PCM20210818_SICP_1.3.3_ProceduresAsGeneralMethods.jl

### A Pluto.jl notebook ###
# v0.19.11

using Markdown
using InteractiveUtils

# ╔═╡ 84eadb69-d953-470d-a70a-76bc06919a4c
using Plots

# ╔═╡ 70b7a0d0-0032-11ec-1d54-e7f5d0bac4c8
md"
======================================================================================
### SICP: [1.3.3 Procedures As General Methods](https://sarabander.github.io/sicp/html/1_002e3.xhtml#g_t1_002e3_002e3)

###### file: PCM20210818\_SICP\_1.3.3\_ProceduresAsGeneralMethods.jl

###### Julia/Pluto.jl-code (1.8.0/19.11) by PCM *** 2021/08/26 ***
======================================================================================
"

# ╔═╡ 2004cbff-f769-4231-b791-1d077fbf7029
md"
##### 1.3.3.1 SICP-Scheme-like *functional* Julia
"

# ╔═╡ 32c843e8-4faf-4feb-a63c-be78c622fd33
md"
###### Finding roots of equations by the half-interval method
"

# ╔═╡ f7e18088-b523-4a3a-bce3-331bceec9f2f
function closeEnough(x, y)
	abs(-(x, y)) < 0.001
end # function closeEnough

# ╔═╡ bc7ae6f4-6b18-4177-ae38-4532b61a8bb3
function search(f, neg_point, pos_point)
	#------------------------------------------------
	average(x, y) = /(+(x, y), 2)
	#------------------------------------------------
	negative(x) = <(x, 0)
	positive(x) = >(x, 0)
	#------------------------------------------------
	let mid_point = average(neg_point, pos_point)
		if closeEnough(neg_point, pos_point)
			mid_point
		else 
			let test_value = f(mid_point)
				if positive(test_value)
					search(f, neg_point, mid_point)
				elseif negative(test_value)
					search(f, mid_point, pos_point)
				else 
					mid_point
				end # if
			end # let
		end # if
	end # let
end # function search

# ╔═╡ 45cc3406-c14c-42c3-9138-78d1ceebfc59
# idiomatic Julia-code with string-interpolation 'x=$x'
function halfIntervalMethod(f, a, b)
	#------------------------------------------------
	negative(x) = <(x, 0)
	positive(x) = >(x, 0)
	#------------------------------------------------
	let (a_value, b_value) = (f(a), f(b))             # parallel assignment
		if negative(a_value) && positive(b_value)     # '&&' must be infix !
			search(f, a, b)
		elseif negative(b_value) && positive(a_value) # '&&' must be infix !
			search(f, b, a)
		else 
			"Values are not of opposite sign, a=$a, b=$b"
		end # if
	end # let
end # function halfIntervalMethod

# ╔═╡ 0be35aec-15b7-4ff3-bf26-4f08ab98debb
let rootPi = halfIntervalMethod(sin, 2.0, 4.0)
	plot(sin::Function, 1.0, 5.0, size=(500, 500), xlim=(-1, 5), aspect_ratio=2, line=:darkblue, framestyle=:zerolines, title="pi := root f(x) = {x | sin x = 0, 2 <= x <= 4}")
	plot!([rootPi, rootPi],[-1, +1], line=(2, :magenta))
end

# ╔═╡ fa9e22cb-667e-43fd-afa9-2820fe1c9e23
let rootPi = halfIntervalMethod(sin, 2.0, 4.0)
	plot(sin::Function, 2, 4, size=(500, 500), xlim=(2.75, 3.5), ylim=(-0.5, +0.5),  line=:darkblue, framestyle=:zerolines, title="pi := root f(x) = {x|sin x=0, 2.5<=x<=3.5}")
	plot!([rootPi, rootPi],[-1, +1], line=(2, :magenta))
end

# ╔═╡ cddd0732-9d37-4b26-83f0-beb0e9b4f3e7
halfIntervalMethod(sin, 2.0, 4.0)

# ╔═╡ 5ec5382e-3416-4986-a9c2-fa5ba66ba165
let root = halfIntervalMethod(x->x^3-2x-3, 1, 2)
	plot(x -> x^3 - 2x - 3, 0.5, 2.5, size=(550, 550),line=:darkblue, xlim=(0.75, 2.5), aspect_ratio=.2, framestyle=:zerolines, title="root f(x): {x | f(x)=x^3-2x-3=0, 0.5<=x<=2.5}")
	plot!([root, root],[-2.5, +2.5], line=(2, :magenta))
end


# ╔═╡ 830bf3bd-5143-4fb5-954b-7d79fab8aff2
# prefix '-' is contrary to the multiary Scheme '-' only binary !
halfIntervalMethod(x-> -(^(x, 3), -(*(2, x), 3)), 1.0, 2.0) 

# ╔═╡ 01678534-e80a-47bd-b2b2-7c508f1504aa
md"
##### Finding fixed points of functions 
---
###### [Iteration:](https://en.wikipedia.org/wiki/Fixed-point_iteration)
$$x_{i+1} = f(x_i) \;\;\text{ where: } i=0, 1, 2, ...$$

###### [Definition:](https://en.wikipedia.org/wiki/Fixed-point_iteration)
$$f: x \mapsto f(x)$$

---
"

# ╔═╡ cd32d6a5-dc18-4761-99cf-f7556471cf7e
tolerance = 1.0E-5

# ╔═╡ a7743ac3-3fda-4c27-97b8-255798307fdc
function fixedPoint1(f, firstGuess)
	#----------------------------------------------
	closeEnough(v1, v2) = abs(v1-v2) < tolerance
	#----------------------------------------------
	function myTry(guess)
			let next = f(guess)
				if closeEnough(guess, next)
					next
				else 
					myTry(next)
				end # if
			end # let
	end # function myTry
	#-----------------------------------------------
	myTry(firstGuess)
	#-----------------------------------------------
end # function fixedPoint1

# ╔═╡ 985fa2b9-1165-4fa2-aa76-b1ec82c22d20
let fixPoint = fixedPoint1(cos, 1.0)
	plot(cos, -1.0, 4.0, size=(500, 500),line=:darkblue, xlim=(-0.5, 3.5), ylim=[-1.5, +1.5], aspect_ratio=1, framestyle=:zerolines, title="f-point f(x): {x | cos(x)=x, -1.0<=x<=4.0}")
	plot!([fixPoint, fixPoint], [-1, +1], line=(2, :magenta))
	plot!([-1, +1], [fixPoint, fixPoint], line=(2, :magenta))
end

# ╔═╡ b0f33571-3439-4532-8567-96fec9519ac3
fixedPoint1(cos, 1.0)

# ╔═╡ 348c13be-69f8-461d-b4d3-d34fff2f4c2e
cos(0.7390822985224023)

# ╔═╡ 029d7a0c-7960-4abf-b5b7-b915cb1ef5a9
let fixPoint = fixedPoint1(y->sin(y)+cos(y), 1)
	plot(y->sin(y)+cos(y), -1.0, 3.5, size=(400, 500),line=:darkblue, xlim=(-1, 5), aspect_ratio=2, framestyle=:zerolines, title="f-point f(x):{x|sin(x)+cos(x)=x}")
	plot!([fixPoint, fixPoint], [-1.0, +1.5], line=(2, :magenta))
	plot!([-1, +1.5], [fixPoint, fixPoint], line=(2, :magenta))
end

# ╔═╡ f4a12356-80e4-4010-b772-ef17f158ad75
fixedPoint1(y-> +(sin(y),cos(y)), 1.0)

# ╔═╡ 18117b84-de2d-480c-9e7a-59b04808de2b
(y->+(sin(y),cos(y)))(1.2587315962971173)

# ╔═╡ 50992a70-53bd-40c6-8f7f-3da1abaa5f74
md"
###### *Derivation* of fixed point from *specification* of square root

---
###### Specification 
$$y^2=x$$
###### Derivation
$$y^2=x \Rightarrow \frac{y^2}{y} = \frac{x}{y} \Rightarrow y = \frac{x}{y}\;\;\;\blacksquare$$
###### Fix point equation
$$y = \frac{x}{y}$$

---
"  

# ╔═╡ 0b8c94bb-a20a-48ad-bf81-14c0be4fa26f
function mySqrt1(x)
	fixedPoint1(y->/(x, y), 1.0)
end

# ╔═╡ 94d1eb71-d09a-4f0b-b7e3-0700026ebe72
mySqrt1(2.0) # StackOverFlow due to missing tco (tail-recursive optimization) in Julia

# ╔═╡ 515da1b3-a77a-4a78-935f-d371da7a3428
md"
---
##### 1.3.3.2 idiomatic *imperative* Julia ...
###### ... with 'while', types
"

# ╔═╡ 00cbb859-3aa9-4213-bcbe-b939d78d0008
FloatOrSigned = Union{AbstractFloat, Signed}

# ╔═╡ 95d524cc-99dd-43fa-8102-acb7d3a24de0
# idiomatic Julia with 'while'

function fixed_point2(f::Function, first_guess::FloatOrSigned)::FloatOrSigned
	#----------------------------------------------
	closeEnough(v1, v2) = abs(v1-v2) < tolerance
	#----------------------------------------------
	function mytry(guess)
		next = f(guess)
		while !closeEnough(guess, next)
			guess = next
			next = f(guess)
		end # while
		next
	end # function mytry
	#-----------------------------------------------
	mytry(first_guess)
	#-----------------------------------------------
end # function fixed_point2

# ╔═╡ 50c5ed96-22ad-4a09-be21-9ea23946fb78
fixed_point2(cos, 1.0)

# ╔═╡ 8ba154a1-f3f2-4427-a5dc-c357fb8ed079
fixed_point2(y->sin(y)+cos(y), 1.0)

# ╔═╡ 2f0df9c1-462d-49fe-b79f-58da37db1d4b
function mysqrt2(x)
	#-------------------------------------
	average(x, y) = (x + y)/2.0
	#-------------------------------------
	fixed_point2(y->average(y, x/y), 1.0)
	#-------------------------------------
end # function mysqrt2

# ╔═╡ 26a3c79b-ae77-48c1-bdf9-2285a64705ae
let (x, average) = (2.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixed_point2(y->average(y, x/y), 1.0)
		plot(y->x/y, [0.5:0.1:4.0], size=(500, 500),line=:darkblue, xlim=(-0.5, 4), aspect_ratio=1, framestyle=:zerolines, title="sqrt($x) := f-point f($x): {y|$x/y=y}")
		plot!([fixPoint, fixPoint], [-0.5, +2], line=(2, :magenta))
		plot!([-0.5, +2], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 8d7294bf-842c-454f-8596-f55fade98382
mysqrt2(2.0)

# ╔═╡ db774e20-74c5-43ed-9ab4-30e9dcf753a7
let (x, average) = (9.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixed_point2(y->average(y, x/y), 1.0)
		plot(y->x/y, [0.5:0.1:9.0], size=(700, 500),line=:darkblue, xlim=(-0.5, 9), aspect_ratio=1, framestyle=:zerolines, title="sqrt($x) := f-point f($x): {y|$x/y=y}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 4830e8f0-7290-4ad2-9734-f6ee8a301c3b
mysqrt2(9.0)

# ╔═╡ 10ea6db7-f046-43a2-8dc5-17fd3577eef1
# removal of local mytry

function fixed_point3(f::Function, first_guess::FloatOrSigned)::FloatOrSigned
	#----------------------------------------------
	closeEnough(v1, v2) = abs(v1-v2) < tolerance
	#----------------------------------------------
	guess = first_guess
	next = f(guess)
	while !closeEnough(guess, next)
		guess = next
		next = f(guess)
	end # while
	next
end # function fixed_point3

# ╔═╡ 0d5abce7-12bc-47fa-9dd0-f54eaf1e86bb
fixed_point3(cos, 1.0)

# ╔═╡ 0ce1f847-08a6-43f5-8f0f-3e78678c2bb1
fixed_point3(y->sin(y)+cos(y), 1.0)

# ╔═╡ 75de942b-f4d9-444d-9ffc-339e25fdfe82
function mysqrt3(x)
	#-------------------------------------
	average(x, y) = (x + y)/2.0
	#-------------------------------------
	fixed_point3(y->average(y, x/y), 1.0)
	#-------------------------------------
end

# ╔═╡ 9f84cab6-8f92-459f-96f9-854187875eea
let (x, average) = (2.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixed_point3(y->average(y, x/y), 1.0)
		plot(y->x/y, [0.5:0.1:4.0], size=(500, 500),line=:darkblue, xlim=(-0.5, 4), aspect_ratio=1, framestyle=:zerolines, title="sqrt($x) := f-point f($x): {y|$x/y=y}")
		plot!([fixPoint, fixPoint], [-0.5, +2], line=(2, :magenta))
		plot!([-0.5, +2], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 65240f19-a154-45ad-a7b0-a3267284fcf4
mysqrt3(2.0)

# ╔═╡ 04742e94-35a9-4744-83a4-396a85f9bf6a
let (x, average) = (9.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixed_point3(y->average(y, x/y), 1.0)
		plot(y->x/y, [0.5:0.1:9.0], size=(500, 500),line=:darkblue, xlim=(-0.5, 9), aspect_ratio=1, framestyle=:zerolines, title="sqrt($x) := f-point f($x): {y|$x/y=y}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ d3197075-f9aa-49fe-b939-da488ed9b3c0
mysqrt3(9.0)

# ╔═╡ b3510e69-4324-43f8-93d6-f46f9f16f024
mysqrt2(100 + 37)

# ╔═╡ f05d7e48-8471-41bf-accc-226442bd38f6
mysqrt3(100 + 37)

# ╔═╡ 44954b59-f7b2-43c8-ab2b-dd573d76b23f
mysqrt2(mysqrt2(2.0) + mysqrt2(3.0))

# ╔═╡ 6314d1dc-d0e8-4621-9e94-823971a7911d
mysqrt3(mysqrt3(2.0) + mysqrt3(3.0))

# ╔═╡ f18d9ba8-3008-4054-b1d4-a3beac6fdde5
mysqrt2(1000.0)^2

# ╔═╡ 8eb5cd3a-488e-4bef-8eee-e8ba9410728b
mysqrt3(1000.0)^2

# ╔═╡ a7e44307-94b6-4be3-a1a6-5c287dfcade9
md"
---
- **Abelson, H., Sussman, G.J. & Sussman, J.**, Structure and Interpretation of Computer Programs, Cambridge, Mass.: MIT Press, (2/e), 1996, [https://sarabander.github.io/sicp/](https://sarabander.github.io/sicp/), last visit 2022/08/26
"

# ╔═╡ e46cf879-01d9-4f0e-b820-313d19de3c18
md"
---
##### end of ch. 1.3.3

====================================================================================

This is a **draft** under the [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/) license. Comments, suggestions for improvement and bug reports are welcome: **claus.moebus(@)uol.de**

====================================================================================
"

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"

[compat]
Plots = "~1.20.1"
"""

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

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[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.1+5"

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

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+1"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "182da592436e287758ded5be6e32c406de3a2e47"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.58.1"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "d59e8320c2747553788e4fc42231489cc602fa50"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.58.1+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[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"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+2"

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

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "44e3b40da000eab4ccb1aecdc4801c040026aeb5"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.13"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

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

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

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

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

[[LaTeXStrings]]
git-tree-sha1 = "c7f1c695e06c01b95a67f0cd1d34994f3e7db104"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.2.1"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a4b12a1bd2ebade87891ab7e36fdbce582301a92"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.6"

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

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

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

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

[[LibVPX_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7"
uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
version = "1.10.0+0"

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

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

[[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"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

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

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "c9551dd26e31ab17b86cbd00c2ede019c08758eb"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+1"

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

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

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "0fb723cd8c45858c22169b2e42269e53271a6df7"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.7"

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

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.0+0"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.0"

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

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.2.1"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

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

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

[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.20+0"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+0"

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

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "477bf42b4d1496b454c10cce46645bb5b8a0cf2c"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.0.2"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "501c20a63a34ac1d015d5304da0e645f42d91c9f"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.11"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
git-tree-sha1 = "8365fa7758e2e8e4443ce866d6106d8ecbb4474e"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.20.1"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

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

[[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 = "c6c0f690d0cc7caddb74cef7aa847b824a16b256"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+1"

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

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

[[RecipesBase]]
git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.1.2"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "2a7a2469ed5d94a98dea0e85c46fa653d76be0cd"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.3.4"

[[Reexport]]
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uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.1.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

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

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

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

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

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

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

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

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

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3240808c6d463ac46f1c1cd7638375cd22abbccb"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.12"

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

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "fed1ec1e65749c4d96fc20dd13bea72b55457e62"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.9"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.0"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "d0c690d37c73aeb5ca063056283fde5585a41710"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.5.0"

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

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

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

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

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

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[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"

[[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"

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

[[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"

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

[[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"

[[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"

[[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"

[[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"

[[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"

[[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"

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

[[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"

[[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"

[[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"

[[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"

[[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"

[[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"

[[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"

[[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"

[[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"

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

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

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

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

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

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

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

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