### A Pluto.jl notebook ###
# v0.17.7

using Markdown
using InteractiveUtils

# ╔═╡ 25a3594e-61d0-4533-a117-8d9787438966
begin

	using Plots
	using PlutoUI
	using Unitful
	using Symbolics
	using DataFrames
	using LinearAlgebra
	using BenchmarkTools
	using ModelingToolkit
	using GeneralAstrodynamics
	using AstrodynamicalModels
	using DifferentialEquations

end

# ╔═╡ 5e01f7a6-06cf-463b-9528-cc317567edf3
let # Write Julia code here! The last result will be displayed above...

	# Modern package manager, documentation, and more
	import Pkg # Pkg.install(...), Pkg.generate(...), Pkg.update(...)

	# Type hierarchy that makes code **composable**
	struct MyVector{ElementType} <: AbstractVector{ElementType}
		data::Vector{ElementType}
	end
	
	# An excellent (and growing) ecosystem of scientific packages
	@variables t x(t) y(t) z(t)
	Symbolics.derivative(x+y+z,t)

end

# ╔═╡ 025bf930-e1dc-4991-ace8-64ff70fb2a9e
md"""
# Welcome! 👋
_If you want to participate with this workshop interactively, download Julia!_


!!! tip "Getting Started"
	Julia is a programming language that _feels_ like Python, and can be almost as fast as C! If you want to participate interactively and learn on-the-fly, download Julia (and optionally this notebook) using the links in the table below.
	
	|Contents|Link|
	|---|---|
	|Julia|[julialang.org/download](https://julialang.org/download)|
	|This Notebook|[github.com/cadojo/jsc-hackathon-2022](https://github.com/cadojo/jsc-hackathon-2022)|

$(html"<button onclick=present()>Toggle Presentation / Notebook</button>")
$(PlutoUI.TableOfContents(title="Introduction to Julia", depth=2))
"""

# ╔═╡ 28a2f730-7ee6-11ec-0d91-5f60b9d53c13
md"""
## Introduction & Motivation
_What's this notebook about?_

!!! correct "Introduction to the Julia Programming Language"
	The [Julia Programming Language](https://julialang.org/downloads) is a fast, dynamic, and composable programming language with tons of applications in scientific computing. All of the buzz-words above will be explained further in this notebook!

"""

# ╔═╡ dc1c8329-d399-474c-977f-e45a9954db37
md"""
## Julia is Dynamic
_And simple to type!_

```cpp
/** 
 * Consider this "Hello, World" C++ program.
 **/

#include <iostream>

int main(int argc, char** argv) {
	int world_id = 42;
	std::cout << "Hello, world #" << world_id << "\n";
	return 0;
}
```

```python
'''
And this simple Python program.
'''

python> world_id = 42
python> print("Hello, world #", world_id)
```
"""

# ╔═╡ d1085fc9-c981-472a-a222-622d0014269e
let # Julia is simple, like Python
	world_id = 42
	@with_terminal print("Hello, world #", world_id)
end

# ╔═╡ eb3f211f-bd69-47fc-8223-4f3adc056b3a
md"""
## Julia is Fast
_Sometimes, as fast as C!_


"""

# ╔═╡ 6bd7d5dc-6f88-4055-920f-9466d533faef
let

	function computation(vector)
		for i in 1:length(vector)
			vector[i] = vector[i]^2
		end
	end

	vector = randn(1_000_000)

	@with_terminal @time computation(vector)
	
end

# ╔═╡ 78ca5e54-1fa6-492b-874e-6c148555e50d
md"""
## Julia is Composable
_In other words, easily shareable!_


"""

# ╔═╡ 2fd25613-4494-4cdc-bfcf-3a3e6a67602e
md"""
I can use functions **I wrote** on types **written by someone else**. Why is that?
"""

# ╔═╡ 31974f06-03c2-4b3b-b9cb-2062d5da60a2
md"""
#### Julia Separates Types & Methods
"""

# ╔═╡ 4f958888-c1ca-49c1-aa0e-a23f47b8de17
struct MyType
	field
end

# ╔═╡ 0dd06d14-9088-41f0-a362-deebe332334d
function myfunction(arg::MyType)
	return arg.field
end;

# ╔═╡ c0fcad43-04ac-4e5b-b2de-358d3ddc799e
md"""
# Computer Architecture in 5 Minutes
_Just so we're all on the same page!_

"""

# ╔═╡ e6df19de-3735-4ea0-938f-edac1a299bdd
md"""
## Let's Build a Computer
_Let's at least **convince ourselves** that it can be done._

- A computer is a bundle of all of the technologies & phenomena shown below

!!! note "There's No Magic Here!"
	|Technology|Explanation|
	|---|---|
	|Operating Systems|A program to run programs for you|
	|Programs|A set of commands for your computer chip to execute|
	|Computer Chips|A collection of digital circuits with an instruction manual|
	|Digital Circuits|Electronic components that perform some function or operation|
	|Voltage|Electromagnetic potential|




"""

# ╔═╡ 684d6fd2-4895-4c25-9ef7-c5d93dd97a2d
# All of the steps above are involved in this code & output!
@with_terminal print("Hello, world!")

# ╔═╡ 99cf9d2f-1ee2-4da1-b44f-40634dee7969
md"""
## Digital Logic (Math)
_Smart folks made math that worked with 0's and 1's._

- We write numbers in groups of $10$, but that's just convenient for us humans!
- We can write numbers in groups of _any_ size, including $2$'s
- Writing a number in groups of twos is typically called a **binary notation**

|Binary Notation|Decimal Notation|
|---|---|
|0|0|
|1|1|
|10|2|
|11|3|
|100|4|
|101|5|
|110|6|
|111|7|

!!! tip
	Binary notation is just awful for humans, but for machines that function with "on" or "off" states, it is useful!
"""

# ╔═╡ 0bda709d-ec32-4037-8318-327f40e8bed9
md"""
## Digital Logic (Circuits)
_The first thing computer architecture professors teach you is 2+2!_

|Digital Circuit|Explanation|
|---|---|
|$(Resource("https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/AND_ANSI_Labelled.svg/240px-AND_ANSI_Labelled.svg.png"))|And-gate|
|$(Resource("https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/OR_ANSI_Labelled.svg/240px-OR_ANSI_Labelled.svg.png"))|Or-gate|
|$(Resource("https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/NOT_ANSI_Labelled.svg/240px-NOT_ANSI_Labelled.svg.png"))|Not-gate|

!!! tip
	You can use *And*, *Or*, and *Not* components to build circuits that add, subtract, multiply, move information, and more!
"""

# ╔═╡ 53ee5ed8-a969-4ef8-a0c6-cb95adc5a145
md"""
## Computer Chips
_Build this if you want a quick buck!_

- We (humans) have designed a math notation that works with "on" and "off" states
- We've built electrical components that utilize binary notation to do math, and move information around
- Let's build a machine that uses these core components
- The instructions that you use to *use* the machine are called **machine code**

!!! tip "Product Idea"
	- Build a machine that combines these electrical components
	- Provide users a manual for how to use the machine
	  - Power on inputs 0, 5, 7, 12, and 13 to activate the "addition" circuit
	  - Power on inputs 0, 2, 7, 13, and 14 to activate the "multiplication" circuit
	  -  $...$

!!! warning "There's One Problem"
	Would *you* want to consult a manual every time you wanted to add a couple of numbers?
"""

# ╔═╡ 1659b93d-5b10-4472-9725-4c9d9a1c9f87
md"""
## Assembly Language
_Use computer chips with human-readable text, not 0's and 1's._

- What if there was $(html"<strike>one</strike>") _a few_ common formats for using computer chips?
- Instead of consulting the computer chip manual for the "addition" circuit number, you could type `ADD` and use the addition circuit on the computer chip

!!! note "Assembly Language vs. Machine Code"
	|Assembly Language|Machine Code|
	|---|---|
	|`add 2 1`|`01011011 10 01`|
	|`mult 2 2`|`01101011 10 10`|

!!! tip
	You could write a program **using machine code** to parse through the plain-text commands, and replace them with the appropriate binary numbers
"""

# ╔═╡ 0b2aec98-2f25-445c-86ef-1a7116592920
md"""
## Higher Level Languages
_Assembly is still too hard!_

- Assembly language is easier than looking up the computer chip manual, but it's so complicated and verbose that it needs a manual of its own
- Higher level programming languages like [C](https://en.wikipedia.org/wiki/C_(programming_language)) allow us write complex programs simply

### C-Code
_This should compile!_
```C
#include <stdio.h>

int main(int argc, char** argv) {
	printf("Hello, world!\n");
	return 0;
}
```

### Assembly-Code
_Assembly code below was copied [from here](https://montcs.bloomu.edu/Information/LowLevel/Assembly/hello-asm.html)._
```assembly
mov  dx, msg      ; the address of or message in dx
mov  ah, 9        ; ah=9 - "print string" sub-function
int  0x21         ; call dos services

mov  ah, 0x4c     ; "terminate program" sub-function
int  0x21         ; call dos services

msg  db 'Hello, World!', 0x0d, 0x0a, '$'   ; $-terminated message
```


"""

# ╔═╡ 69ed5559-62c5-43f3-a6b8-b53e8d7ceeff
# What are some other programming languges?
programming_languages = [];

# ╔═╡ 2a822fd3-8749-4303-9a59-7a5f4e956be2
md"""
## Summary
_Let's re-cap._

!!! note "To Execute a Command on a Computer..."
	Write code in a higher level programming language (like C)
	 
	Use a pre-written program (compiler) to convert high-level code into assembly or machine code
	
	If necessary, use another pre-written program to convert the assembly into machine code

### Other Languages

$(
	DataFrame("Write Programs With..." => programming_languages, 
			  "Execute Programs As..." => (["Machine Code" for lang in programming_languages]))
)

"""

# ╔═╡ ec7b33ac-0246-4543-8209-ea22384e2f70
md"""
# Scientific Computing with Julia
_What makes Julia different?_

"""

# ╔═╡ e4e6813c-59cd-4c71-bd68-a6b25717413a
md"""

## How Julia Works
_Code is compiled **just in time**_.

- For a long time, scientists engineers have used two different kinds of programming languages

|Compiled Languages (faster, static)|Interpreted Languages (slower, dynamic)|
|---|---|
|C|Python|
|C++|Ruby|
|Rust|R|

- Julia aims to be a one-stop-shop for **fast** and **dynamic** programming
  - Program *interactively* in a terminal, or notebook environment
  - Code is compiled under the hood on-the-fly, so it's fast!

"""

# ╔═╡ b59d4510-6dfd-4930-aaa5-a6bbbdc574f8
# Watch this compile and run!
@with_terminal let

	function lunarmission(departure, arrival)
		print(
			"Planning a mission to leave Earth on ", departure,
			" and arrive at the moon on ", arrival, ".\n\n"
		)
	end
	
	@time lunarmission("Friday", "Tuesday")

end

# ╔═╡ c7fb7d8c-e610-4fde-a017-13a25768c73d
md"""
## Why JIT Compilation?
_You get an optimized implementation of your functions for every **type** passed as an argument._

- This can be accomplished by the Julia compiler automatically
"""

# ╔═╡ b36302d4-b46a-43e0-be44-65c0dc9cfad4
@with_terminal let

	function multiply(arg1, arg2)
		return arg1 * arg2
	end

	
	@code_native multiply(2, 2.0)
	
end

# ╔═╡ 90ef754e-5c14-41d7-97ab-518778bcdeb7
md"""
## Manual JIT Compilation
_Users can take advantage of this explicitly!_
"""

# ╔═╡ a9077987-5bc5-45d7-addd-0fb0de1e30ea
@with_terminal let

	"""
	Scalar multiplication.
	"""
	function multiply(arg1::Number, arg2::Number) 
		print("Scalar Multiplication: ", arg1*arg2)
	end

	"""
	Matrix multiplication.
	"""
	function multiply(arg1::Matrix, arg2::Matrix)
		print("Matrix Multiplication: ", arg1*arg2)
	end

	@code_native multiply(1,0)
	
end

# ╔═╡ cfcc1690-e0cf-49ad-927e-d743ddedc8c8
md"""
## Custom Types
_Like other languages, you can make your own types._

- Unlike other languages, your custom type can be plug-and-play with other packages out of the box!
"""

# ╔═╡ b9b5070a-3df3-4653-83a8-0af5a7ee7632
"""
Computes dynamic pressure.
"""
dynamicpressure(ρ, v) = 1/2 * ρ * v * v;

# ╔═╡ 178c1dff-10b7-40e1-bb60-81c18951e32b
begin
	
	let ρ = 1.225u"kg/m^3", v = 1.0u"km/s"
		pressure = dynamicpressure(ρ, v)
		upreferred(pressure)
	end
	
end

# ╔═╡ dd21bcb1-fef3-41c3-94c5-2f5ee142c193
let

	"""
	A custom `Number` type.
	"""
	struct MyNumber{N<:Number} <: Number
		value::N
	end

	Base.convert(::Type{N}, num::MyNumber{M}) where {N<:Number, M} = N(num.value)
	Base.promote_rule(::Type{M}, ::Type{N}) where {M <: MyNumber, N <: Number} = N

	let ρ = MyNumber(5.0), v = MyNumber(10.0)
		dynamicpressure(ρ,v)
	end
	
end

# ╔═╡ b037a4e3-2107-44a9-8eaf-92502fa93087
md"""
## Type Tree
_All types exist somewhere on a **tree** of types._

- When you make a **concrete** (instantiable) type, the type must be a **leaf** on this tree
- When you make an **abstract** (not instantiable) type, the type is a **node** on this tree
"""

# ╔═╡ 0af1c764-f3c3-4906-8d99-e106d81f94ce
supertypes(MyNumber)

# ╔═╡ 353d7a07-4f81-43d5-96ce-e074d0b7623c
isabstracttype(Number)

# ╔═╡ 87bbb4a2-2a87-48f2-8c3b-d5c8ee577ce2
isconcretetype(MyNumber)

# ╔═╡ a3b2b7ca-0ea0-4fe3-aabe-72c905265c2a
isconcretetype(MyNumber{Int})

# ╔═╡ 27c716b9-9d99-4de1-b781-e677dae305f1
md"""
## Julia Syntax
_How does Julia code syntax compare to other languages?_
"""

# ╔═╡ 8a249bf4-5506-48f3-aef2-2a6fcf173abe
md"""
|MATLAB|Python|Julia|Action|
|---|---|---|---|
|randn(4,4) * randn(4,4)|randn(4,4) @ randn(4,4)|randn(4) * randn(4,4)|Multiply two random matrices|
||||
|for i = 1:10|for i in range(10):|for i in 1:10|Start of for loop|
||||
ode45(@func, tspan, x0)|solve_ivp(func, tspan, x0)|solve(problem)|Numerically solve a differential equation|
||||
|N/A|import scipy|using DifferentialEquations|Load a package|
||||
|function computation(varargin)|def computation(**kwargs):|function computation(kwargs...)|Keyword arguments|

"""

# ╔═╡ cee46d6a-f4e0-4c8b-9380-0d90cf9f50f9
md"""
# Julia Demo
_In ✨ S P A C E ✨!_

!!! note "Let's do astrodynamics!"
	This gives us a good opportunity to use some of Julia's fun number-crunching packages.
"""

# ╔═╡ dba2528a-fd38-46ad-bb5d-31a38429c431
md"""
## Orbital Mechanics
_The simple kind: the Restricted Two-body Problem._
"""

# ╔═╡ 7132fa01-9688-42ff-996f-84e9e6d067a7
begin
	model = R2BP()
end

# ╔═╡ 87dd133d-1d69-4213-bbd0-f4a564ee7f48
md"""
## Interplanetary Superhighways
_Invariant manifolds in the Circular Restricted Three-body Problem!_
"""

# ╔═╡ 3ce19df1-82f6-486e-be82-08908274b763
begin
	
end

# ╔═╡ 6357d4a9-f4d6-427a-835a-fe333c3ffcfb
md"""
# Julia Resources
_Where to look for more information!_
"""

# ╔═╡ ea717dd3-fc97-44e2-a073-007b22ca43f3
md"""
## YouTube
_There are lots of helpful tutorials on there!_
"""

# ╔═╡ aa0c7efb-28ca-4933-ab27-93961458f7c3
html"""
<iframe width="280" height="315" src="https://www.youtube-nocookie.com/embed/videoseries?list=PLP8iPy9hna6SCcFv3FvY_qjAmtTsNYHQE" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
<iframe width="280" height="315" src="https://www.youtube-nocookie.com/embed/kc9HwsxE1OY" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
"""

# ╔═╡ 2148d759-dc63-42c6-94b1-3676c190b378
md"""
## Documentation
_Official language documentation._
"""

# ╔═╡ c09fa83f-cdb9-46a5-b67c-7b83440b78b9
html"""
<iframe width="660" height="500" src="https://docs.julialang.org/en/v1/" 
</iframe>
"""

# ╔═╡ e9c7094c-aeee-4cf2-acd5-174e31734fb8
md"""
## Discourse
_A forum filled with friendly users. We want to help!_
"""

# ╔═╡ 48a4bdc6-74d4-4659-953d-f56e5cd9d1f3
html"""
<iframe width="660" height="500" src="https://discourse.julialang.org/sdfg" 
</iframe>
"""

# ╔═╡ 7f52731b-0de2-4a89-a1c8-82ede329b228
md"""
# Supporting Code
"""

# ╔═╡ 157e0251-c750-4edc-a23c-82d0b1ea57d8
md"""
## Dependencies
_Julia packages used in this notebook._
"""

# ╔═╡ d1004605-44e3-49a8-9a41-b1d629eb34ad
# Use the plotly backend
plotly()

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
AstrodynamicalModels = "4282b555-f590-4262-b575-3e516e1493a7"
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
GeneralAstrodynamics = "8068df5b-8501-4530-bd82-d24d3c9619db"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[compat]
AstrodynamicalModels = "~1.0.2"
BenchmarkTools = "~1.2.2"
DataFrames = "~1.3.2"
DifferentialEquations = "~6.21.0"
GeneralAstrodynamics = "~0.10.4"
ModelingToolkit = "~6.7.1"
Plots = "~1.25.7"
PlutoUI = "~0.7.32"
Symbolics = "~3.5.1"
Unitful = "~1.10.1"
"""

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

[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
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[[AbstractTrees]]
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[[Adapt]]
deps = ["LinearAlgebra"]
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version = "3.3.3"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.1.0"

[[ArrayInterface]]
deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "1ee88c4c76caa995a885dc2f22a5d548dfbbc0ba"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "3.2.2"

[[ArrayLayouts]]
deps = ["FillArrays", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "e1ba79094cae97b688fb42d31cbbfd63a69706e4"
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version = "0.7.8"

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

[[AstroTime]]
deps = ["Dates", "EarthOrientation", "ItemGraphs", "LeapSeconds", "MacroTools", "MuladdMacro", "Reexport"]
git-tree-sha1 = "b3217075a2453321b304746f64311e748f9725a7"
uuid = "c61b5328-d09d-5e37-a9a8-0eb41c39009c"
version = "0.7.0"

[[AstrodynamicalModels]]
deps = ["DocStringExtensions", "LinearAlgebra", "Memoize", "ModelingToolkit", "RuntimeGeneratedFunctions", "StaticArrays", "Symbolics"]
git-tree-sha1 = "fb801f6632b677772520af2bcccc40481cfbc6c2"
uuid = "4282b555-f590-4262-b575-3e516e1493a7"
version = "1.0.2"

[[BandedMatrices]]
deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "Random", "SparseArrays"]
git-tree-sha1 = "ce68f8c2162062733f9b4c9e3700d5efc4a8ec47"
uuid = "aae01518-5342-5314-be14-df237901396f"
version = "0.16.11"

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

[[BenchmarkTools]]
deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"]
git-tree-sha1 = "940001114a0147b6e4d10624276d56d531dd9b49"
uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
version = "1.2.2"

[[Bijections]]
git-tree-sha1 = "705e7822597b432ebe152baa844b49f8026df090"
uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
version = "0.1.3"

[[BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "5e98d6a6aa92e5758c4d58501b7bf23732699fa3"
uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
version = "0.1.2"

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[[SteadyStateDiffEq]]
deps = ["DiffEqBase", "DiffEqCallbacks", "LinearAlgebra", "NLsolve", "Reexport", "SciMLBase"]
git-tree-sha1 = "3e057e1f9f12d18cac32011aed9e61eef6c1c0ce"
uuid = "9672c7b4-1e72-59bd-8a11-6ac3964bc41f"
version = "1.6.6"

[[StochasticDiffEq]]
deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqJump", "DiffEqNoiseProcess", "DocStringExtensions", "FillArrays", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
git-tree-sha1 = "5f88440e7470baad99f559eed674a46d2b6b96f7"
uuid = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
version = "6.44.0"

[[StrideArraysCore]]
deps = ["ArrayInterface", "CloseOpenIntervals", "IfElse", "LayoutPointers", "ManualMemory", "Requires", "SIMDTypes", "Static", "ThreadingUtilities"]
git-tree-sha1 = "12cf3253ebd8e2a3214ae171fbfe51e7e8d8ad28"
uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
version = "0.2.9"

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

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"

[[Sundials]]
deps = ["CEnum", "DataStructures", "DiffEqBase", "Libdl", "LinearAlgebra", "Logging", "Reexport", "SparseArrays", "Sundials_jll"]
git-tree-sha1 = "ce11202f487f429dbe7f937c40ff54f6a7e7259e"
uuid = "c3572dad-4567-51f8-b174-8c6c989267f4"
version = "4.9.1"

[[Sundials_jll]]
deps = ["CompilerSupportLibraries_jll", "Libdl", "OpenBLAS_jll", "Pkg", "SuiteSparse_jll"]
git-tree-sha1 = "013ff4504fc1d475aa80c63b455b6b3a58767db2"
uuid = "fb77eaff-e24c-56d4-86b1-d163f2edb164"
version = "5.2.0+1"

[[SymbolicUtils]]
deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TermInterface", "TimerOutputs"]
git-tree-sha1 = "b747ed621b12281f9bc69e7a6e5337334b1d0c7f"
uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
version = "0.16.0"

[[Symbolics]]
deps = ["ConstructionBase", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TreeViews"]
git-tree-sha1 = "f7111115caa28991f3f019c572866af8abdbfae8"
uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
version = "3.5.1"

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

[[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 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

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

[[TermInterface]]
git-tree-sha1 = "02a620218eaaa1c1914d228d0e75da122224a502"
uuid = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
version = "0.1.8"

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

[[ThreadingUtilities]]
deps = ["ManualMemory"]
git-tree-sha1 = "884539ba8c4584a3a8173cb4ee7b61049955b79c"
uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
version = "0.4.7"

[[TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "97e999be94a7147d0609d0b9fc9feca4bf24d76b"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.15"

[[Tokenize]]
git-tree-sha1 = "0952c9cee34988092d73a5708780b3917166a0dd"
uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
version = "0.5.21"

[[TreeViews]]
deps = ["Test"]
git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"

[[TriangularSolve]]
deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
git-tree-sha1 = "c3ab8b77b82fd92e2b6eea8a275a794d5a6e4011"
uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
version = "0.1.9"

[[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"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

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

[[Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "b95e0b8a8d1b6a6c3e0b3ca393a7a285af47c264"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.10.1"

[[UnitfulAngles]]
deps = ["Dates", "Unitful"]
git-tree-sha1 = "dd21b5420bf6e9b76a8c6e56fb575319e7b1f895"
uuid = "6fb2a4bd-7999-5318-a3b2-8ad61056cd98"
version = "0.6.1"

[[UnitfulAstro]]
deps = ["Unitful", "UnitfulAngles"]
git-tree-sha1 = "c4e1c470a94063b911fd1b1a204cd2bb34a8cd15"
uuid = "6112ee07-acf9-5e0f-b108-d242c714bf9f"
version = "1.1.1"

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

[[VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "e9a35d501b24c127af57ca5228bcfb806eda7507"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.24"

[[VertexSafeGraphs]]
deps = ["Graphs"]
git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.2.0"

[[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"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[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"

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

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[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"

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

[[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"

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

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

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

[[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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