PCM20210820_SICP_1.3.4_ProceduresAsReturnedValues.jl

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

using Markdown
using InteractiveUtils

# ╔═╡ 50cbd85a-2a84-4f2c-836b-7a121a2f4a89
using Plots

# ╔═╡ 3ab9a060-01a8-11ec-26b0-f58b434fab4c
md"
======================================================================================
### SICP: [1.3.4 Procedures As Returned Values](https://sarabander.github.io/sicp/html/1_002e3.xhtml#g_t1_002e3_002e4)

###### file: PCM20210820\_SICP\_1.3.4\_ProceduresAsReturnedValues.jl

###### Julia/Pluto.jl-code (1.8.0/19.11) by PCM *** 2022/08/26 ***
======================================================================================
"

# ╔═╡ a378aca9-2d79-4124-bea6-ba62ab1c3d83
md"
---
#### 1.3.4.1 Square and cube root as fix points
$$\sqrt \; : x \mapsto y \in \{y \;|\; (y > 0) \land (y^2 = x)\}$$
$$\sqrt \; : x \mapsto f(x)$$
$$f(x) := x/y$$

---
"

# ╔═╡ e4443263-e26f-462e-b11a-294fbd259e9a
md"
##### 1.3.4.1.1 SICP-Scheme-like *functional* Julia
"

# ╔═╡ 3df9dd3c-058b-47b6-b39d-570443cc51b9
function averageDamp(f)
	average(x, y) = /(+(x, y), 2)
	function (x)           # definition of anonymous function λ
		average(x, f(x))
	end # λ
end # function averageDamp

# ╔═╡ 2a56d3e3-bb2e-4382-864c-9d3c099cb177
square(x) = ^(x, 2)

# ╔═╡ 53b7806d-489d-45ba-80a9-17bf9ebfc434
averageDamp(square)(10)       # two '(' and two ')'

# ╔═╡ f5a15cb0-a039-43a1-ba4c-2674e672e6ff
(averageDamp(square))(10)     # three '(' and three ')'

# ╔═╡ 81ecbeb5-7c4d-40e8-aeb1-2386277de71d
((averageDamp(square))(10))   # three '(' and three ')'

# ╔═╡ 1fc90de5-9e3d-417b-8475-1ae507eb355c
(averageDamp(square)(10))     # three '(' and three ')'

# ╔═╡ 73c57933-68f8-4e92-8a2a-edf4da95d723
md"
---
##### Cube root as fix point:

$$^3\sqrt \; : x \mapsto y \in \{y \;|\; (y>0) \land (y^3 = x)\}$$
$$^3\sqrt \; : x \mapsto g(x)$$
$$g(x) = x/y^2$$

---
"

# ╔═╡ f05fca2a-638f-47f3-9b64-b1845b4169c7
md"
---
##### 1.3.4.1.2 idiomatic *imperative* Julia ...
###### ... with self-defined abstrac type 'FloatOrInteger', while, ...
"

# ╔═╡ 9b740450-2b0f-4955-a2c7-06b926cd7191
FloatOrSigned = Union{AbstractFloat, Signed}

# ╔═╡ 061844e7-ff4d-4697-9179-7470ca4a0f19
tolerance = 1.0E-6

# ╔═╡ 744ed935-2298-467b-8042-a4ff00f3e40c
function fixedPoint3(f::Function, first_guess::FloatOrSigned)::FloatOrSigned
	#----------------------------------------------
	close_enough(v1, v2) = abs(v1-v2) < tolerance
	#----------------------------------------------
	guess = first_guess
	next = f(guess)
	while !close_enough(guess, next)
		guess = next
		next = f(guess)
	end
	next
end

# ╔═╡ 78462eeb-5f46-48e8-bb0e-a09a35914955
mySqrt1(x) = 
	fixedPoint3(averageDamp(function(y) /(x, y) end), 1.0)

# ╔═╡ 9481d639-2588-4980-b89c-3973b430aa19
mySqrt1(2.0)

# ╔═╡ 1341a65e-4036-4cb4-8c11-51b53abe2c81
mySqrt1(9.0)

# ╔═╡ 50f7fbb2-2b0d-4248-bb9b-5e5539a0ed02
mySqrt1(1000.0)

# ╔═╡ 84279927-18e6-4dce-b622-d7394243162c
mySqrt1(1000.0)^2

# ╔═╡ 8de553b3-28b4-4c72-b1cf-f3420d9df62e
let (x, average) = (2.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixedPoint3(averageDamp(function(y) x/y end), 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($x) := f-point($x):  {y|y >0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +2], line=(2, :magenta))
		plot!([-0.5, +2], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 90dde354-4e26-41c4-8a45-c94f2d524b41
let (x, average) = (9.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixedPoint3(averageDamp(function(y) x/y end), 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($x) := f-point($x): {y|y>0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 3b884275-d00c-44d6-82dc-93fdd164ef84
myCubeRoot(x) = 
	fixedPoint3(averageDamp(function(y) /(x, ^(y, 2)) end), 1.0)

# ╔═╡ b68f57d8-632c-44e8-b01f-97896eb61a87
myCubeRoot(8)

# ╔═╡ 4e9d7bdc-a11a-4a5e-8ce8-eb6729f8bb22
let (x, average) = (8.0, (x, y) -> (x + y)/2.0)
	let fixPoint = myCubeRoot(x)
		plot(y->x/y^2, [0.5:0.1:9.0], size=(500, 500),line=:darkblue, xlim=(-0.5, 9), aspect_ratio=1, framestyle=:zerolines, title="cube-rt($x):=f-point($x):{y|y>0,y->$x/y^2}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 476b8f63-3e5c-4ff4-9913-52d45cfbf5d2
myCubeRoot(1000)

# ╔═╡ 8c2f1771-6e34-4f5c-8bc3-6c44efcbd831
^(myCubeRoot(1000), 3)

# ╔═╡ 0f2fb30c-953c-4763-82ea-63cc7b655283
md"
---
#### 1.3.4.2 [Newton's method](https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-12.html#%_sec_1.3.4)
#### 1.3.4.2.1 SICP-Scheme-like *functional* Julia
"

# ╔═╡ 9721c79d-3108-4822-8e4e-6cf1832043c1
md"
###### if $$x \mapsto g(x)$$ is a differentiable function then the root $$x$$ of $$g(x)=0$$ is the fixed point of $$x \mapsto f(x)$$ , where:
$$f(x) = x - \frac{g(x)}{Dg(x)}$$

###### and $$Dg(x)$$ is the derivative of $$g(x)$$ evaluated at $$x$$:
$$Dg(x) = \frac{g(x+dx)-g(x)}{dx}\;.$$
"

# ╔═╡ adb7ddea-c6f1-4fdb-8ee8-d88f9d66245b
dx = 1.0E-5

# ╔═╡ a98ed3b7-3c29-43a2-b286-96201a90e3b0
md"
###### 1st (default) *untyped* method of function 'deriv'
"

# ╔═╡ 9cebf2db-98d3-45ff-a6c0-9aee5eef8800
function deriv(g)                      # higher order function
	x -> /(-(g(+(x, dx), g(x))), dx)   # return of anonymous function
end # function deriv

# ╔═╡ 5fd66bfc-79ed-4418-bb25-2c76ea5f85bc
cube(x) = ^(x, 3)

# ╔═╡ bf3e45d1-f1b4-4629-87ac-c8a201231486
md"
---
$$\frac{d x^3}{dx}=3x^2$$
---
"

# ╔═╡ cb39b588-c563-47cf-ac08-a128439982ea
md"
---
###### higher-order function *newtonTransform*:
$$f(x) := x - \frac{g(x)}{Dg(x)}$$

---
"

# ╔═╡ 632e3dcc-12ac-40f9-8175-8ca3c5f149c9
md"
###### 1st (default) *untyped* method of function 'newtonTransform'
"

# ╔═╡ c46bff7d-97b5-4ea6-983f-34a90bf994a4
md"
###### 1st (default) *untyped* method of function 'newtonsMethod'
"

# ╔═╡ 66dd1ad7-4d0e-4ced-bb5f-81b3cae32a3a
md"
###### Abstractions and first-class procedures
"

# ╔═╡ 2477acc6-2c99-41c6-8df9-e5d96b343686
md"
###### 1st (default) *untyped* method of function 'fixedPointOfTransform'
"

# ╔═╡ 7ea6c3cc-acf8-4264-bd38-c9e688540bec
function fixedPointOfTransform(g, transform, guess)
	fixedPoint3(transform(g), guess)
end # function fixedPointOfTransform

# ╔═╡ d07869fd-7609-4944-a000-eb771cca1084
md"
---
##### 1.3.4.2.2 idiomatic *imperative* or *typed* Julia
"

# ╔═╡ c28ec2c2-db7b-4486-b0b2-9bd4ddf88e5a
md"
###### 2nd (specialized) *typed* method of function 'deriv'
"

# ╔═╡ b46d2660-b9b5-483f-a23e-fb54e8da978d
function deriv(g::Function)::Function  # higher order function
	x -> (g(x + dx) - g(x))/dx         # return of anonymous function
end # function deriv

# ╔═╡ da57e720-bc7c-4d88-839b-bc6be801fd04
deriv(cube)(5)                   # should be 3*5^2 = 3*25 = 75

# ╔═╡ 3f410f9f-88a0-420d-8b24-46b0ddc03ec9
function newtonTransform(g)
	x -> x - /(g(x), deriv(cube))(x)
end # function newtonTransform

# ╔═╡ 17690bef-d073-4059-9326-1cbbdd04838c
md"
###### 2nd (specialized) *typed* method of function 'newtonTransform'
"

# ╔═╡ 1c6986f9-3fb7-4b5b-9602-c61c78aa2ab8
function newtonTransform(g::Function)::Function
	x -> x - g(x)/deriv(cube)(x)
end # function newtonTransform

# ╔═╡ 3ba4a946-4955-4ddd-91d4-a2a9b6254931
function newtonsMethod(g, guess)
	fixedPoint3(newtonTransform(g), guess)
end # newtonsMethod

# ╔═╡ bee17d7c-beb7-41ff-93c6-671528798b07
md"
###### 2nd (specialized) *typed* method of function 'newtonsMethod'
"

# ╔═╡ cfd15032-261a-49b5-8b48-5d8a5d61263c
function newtonsMethod(g::Function, guess::FloatOrSigned)::FloatOrSigned
	fixedPoint3(newtonTransform(g), guess)
end # function newtonsMethod

# ╔═╡ e2adc870-3c6f-4976-984a-ee25191f37ac
function mySqrt2(x)
	newtonsMethod(y -> -(^(y, 2), x), 1.0)
end # function mySqrt2

# ╔═╡ 8c45df3f-7677-417f-93ec-951cd7e42407
mySqrt2(2.0)

# ╔═╡ 670e471e-4a07-45e3-a912-170c94bb3743
mySqrt2(9.0)

# ╔═╡ 6b08ae2f-68fb-4ff1-9489-2a28da1e635b
mySqrt2(1000.0)

# ╔═╡ 76818ee1-925c-40db-9117-734a6127c2b7
^(mySqrt2(1000.0), 2)

# ╔═╡ aa829480-9608-448d-bf3d-d5bff22a0a7f
let (x, average) = (2.0, (x, y) -> (x + y)/2.0)
	let fixPoint = newtonsMethod(y -> y^2 - x, 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($x) := f-point($x): {y|y>0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +2], line=(2, :magenta))
		plot!([-0.5, +2], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 6c7c3dda-27b6-4674-b83d-b38f7d050416
let (x, average) = (9.0, (x, y) -> (x + y)/2.0)
	let fixPoint = newtonsMethod(y -> y^2 - x, 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($x) := f-point($x): {y|y >0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ ebcf1358-dbc0-4c6e-9a16-67da0144aa49
md"
###### 2nd (specialized) *typed* method of function 'fixedPointOfTransform'
"

# ╔═╡ 2bd909d0-69b7-40ff-b51b-7330e3f7bb22
function fixedPointOfTransform(g::Function, transform::Function, guess::FloatOrSigned)::FloatOrSigned
	fixedPoint3(transform(g), guess)
end # function fixedPointOfTransform

# ╔═╡ e1e9e42c-4f18-4460-8d10-4242922ffa32
function mySqrt3(x)
	fixedPointOfTransform(y -> /(x, y), averageDamp, 1.0)
end # function mySqrt3

# ╔═╡ 7be65548-fd6f-4df7-9ac5-8613d7b4252d
mySqrt3(2.0)

# ╔═╡ 7575ace3-5894-494b-9fd2-d2559f7b67cf
mySqrt3(9.0)

# ╔═╡ 0e3f8751-c551-4264-8016-810ed7348281
mySqrt3(1000.0)

# ╔═╡ 0f84bc85-ff1a-4578-a320-c8fcddd80596
^(mySqrt3(1000.0), 2)

# ╔═╡ 108a414a-f2df-4944-8a17-2b392cd35375
let (x, average) = (2.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixedPointOfTransform(y -> x/y, averageDamp, 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($x) := f-point($x): {y|y>0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +2], line=(2, :magenta))
		plot!([-0.5, +2], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 881062cb-646a-49c9-a983-ff95b5df51a1
let (x, average) = (9.0, (x, y) -> (x + y)/2.0)
	let fixPoint = fixedPointOfTransform(y -> x/y, averageDamp, 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($x) := f-point($x): {y|y>0, y->$x/y}")
		plot!([fixPoint, fixPoint], [-0.5, +4], line=(2, :magenta))
		plot!([-0.5, +4], [fixPoint, fixPoint], line=(2, :magenta))
	end
end

# ╔═╡ 5790449c-19c6-4a54-b4e1-2178724aecaa
md"
##### References
- **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

"

# ╔═╡ f03d6c69-ace6-4f91-8f47-685474177934
md"
---
##### end of ch. 1.3.4

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

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**

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

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

[[deps.RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "37c1631cb3cc36a535105e6d5557864c82cd8c2b"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.5.0"

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

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "cdbd3b1338c72ce29d9584fdbe9e9b70eeb5adca"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "0.1.3"

[[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 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

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

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

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

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

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

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

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "95c6a5d0e8c69555842fc4a927fc485040ccc31c"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.3.5"

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

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c3d8ba7f3fa0625b062b82853a7d5229cb728b6b"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.1"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.16"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.4"

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

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

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

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

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

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

[[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.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.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"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[deps.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"

[[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 = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+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", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+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 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╠═2a56d3e3-bb2e-4382-864c-9d3c099cb177
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# ╠═f5a15cb0-a039-43a1-ba4c-2674e672e6ff
# ╠═81ecbeb5-7c4d-40e8-aeb1-2386277de71d
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# ╠═9481d639-2588-4980-b89c-3973b430aa19
# ╠═50cbd85a-2a84-4f2c-836b-7a121a2f4a89
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# ╠═1341a65e-4036-4cb4-8c11-51b53abe2c81
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# ╠═b68f57d8-632c-44e8-b01f-97896eb61a87
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# ╠═8c2f1771-6e34-4f5c-8bc3-6c44efcbd831
# ╟─f05fca2a-638f-47f3-9b64-b1845b4169c7
# ╠═9b740450-2b0f-4955-a2c7-06b926cd7191
# ╠═061844e7-ff4d-4697-9179-7470ca4a0f19
# ╠═744ed935-2298-467b-8042-a4ff00f3e40c
# ╟─0f2fb30c-953c-4763-82ea-63cc7b655283
# ╟─9721c79d-3108-4822-8e4e-6cf1832043c1
# ╠═adb7ddea-c6f1-4fdb-8ee8-d88f9d66245b
# ╟─a98ed3b7-3c29-43a2-b286-96201a90e3b0
# ╠═9cebf2db-98d3-45ff-a6c0-9aee5eef8800
# ╠═5fd66bfc-79ed-4418-bb25-2c76ea5f85bc
# ╟─bf3e45d1-f1b4-4629-87ac-c8a201231486
# ╠═da57e720-bc7c-4d88-839b-bc6be801fd04
# ╟─cb39b588-c563-47cf-ac08-a128439982ea
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