end

# ╔═╡ 897a6954-9e77-41d8-a88d-d43b4c9902c6
md"""
##### Observation #2
$(1+x)^{-1/2}=\sum_{n=0}^\infty\frac{(-1)^n(2n)!x^n}{2^{2n}(n!)^2}, \quad x\in(-1,1].$

For any $\varepsilon\in(0,1)$, 

$\max_{x\in[-1+\varepsilon,1]}
\left\lvert
(1+x)^{-1/2}
-
\sum_{n=0}^N
\frac{(-1)^n(2n)!x^n}{2^{2n}(n!)^2}
\right\rvert 
\rightarrow 0 \quad (N\rightarrow\infty).$
"""

# ╔═╡ e956146c-d9f1-4c0f-8422-32c29e6d5b69
begin
    f2=(ones(221)+x).^(-1/2);
	s2=zeros(N+1,221);
	for n=1:N
	    for l=1:221
	        s2[n,l]=(-1)^n*factorial(big(2*n))*x[l]^n/2^(2*n)/factorial(big(n))/factorial(big(n));
        end
    end
	S2=zeros(N+1,221);
	S2[1,:]=ones(221);
	for l=1:221
	    for n=2:N+1
		    S2[n,l]=S2[n-1,l]+s2[n-1,l];
	    end
    end
end

# ╔═╡ c05b1f88-2750-4f76-8af0-10091651289a
md"""
N= $(@bind l2 Slider(0:N, show_value=true))
"""

# ╔═╡ cb7d861a-8d69-4e08-a69d-7638de638e3f
begin
	h2=S2[l2+1,:];
    plot([f2,h2],grid=false,linewidth=2,ylim=(0,4),
		title="(1+x)^(-1/2) and its Taylor Series",
		xticks = ([0 101 201;], [-1 0 1]),xlabel="x",
		label=["(1+x)^(-1/2)" "Taylor Polynomial"],legend=:top,legendfont=font(12))
end

# ╔═╡ 596f1b0f-7a83-4f48-9316-17ef15d88cbe
md"""
##### Examples of Taylor Expansion #2

$e^x=\sum_{n=0}^\infty\frac{x^n}{n!}, \quad \cos{x}=\sum_{k=0}^\infty\frac{(-1)^kx^{2k}}{(2k)!}, \quad \sin{x}=\sum_{k=0}^\infty\frac{(-1)^kx^{2k+1}}{(2k+1)!}, \quad x\in\mathbb{R}.$

"""

# ╔═╡ 8ca3ca65-60cd-49a6-8e49-7e64df935d48
md"""
##### Observation #3
$\sin{x}=\sum_{k=0}^\infty\frac{(-1)^kx^{2k+1}}{(2k+1)!}, \quad x\in\mathbb{R}.$

For any $R>0$, 

$\max_{x\in[-R,R]}
\left\lvert
\sin{x}
-
\sum_{k=0}^K
\frac{(-1)^kx^{2k+1}}{(2k+1)!}
\right\rvert
\rightarrow 0 \quad (K\rightarrow\infty).$

"""

# ╔═╡ 1e890c43-ef8f-4455-84e3-d488fec7f8d2
begin
    y = range(-3*pi, 3*pi, length = 301);
	f3=sin.(y);
	K=15;
	s3=zeros(K,301);
	for k=1:K
	    for l=1:301
	        s3[k,l]=(-1)^(k-1)*y[l]^(2*k-1)/factorial(big(2*k-1));
        end
	end
	S3=zeros(K,301);
	S3[1,:]=s3[1,:];
	for l=1:301
	    for k=2:K
		    S3[k,l]=S3[k-1,l]+s3[k,l];
	    end
	end
end

# ╔═╡ 14bcb950-41f8-4adf-bc42-340fc50515cd
md"""
K = $(@bind l3 Slider(1:K, show_value=true))
"""

# ╔═╡ 45804075-3dba-4760-8560-ecf3f0445fb1
begin
	h3=S3[l3,:];
    plot([f3,h3],grid=false,linewidth=2,ylim=(-1.2,1.2),
		title="sin(x) and its Taylor Series",
		xticks = ([0 50 100 151 201 251 301;], ["-3π" "-2π" "-π" "0" "π" "2π" "3π"]),xlabel="x",
		label=["sin(x)" "Taylor"],legend=:topleft,legendfont=font(8))end

# ╔═╡ a8563bdb-5391-4288-aca7-a279657f7ca0
md"""
##### Approximation of $e$

$e= 2.7182818284590452353602874713...$

$e
=
\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n
=
\sum_{n=0}^\infty
\frac{1}{n!}.$

$a(n)
:=
\left(1+\frac{1}{n}\right)^n,
\quad
b(n)
:=
\sum_{k=0}^n
\frac{1}{k!}.$

"""

# ╔═╡ 69451c4b-eee9-46c1-9e6b-94c771ad7109
N１=100;

# ╔═╡ 7b6a3f4e-6b84-414a-b524-07b16847b0b2
begin
    a=zeros(N１);
	b=zeros(N１);
	a[1]=2;
	b[1]=2
	for n=2:N１
		a[n]=(1+1/n)^n;
		b[n]=b[n-1]+1/factorial(big(n));
	end
end

# ╔═╡ 570aaa20-7c3f-4f79-90c9-a3a6acbf7c56
md"""
n = $(@bind k1 Slider(1:N１, show_value=true))
"""

# ╔═╡ 67e28e2e-b27e-473c-a333-43c27e61df2e
begin
	plot([a[1:k1] b[1:k1]],xlim=[1,N１],ylim=[2.62,2.74],seriestype=:scatter, legend=:bottomright, label=["a(n)" "b(n)"],title="Approximation of e")
end

# ╔═╡ 235d5b25-f044-476c-ad2f-39d1fffbd9c2
md"""
##### Approximation of $\pi$

$\pi= 3.14159265358979323846…$

$\pi
=
4\operatorname{Arctan}1
=
4
\sum_{k=0}^\infty
\frac{(-1)^k}{2k+1}.$

$c(n)
:=
4
\sum_{k=0}^n
\frac{(-1)^k}{(2k+1)}.$

$\pi
=
6\operatorname{Arctan}\left(\frac{1}{\sqrt{3}}\right)
=
6
\sum_{n=0}^\infty
\frac{(-1)^k}{(2k+1)3^{(2k+1)/2}}.$

$d(n)
:=
6
\sum_{k=0}^n
\frac{(-1)^k}{(2k+1)3^{(2k+1)/2}}.$

"""

# ╔═╡ af34278d-13b2-43e5-baf4-21a9884c643f
N2=100;

# ╔═╡ 72d898c8-18b3-44e1-b73d-eeb68dca189a
begin
	c=zeros(N2);
	c[1]=4*(1-1/3);
	d=zeros(N2);
	d[1]=6/3^(1/2)*(1-1/9);
	for n=2:N2
		c[n]=c[n-1]+4*(-1)^n/(2*n+1);
		d[n]=d[n-1]+6*(-1)^n/(2*n+1)/3^(n+1/2);
	end
end

# ╔═╡ 39bc3df4-aeb6-480c-8068-e549ada0397b
md"""
n = $(@bind k2 Slider(1:N2, show_value=true))
"""

# ╔═╡ 3e22df11-977b-436b-bf6c-f05f849202f0
begin
	plot([c[1:k2] d[1:k2]],xlim=[1,N2],ylim=[3,3.3],seriestype=:scatter, legend=:bottomright, label=["c(n)" "d(n)"], title="Approximation of π")
	#savefig("./4arctan1.png")
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
Colors = "~0.12.10"
Plots = "~1.38.16"
PlutoUI = "~0.7.51"
"""

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

julia_version = "1.9.3"
manifest_format = "2.0"
project_hash = "f4993a178da6f189ebeafca4e45d8e0e0e6d67ce"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

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

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

[[deps.BitFlags]]
git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.7"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "9c209fb7536406834aa938fb149964b985de6c83"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.1"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "be6ab11021cd29f0344d5c4357b163af05a48cba"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.21.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.4"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.10"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.10"

[[deps.Compat]]
deps = ["UUIDs"]
git-tree-sha1 = "7a60c856b9fa189eb34f5f8a6f6b5529b7942957"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.6.1"
weakdeps = ["Dates", "LinearAlgebra"]

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

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.0.5+0"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "96d823b94ba8d187a6d8f0826e731195a74b90e9"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.2.0"

[[deps.ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "738fec4d684a9a6ee9598a8bfee305b26831f28c"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.5.2"

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

    [deps.ConstructionBase.weakdeps]
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[[deps.Contour]]
git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.2"

[[deps.DataAPI]]
git-tree-sha1 = "8da84edb865b0b5b0100c0666a9bc9a0b71c553c"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.15.0"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.13"

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

[[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.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.8+0"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.2+2"

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

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[deps.Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.8+0"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
git-tree-sha1 = "8b8a2fd4536ece6e554168c21860b6820a8a83db"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.72.7"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "19fad9cd9ae44847fe842558a744748084a722d1"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.72.7+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", "Pkg", "Zlib_jll"]
git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.74.0+2"

[[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", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "5e77dbf117412d4f164a464d610ee6050cc75272"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.9.6"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "c47c5fa4c5308f27ccaac35504858d8914e102f9"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.4"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "d75853a0bdbfb1ac815478bacd89cd27b550ace6"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.3"

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

[[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 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.5"

[[deps.JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"

[[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 = "6f2675ef130a300a112286de91973805fcc5ffbc"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.91+0"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+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", "Pkg"]
git-tree-sha1 = "f689897ccbe049adb19a065c495e75f372ecd42b"
uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
version = "15.0.4+0"

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[deps.LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.16.1"

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

    [deps.Latexify.weakdeps]
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.3"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.84.0+0"

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

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.10.2+0"

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

[[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", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+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", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+2"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.4.0+0"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

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

[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "c3ce8e7420b3a6e071e0fe4745f5d4300e37b13f"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.24"

    [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"

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "cedb76b37bc5a6c702ade66be44f831fa23c681e"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.0.0"

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

[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.10"

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

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
git-tree-sha1 = "03a9b9718f5682ecb107ac9f7308991db4ce395b"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.7"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.2+0"

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

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.1.0"

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

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.10.11"

[[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 = "0.3.21+4"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+0"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "51901a49222b09e3743c65b8847687ae5fc78eb2"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.4.1"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1aa4b74f80b01c6bc2b89992b861b5f210e665b5"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.21+0"

[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "d321bf2de576bf25ec4d3e4360faca399afca282"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.0"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.42.0+0"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "5a6ab2f64388fd1175effdf73fe5933ef1e0bac0"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.7.0"

[[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 = "64779bc4c9784fee475689a1752ef4d5747c5e87"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.42.2+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.9.2"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.1.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "f92e1315dadf8c46561fb9396e525f7200cdc227"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.3.5"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Preferences", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
git-tree-sha1 = "75ca67b2c6512ad2d0c767a7cfc55e75075f8bbc"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.38.16"

    [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 = "b478a748be27bd2f2c73a7690da219d0844db305"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.51"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "9673d39decc5feece56ef3940e5dafba15ba0f81"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.1.2"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "7eb1686b4f04b82f96ed7a4ea5890a4f0c7a09f1"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.0"

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

[[deps.Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "0c03844e2231e12fda4d0086fd7cbe4098ee8dc5"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+2"

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

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

[[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 = "90bc7a7c96410424509e4263e277e43250c05691"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.0"

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

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

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "30449ee12237627992a99d5e30ae63e4d78cd24a"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.0"

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

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

[[deps.SimpleBufferStream]]
git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.1.0"

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

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "a4ada03f999bd01b3a25dcaa30b2d929fe537e00"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.1.0"

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

[[deps.SpecialFunctions]]
deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "ef28127915f4229c971eb43f3fc075dd3fe91880"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.2.0"

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

    [deps.SpecialFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.9.0"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "45a7769a04a3cf80da1c1c7c60caf932e6f4c9f7"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.6.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "75ebe04c5bed70b91614d684259b661c9e6274a4"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.0"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "5.10.1+6"

[[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"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "9a6ae7ed916312b41236fcef7e0af564ef934769"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.13"

[[deps.Tricks]]
git-tree-sha1 = "aadb748be58b492045b4f56166b5188aa63ce549"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.7"

[[deps.URIs]]
git-tree-sha1 = "074f993b0ca030848b897beff716d93aca60f06a"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.2"

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

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

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

[[deps.Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "ba4aa36b2d5c98d6ed1f149da916b3ba46527b2b"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.14.0"

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

    [deps.Unitful.weakdeps]
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

[[deps.UnitfulLatexify]]
deps = ["LaTeXStrings", "Latexify", "Unitful"]
git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
version = "1.6.3"

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

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.10.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[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", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[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", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[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", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+0"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[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 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
# ╟─581f8ff0-d1fc-11ec-3cab-5f335ec587ad
# ╟─c299148e-4b85-4bf3-a514-20d1dff0dc59
# ╟─6f6479b6-265a-4474-8a90-3df0ff98cfac
# ╟─fd9270b6-bcb1-444a-b2e8-bc07efee3a24
# ╠═3edf319a-48e4-48f0-82ab-f81e5f2c581c
# ╟─a1aa2ce7-db42-44d2-a9d8-4ae67976f76f
# ╟─cceffb37-cb1f-4436-aab6-17f325504276
# ╟─897a6954-9e77-41d8-a88d-d43b4c9902c6
# ╟─e956146c-d9f1-4c0f-8422-32c29e6d5b69
# ╟─c05b1f88-2750-4f76-8af0-10091651289a
# ╟─cb7d861a-8d69-4e08-a69d-7638de638e3f
# ╟─596f1b0f-7a83-4f48-9316-17ef15d88cbe
# ╟─8ca3ca65-60cd-49a6-8e49-7e64df935d48
# ╟─1e890c43-ef8f-4455-84e3-d488fec7f8d2
# ╟─14bcb950-41f8-4adf-bc42-340fc50515cd
# ╟─45804075-3dba-4760-8560-ecf3f0445fb1
# ╟─a8563bdb-5391-4288-aca7-a279657f7ca0
# ╟─69451c4b-eee9-46c1-9e6b-94c771ad7109
# ╟─7b6a3f4e-6b84-414a-b524-07b16847b0b2
# ╟─570aaa20-7c3f-4f79-90c9-a3a6acbf7c56
# ╟─67e28e2e-b27e-473c-a333-43c27e61df2e
# ╟─235d5b25-f044-476c-ad2f-39d1fffbd9c2
# ╟─af34278d-13b2-43e5-baf4-21a9884c643f
# ╟─72d898c8-18b3-44e1-b73d-eeb68dca189a
# ╟─39bc3df4-aeb6-480c-8068-e549ada0397b
# ╟─3e22df11-977b-436b-bf6c-f05f849202f0
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002