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

using Markdown
using InteractiveUtils

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

# ╔═╡ 88783514-beb7-4bc7-956e-98cc71f6de9b
using Plots 

# ╔═╡ e527d871-3b0e-4bc6-ac80-cf3f9c67a794
using DifferentialEquations

# ╔═╡ 65434c34-8073-45b2-8a07-7a35f4df9214
using ParameterizedFunctions

# ╔═╡ cb631358-60c6-437e-bf29-37abd69c16e2
using PlutoUI

# ╔═╡ 53837fab-f211-4b61-b568-f0249b45b78d
using HypertextLiteral

# ╔═╡ 533a59ad-d026-4312-a20b-b5ece2269e62
md" ## 4. Matrix Formulation for systems of interactions

Sometimes, it is convinient to write down a system of interacting species as a vector-matrix formulation. This will be useful when dealing with large numbers of species and or interactions. Consider the familiar chemical reaction for the formation of water:

```math
2H_2 + O_2 \overset{k}{\longrightarrow}  2 H_2O \tag{33}
```

The previous equation can be rewritten in a more general form as
 
```math
2 X_1 + X_2 \overset{k}{\longrightarrow}  2 X_3 \tag{34}
```

where $X_1$, $X_2$, and $X_3$ are the species $H_2$, $O_2$, and $H_2O$, respectively
 
The first step to write the system as a matrix form, we place all reactants at both sides of the reaction.

  ```math 
2 X_1 + X_2  + 0 X_3 \overset{k}{\longrightarrow}  0 X_1 +  0 X_2  + 2 X_3 \tag{35}
``` 

The values in front of each number are the stoichimetric coefficients, which state the number of molecules that participate in each reaction. We can write these stoichiometric coefficiens as
 
```math 
A_1 X_1 + A_2 X_2  + A_3 X_3 \overset{k}{\longrightarrow}  B_1 X_1 +  B_2 X_2  + B_3 X_3 \tag{36}
```

where $A_1$ = 2, $A_2$ = 1, $A_3$ = 0, $B_1$ = 0, $B_2$ = 0, and $B_3$ = 2.

In compact form, the reaction can be written as:

```math 
\sum_{j=1}^{3} A_j X_j \overset{k}{\longrightarrow}  \sum_{j=1}^{3} B_j X_j \tag{37}
```

or in vector form:
```math 
A X \overset{k}{\longrightarrow} B X  \tag{38}
```

that represents the compact general formulation for a system of interacting species. Here, `X` is the state vector (i.e, the vector with all species), and `A` and `B` are the matrices of stoichiometric coefficients. For the particular case of the formation of water, we obtain:

```math 
\begin{align*}
X&=\begin{bmatrix}X_1\\X_2\\X_3]\end{bmatrix}=\begin{bmatrix}H_2\\O_2\\H_2O\end{bmatrix} \tag{39}\\
A&=\begin{bmatrix}A_1 & A_2 & A_3 \end{bmatrix}=\begin{bmatrix} 2  &1 & 0 \end{bmatrix} \tag{40}\\
B&=\begin{bmatrix} B_1 & B_2 & B_3\end{bmatrix}=\begin{bmatrix} 0 & 0 & 2 \end{bmatrix} \tag{41}\\
\end{align*}
```



"

# ╔═╡ eb1c4140-31b5-4b5e-a6c7-bd4baeb106b6
md" To learn how to write reversible reactions as a matrix form, let's practice with the following reaction:

```math
NaCO_3 + CaCl_2 \overset{k_1}{\underset{k_2}{\longleftrightarrow}} CaCO_3 + 2 \cdot NaCl \tag{42}
```

We will decouple the reversible reaction into two irreversible steps:

```math
\begin{align*}
NaCO_3 + CaCl_2 \overset{k_1}{\longrightarrow} CaCO_3 + 2 \cdot NaCl \tag{43}\\ 
CaCO_3 + 2 \cdot NaCl \overset{k_2}{\longrightarrow} NaCO_3 + CaCl_2 \tag{44}
\end{align*}
```

Using the same matrix notation as in Eq. 13: 

```math
\begin{align*}
X_1 + X_2 \overset{k_1}{\longrightarrow} X_3 + 2 \cdot X_4 \tag{45}\\ 
X_3 + 2 \cdot X_4 \overset{k_2}{\longrightarrow} X_1 + X_2 \tag{46}
\end{align*}
```


where $X_1 = Na_2CO_3$, $X_2  = Ca_2Cl$,$X_3  = CaCO_3$, $X_4 = NaCl$. Now we put all reactants at both sides of the reaction.  

```math
\begin{align*}
1 \cdot X_1 + 1 \cdot X_2  + 0 \cdot X_3  + 0 \cdot X_4 & \overset{k_1}  \longrightarrow  0 \cdot X_1+ 0 \cdot X_2 + 1 \cdot X_3 + 2\cdot  X_4 \tag{47}\\
 0 \cdot X_1+ 0 \cdot X_2 +1 \cdot X_3 + 2\cdot X_4 &\overset{k_2} \longrightarrow 1 \cdot X_1 + 1\cdot  X_2 + 0 \cdot X_3 + 0 \cdot X_4 \tag{48}
\end{align*}
```

in a more general form:
```math
\begin{align*}
A_{11} X_1 + A_{12} X_2  + A_{13} + A_{14} X_4 &\overset{k_1}  \longrightarrow  B_{11}X_1+  B_{12} X_2 +  B_{13} X_3 + B_{14} X_4 \tag{49}\\
A_{21} X_1+ A_{22} X_2 +A_{23} X_3 + A_{24} X_4 & \overset{k_2} \longrightarrow B_{21}  X_1 + B_{22}  X_2 + B_{23} X_3 + B_{24} X_4 \tag{50}
\end{align*}
```

The numbers $A_{ij}$ are the stoichiometric coefficientes of the reactants, $B_{ij}$ are the stoichiometric coefficientes of the products.  Using the matrix notation expalined above, these values are now the components of matrices `A` and `B`:

```math
A=\begin{bmatrix}
 1& 1 & 0 & 0  \\ 
 0 & 0 &1   &2  
\end{bmatrix} ;
B=\begin{bmatrix}
0 & 0 &1   &2 \tag{51}\\ 
1 & 1 &0   &0  
\end{bmatrix}
```

The numbers of rows $i= 1...r$, corresponds to the numbert of reactions `r` involved. The number of columns $j= 1...s$ corresponds to the number of species involved `s`. In conclusion, when we want to write the mass action law for `r` reactions, `k` is now also a vector with components:

```math
k=[k_1,k_2,...k_r]^T \tag{52}
```


altogether we have 


```math
\sum_{j=1}^{s} A_{ij} X_j \overset{k}{\longrightarrow}  \sum_{j=1}^{s} B_{ij} X_j,\,\,\,\, \,\,\,\,\,\,\,\, \,\,\,\,  i=1...r\tag{53}
```



"
 


# ╔═╡ 7178eabf-b4bc-439a-b6c5-86fcf5c7ebef
@htl("""

<div class='blue-background'>
Hello!
</div>

<script>
// more about selecting elements later!
currentScript.previousElementSibling.innerText = "Computer Task 2: Write a function to take as input the matrices A and B corresponding to the reaction 30 and returns the value (B-A)' "

</script>

<style>
.blue-background {
	padding: .5em;
	background: lightblue;
	color: black;
}
</style>

""")

# ╔═╡ e4a6d196-0fe9-4510-ab44-667221cfc995
@htl("""

<div class='red-background'>
Hello!
</div>

<script>
// more about selecting elements later!
currentScript.previousElementSibling.innerText = "Solution Computer Task 2"

</script>

<style>
.red-background {
	padding: .5em;
	background: lightgreen;
	color: black;
}
</style>

""")

# ╔═╡ 203851ad-52d4-4554-bc24-05bdad952ae6
function Calculate_BA_transpose(A,B)
    return (B-A)'
end

# ╔═╡ 6343af59-2e6f-4b06-b6cc-7a803fb80013
A=[1 1 0 0; 0 0 1 2]

# ╔═╡ 4fdea100-e91b-4835-a7a3-e93ba9c649c0
	B=[0 0 1 2; 1 1 0 0]

# ╔═╡ a15dea76-b7e9-49e7-9b04-5ec301bfc6d2
Calculate_BA_transpose(A,B)

# ╔═╡ b664a7e5-1218-41cb-92dc-5c00ecd85915
md"## 5. Order of a reaction and units of the rate constants


In this general formulation, we can directly know,  the order of a given reaction $i =1…r$ as:

```math 
\sum_{j=1}^{s} A_{ij} \tag{54}
```

i.e., the reaction order corresponds to the sum of the stoichiometric coefficients of the species appearing in the reactant of the $i$ reaction. 
For example, in the reaction 

```math 
NaCO_3 + CaCl_2 \overset{k_1}{\underset{k_2}{\longleftrightarrow}} CaCO_3 + 2 \cdot NaCl \tag{55}
```
with a stoichiometrix coefficient matrix $A$ , 

```math 
A=\begin{bmatrix}
 1& 1 & 0 & 0  \\  \tag{56}
 0 & 0 &1  &2  
\end{bmatrix} 
```

The forward reaction $i=1$ has an order or 2, the backward reaction $i=2$ has an order of 3. The units of the kinetic constant $k_i$ of each reaction $i$ can be written in terms of the order of the reaction:

```math 
[k_i]=\frac{M^{1-\sum_{j=1}^{s} A_{ij}}}{s} \tag{57}
```
"

# ╔═╡ c99af17a-b811-483a-a3a9-d60e8e830615
Print("The order of the 1st reaction is $(sum(A[1]))")

# ╔═╡ 899739cc-fe85-45b2-8e62-104335e839f1
Print("The order of the 2st reaction is $(sum(A[2]))")

# ╔═╡ 57381f59-0f71-4136-93e8-95102760281d
Print("The Units of k1 are s^-1 . k^$(1-(sum(A[1])))")

# ╔═╡ b1255e2a-43ee-40be-a8a9-fc9d2f813b3a
Print("The Units of k2 are s^-1 . k^$(1-(sum(A[2])))")

# ╔═╡ a51fdc58-4e7b-4f20-933f-403bdb9ae541
@htl("""

<div class='blue-background'>
Hello!
</div>

<script>
// more about selecting elements later!
currentScript.previousElementSibling.innerText = "Computer Task 3: B-A'"

</script>

<style>
.blue-background {
	padding: .5em;
	background: lightblue;
	color: black;
}
</style>

""")

# ╔═╡ aaec1bd4-bca5-46db-9ab8-2a1921cd610f
md" Generalize the funcion developed for 'Computer Task 2' to account any reaction, i.e., to take as input reactions with an arbitrary number of reactants and reactions (set by the size of matrices A and B).

Update the function to show also as output the order of each reaction, the units of each of the rate constants, and the matrix (B-A)'. "

# ╔═╡ 89b43a03-1229-4c82-af07-85a7fbec5b7e
@htl("""

<div class='red-background'>
Hello!
</div>

<script>
// more about selecting elements later!
currentScript.previousElementSibling.innerText = "Solution Computer Task 3"

</script>

<style>
.red-background {
	padding: .5em;
	background: lightgreen;
	color: black;
}
</style>

""")

# ╔═╡ 77edc692-309c-4de5-9e88-6096a791664b
function Calculate_Keq_stoichiometric_generic(A,B)

 for i=1:size(A)[1]
    println("The order of the reaction $i is ", sum(A[i,:]))
    println("The Units of k$i are s^-1 . k^$(1-(sum(A[i,:])))")
 end
    stoichiometric_matrix= (B-A)'
    println("The stoichiometric matrix is $stoichiometric_matrix ")
end

# ╔═╡ 5fef2534-d1cb-425c-bcca-1964a4a24e6f
Calculate_Keq_stoichiometric_generic(A,B)

# ╔═╡ 2468b482-48a6-4a94-844d-1755f3ad571e
md" ## 6. Practical Tasks

1. If $K_{eq}=0.40$ at a given temperature for the following reaction

```math
H_2+ I_2 \overset{k_1}{\underset{k_2}{\longleftrightarrow}} 2IH
```

If at equilibrium [$HI$]=0.060 M and [$I_2$]=0.90 M, what is the equilibrium concentration of [$H_2$]?

2. The following reaction is at equilibrium:

```math
N_2 + 3 H_2  \overset{k_1}{\underset{k_2}{\longleftrightarrow}} 2 NH_3
```

If $K_eq=13.7$ at a particular temperature, the equilibrium is reached for [$N_2$]= 1.88 M and [$NH_3$] = 6.62 M, a) what is the concentration of [$H_2$]? b) In which direction does the reaction shift if: $H_2$ is added; $NH_3$ is added; $NH_3$ is removed."

# ╔═╡ dec49b7a-9a5e-43aa-ae4a-450643809b66
md"""*Task 1*

`Value of equilibrium Constant = ` $(@bind K_eq1 html"<input type=text >")

`Value of concetration of HI= ` $(@bind HI html"<input type=text >")

`Value of concentration of I2= ` $(@bind I2 html"<input type=text >")

	"""

# ╔═╡ 913e242a-7364-4589-bb29-a1fd26e4a7dd
	H2_task1=round((parse(Float64, HI))^2 / parse(Float64, K_eq1)*parse(Float64, I2),sigdigits=2)

# ╔═╡ ce663698-1b2e-4002-b014-6cf2961e0e3e
md"""*Task 2*

`Value of equilibrium Constant = ` $(@bind K_eq2 html"<input type=text >")

`Value of concetration of N2= ` $(@bind N2 html"<input type=text >")

`Value of concentration of NH3= ` $(@bind NH3 html"<input type=text >")

	"""

# ╔═╡ 3fabcd7d-db29-4f10-b2d8-b5d28e806ad7
H2_task2=round(((parse(Float64, NH3))^2 / (parse(Float64, K_eq2)*parse(Float64, N2)))^(1/3),sigdigits=3)

# ╔═╡ f4e391c8-8a12-4c0e-a6d0-3667426aaf14
# Task 2b
 Print("1. towards producs")

# ╔═╡ d7c1d683-cf0e-42aa-9449-09895fb81cb6
Print("2. towards reactants")

# ╔═╡ 88345e34-bc0d-4ef7-8f6b-dd4649e33062
Print("3. towards producs")

# ╔═╡ 00000000-0000-0000-0000-000000000001
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git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

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

[[deps.Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "b649200e887a487468b71821e2644382699f1b0f"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.11.0"

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

[[deps.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"

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

[[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"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

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

[[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"

[[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"

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

[[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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# ╟─b664a7e5-1218-41cb-92dc-5c00ecd85915
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# ╠═913e242a-7364-4589-bb29-a1fd26e4a7dd
# ╟─ce663698-1b2e-4002-b014-6cf2961e0e3e
# ╠═3fabcd7d-db29-4f10-b2d8-b5d28e806ad7
# ╟─f4e391c8-8a12-4c0e-a6d0-3667426aaf14
# ╟─d7c1d683-cf0e-42aa-9449-09895fb81cb6
# ╟─88345e34-bc0d-4ef7-8f6b-dd4649e33062
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
