### A Pluto.jl notebook ###
# v0.18.4

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

# ╔═╡ 3ea3f970-b03d-11ec-1934-d3426ffdd91e
begin
	using Markdown
	using Interact        # lai veidotu manipulatorus
	using QuadGK          # lai veiktu skaitlisko integrēšanu
	using Unitful         # lai pievienotu mērvienības
	using Plots           # lai zīmētu grafikus
	using UnitfulRecipes
	using LsqFit          # Veikt fit kādiem datiem
#	using WebIO
	using PlutoUI
	plotly()              # PlotlyBase lai pievienotu funkcionalitāti grāfikām (piem. interaktivitāte)
end

# ╔═╡ 39c34251-82b2-439e-ba92-d47d69ac7ce4
md"""
# Melna ķermeņa starojums #
Šajā klādē rēķināsim melna ķermeņa starojumu. 

## Mācību mērķi ##
Pēc šīs aktivitātes, studenti varēs:
1. Skaitliski rēķināt melna ķermeņa emisijas spektru
2. Skaitliski integrēt melna ķermeņa emisijas spektru pa viļņa garumu, lai iegūtu emisijas spēju jeb enerģētisko spīdību
3. Empiriski iegūt Vīna pārbīdes likumu par viļņa garumu, pie kura melnais ķermenis izstaro maksimālo intensitāti
4. Saistīt zvaigžņu krāsas ar to temperatūru
5. Empiriski iegūt Stefāna-Bolcmaņa likumu par absolūti melna ķermeņa integrālo emisijas spēju

## Teorija ##
Maks Planks uzrakstīja formulu, lai rēķinātu absolūti melna ķermeņa emisijas spektru, t.i., spektrālā intensitāte, ko izstaro absolūti melnais ķermenis ar temperatūru $T$ pie viļņa garuma $\lambda$.

``
B_{\lambda}(\lambda,T)=2\frac{hc^2}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda k_B T}}-1}
``

Mērvienības ir $\mathrm{W}\mathrm{m}^{-2}\mathrm{sr}^{-1}$. Tas nozīmē, ja mēs gribam rēķināt enerģiju, ko izstaro absolūti melnais ķermenis, mums ir jāreizina ar melnā ķermeņa virsmas laukumu un atveres leņķi uz kuru staro. 
"""

# ╔═╡ c28038a8-8933-4bbc-bf82-f1777773a589
md"""
## Dažas tehniskas piezīmes ##
### Julia valoda ###
Mēs izmantosim [_Julia_](https://julialang.org/) valodu. _Julia_ valoda ir salīdzinoši vienkārša, līdzīgi kā _python_, iespējams vēl vienkāršāk izmantot. Tomēr, _Julia_ rēķina gandrīz tik pat ātri kā _C/C++_. 


### Julia instalešana ###
Pirms sākt rēķināt, mums ir jāizmanto dažas specializētas programmatūras paketes. Tie ir jābūt jau installētiem mūsu Julia vidē izmantojot paketes menedžeri jeb komandas:

`using Pkg 
Pkg.add("myPackage")
`

Šim uzdevumam izmantosim šāda paketes:
1. [Interact.jl](https://www.juliapackages.com/p/interact) Šī pakete ļaujs interaktīvi manipulēt grafiskas vides
2. [QuadGK.jl](https://www.juliapackages.com/p/quadgk)    Šī pakete ļaujs skaitliski integrēt kādu funkciju
3. [Unitful.jl](https://www.juliapackages.com/p/unitful)   Šī pakete ļaujs definēt mērvienības mūsu mainīgajiem
4. [UniftulRecipes.jl](https://juliapackages.com/p/unitfulrecipes)   Šī pakete ļaujs zīmēt grafikus ar mērvienībām
4. [Plots.jl](https://www.juliapackages.com/p/plots)     Šī pakete ļaujs veidot grafikus
5. [PlotlyBase.jl](https://juliapackages.com/p/plotlybase)     Šī pakete dos papildus funkcionalitāti grafikiem
6. [LsqFit.jl](https://www.juliapackages.com/p/lsqfit)    Šī pakete veiks fitus datiem

Turklāt izmantosim plotly() funkciju, kas ļauj interaktīvi strādāt ar grafikiem. 
"""

# ╔═╡ 1c657f2f-c40f-4295-bb89-7bcf5205c0b4
md"""
## Konstantes ##
Tagad definēsim konstantes, kas būs jāizmanto:
1. Planka konstante $h$
2. Gaismas ātrums $c$
3. Bolcmaņa konstante $k_B$
"""

# ╔═╡ b7e0aa75-2faa-4282-a057-92fd1c2097ad
begin
	h=6.63e-34u"J*s"     # Planka konstante
	c=2.99792e8u"m/s"    # gaismas ātrums 
	k_B=1.381e-23u"J/K"  # Bolcmaņa konstante
end

# ╔═╡ 2aa42dfd-c7e5-47eb-8096-1b225a8deb8f
md"""
## Funkcijas definēšana ##
Nākamais solis ir definēt funkciju, kas rēķinās absolūti melnā ķermeņa emisijas intensitāti pie dotas temperatūras un viļņa garuma. 

_Julia_ valodā definēsim funkciju šādi:

```julia
function manaFukcija(mainigais1,mainigais2,...)
  [izteiksmes]
end
```

Principā, funkcija dod atpakaļ pēdējo objektu, kas tika rēķinātā funkcijā. To var precizēt ar pavēli `return mansRezultats`
"""

# ╔═╡ 5813f691-7c35-447d-bd2a-c2984c9528a4
begin
	# Definēsim funkciju B. 
	# Funkcijai dod viļņa garumu λ un melņā ķermeņa temperatūru T
	# Funkcija did atpakaļ meļņa ķermeņa izstarotu intensitāti pie viļņa garumu λ 
	function B(λ,T)
    	return 2*(h*c^2/λ^5)*1/(exp(h*c/(λ*k_B*T))-1)
	end
end

# ╔═╡ b675b485-5200-49f8-9ce3-b7668966fed1
md"""
## Funkcijas tests ##
Tagad testēsim funkciju, dodot funkcijai konkrētas mainīgo vērtības. 
Tā kā izmantojām paketi Unitful.jl, varam dod mērvienības un saņemt atbildi pareizās mērvienībās.
"""

# ╔═╡ 3512adef-5b11-4933-95ff-f65cf0e9f52b
B(500e-9u"m",5000u"K")  # Melna ķermeņa spīdība pie 500 nm un 5000 K

# ╔═╡ 1d5f5fe5-7c5f-4d0e-88af-7abc51108204
md"""
## Spektra integrēšana ##
Ir labi zināt intensitāti pie konkrētās frekvences, bet parasti ir jāzina kopīgā jauda, kura tiek izstarota pa kādu diapazonu. Lai to zinātu, ir jāintegrē spektrs. Mēs izmantosim paketi QuadGK.jl un funkciju ```quadgk()```. Tā funkcija ļauj integrēt funkcija $f(x)$ vienā dimensijā šādi:

```julia
integrāls, kļūda = quadgk(x->f(x), no, līdz, pielaujama kļūda)
```

Tātad ```quadgk(x->f(x), no, līdz, pielaujama kļūda)``` $=\int_{no}^{līdz} f(x) \mathrm{dx}$.

Šeit rezultātu dod, kā _Tuple_ ar diviem elementiem. 
"""

# ╔═╡ fa795d58-9108-4ac5-8a82-df7ab6cfa569
begin
	# Izmantojot funkciju quadgk, skaitliski integrēsim funciju π*B(λ,T) pie T=5000K no λ=0 līdz λ=10 μm.
	Radiance, err=quadgk(λ->pi*B(λ,5000u"K"), 0u"m", 10e-6u"m", rtol=1e-9)
end

# ╔═╡ 0d15db70-91cc-4a77-b04b-446c99c03225
md"""
## Zīmēt spektru ##
Lai zimētu spektru, mums ir jādefinē kādu diapazonu ```λ_range=sākums:solis:beigas``` pa kuram vēlāmies zīmēt.
Jādomā par soli. Liels solis dod lielu precizitāti, bet rēķinās lēni. 

Objektam ```λ_range``` ir daudz elementi. Funkcija ```B(λ,T)``` gaida tikai divus skaitļus - viļņa garumu un temperatūru -
bet rakstot ```B.(λ_range,T)```, funkcija tiek izvērtēta atsevišķi pie katra ```λ_range``` elementa. Attiecīgi rezultāts būs
objekts are daudziem elementiem. 

Zīmēsim ar citu funkciju, ```plot```. Pirmie elementi, ko dodām ```plot``` ir objekts ar x-vertībam `λ_range` un objekts ar 
y-vertībām `Bvals`. Pēc tam var dod parametrus. Pēc tam, saucot funkcija ```plot!()``` ar "!" updeito esošo grafiku.

Tik zīmētas vertikālās līnijas pie 400 nm un 700 nm, lai atzīmētu, attiecīgi, redzamās gaismas diapazona violeto un sarkāno robežu. 
"""

# ╔═╡ f7cb975f-1499-49d3-b000-5fe3be3b2ad2
begin
	# Tagad taisīsim vienkāršo grafiku
	λ_range=0.1e-6u"m":0.01e-6u"m":5.0e-6u"m"   # definēsim λ diapazonu (sākums:solis:beigas)
	T=5000u"K"                                  # definēsim temperatūru
	# Lai pielietotu funkciju uz vektoru (λ_range) jāizmanto ".", lai pielietotu "pa elementiem"
	Bvals=B.(λ_range,T);  # semikols slep rezultātus. Citādi mums varētu būt garš saraksts ar rezultātiem.
	Radiance1, err1=quadgk(λ->pi*B(λ,T), 0u"m", 10e-6u"m", rtol=1e-9)  # Rēķināsim kopējo emisiju
	println("Radiance = ", Radiance1)   # Drukāsim
	plot(λ_range, Bvals,xlabel="Viļņa garums", ylabel="Emisijas jauda",label=T)
	myText=string("Integrālā emisija = ", string(Radiance))    # Veidot tekstu ar rezultātu
	annotate!(λ_range[1],Bvals[1],(myText,:red,:left))         # Pievienot tekstu ("!" nozīmē "updeito esošo objektu")
	title!("Melna ķermeņa emisijas spektrs")                   # Pievienot virsrakstu ("!" nozīmē "updeito esošo objektu")
	plot!([700e-9],seriestype="vline",color="red") # redzāmās gaismas diapazona sarkānā robeža
	plot!([400e-9],seriestype="vline",color="violet") # redzāmās gaismas diapazona violeta robeža
end

# ╔═╡ 688cfd30-022f-4cb3-bfa1-85ff36dc3cbc
md"""
## Interaktīva grafika ##
Tagad veidosim interaktīvu grafiku izmantojot makro ```@bind``` no paketes *PlutoUI*. Tas strādā šādi:

```Julia
@bind mansMainīgais Slider(minimums:solis:maksimums, default=manaDefaultVertiba)
```
Pēc tam, nākamajā šūnā, izmantosim mainīgo ```mansMainīgais```, lai rēķinātu emisijas spektru un veidotu grafiku.
"""

# ╔═╡ 282e816a-81a6-42a4-997d-a9a576fbfe4d
@bind Tslider3 Slider(200u"K":50u"K":10000u"K",default= 6000u"K")

# ╔═╡ 473bdf0d-2921-4693-9cdf-4f7a01e955e2
begin
	λ_range3=0.1e-6u"m":0.01e-6u"m":5.0e-6u"m"
   	Bvals3=B.(λ_range3,Tslider3);  # semikols slep rezultātus. Citādi mums varētu būt garš saraksts ar rezultātiem.
	Radiance3, err3=quadgk(λ_range3->pi*B(λ_range3,Tslider3), 0u"m", 10e-6u"m", rtol=1e-9)
	myText3=string("Integrālā emisija = ", string(Radiance3))
	println(myText3)
   	plot(λ_range3, Bvals3, xlabel="Viļņa garums", ylabel="Emisijas jauda",label=Tslider3)
	
#   	annotate!(λ_range2[100],Bvals2[100],(myText,:red,:left))
   	title!("Melna ķermeņa emisijas spektrs")
	plot!([700e-9],seriestype="vline",color="red") # redzāmās gaismas diapazona sarkānā robeža
	plot!([400e-9],seriestype="vline",color="violet") # redzāmās gaismas diapazona violeta robeža
end

# ╔═╡ f439534b-7730-4098-aa02-82f4cfd242e5
md"""
## Kā pielāgot funkciju datiem ##
Bieži mums ir modelis par kādu fizikālo procesu, un mēs vēlāmies zināt, cik tas modelis apraksta datus, 
vai kādi parametri ir vajadzīgi, lai labi aprakstītu datus. 

Sāksim ar vienkāršiem uzdevumiem vienā dimensijā. Pieņemsim, ka mums ir funkcija $y=p_1x+p_2$.
Šim modelim ir divi parametri: $p_1$ un $p_2$. Mēs varam definēt vektoru p=[$p_1$, $p_2$]. 
Tātad p[1]=$p_1$ un p[2]=$p_2$. 

Veidosim modeli izmantojot makro. Atcerēsimies, ka "." nozīmē, ka mēs varam dod funkcijai iteratīvo objektu 
(piemēram vektoru vai sarakstu), un funkcija dos rezultātu katram elementam. 

Pēc tam definēsim iteratīvo objektu ar $x$-datiem. Definēsim p un veidosim datus, pievienojot mazu 
nejaušo kļūdu ar funkciju ```randn```. 

Pēc tam izmantosim funkciju ```curve_fit```, kurai dodam modeli, $x$-datus, $y$-datus, un kādu minējumu par 
parametriem p0. Tā funkcija izdot `Lsqfit` objektu, no kura var dabūt informāciju par fitu - parametrus, 
kļūda, utt.
"""

# ╔═╡ 156102f5-5a08-40ce-98a3-75a506c36802
begin
	@. model(x,p) =p[1]*x+p[2]

	xdata=range(0,stop=10,length=21)
	p=[2.0,1.0]
	ydata=model(xdata,p)+0.5.*randn(length(xdata))
	p0=[1.0,1.0]
	fit=curve_fit(model,xdata,ydata,p0)
	println("p = ",fit.param)
	println("stderr = ", stderror(fit))
	plot(xdata,ydata,linestyle=:auto,linewidth=0,markershape=:circle, markercolor=:red)
	plot!(xdata,model(xdata,fit.param))
end

# ╔═╡ 67f54312-4965-449c-977b-892dc3c04811
md"""
## Tagad Jūsu kārta ##
Uzdevumu mērķis ir palīdzēt saprast fizikālus jēdzienus. Tika izveidota šī klāde, lai pēc iespējas atveiglotu aprēķinus ar sekunāru mērķi iepazīties ar skaitliskām metodēm, kurs varētu noderēt fizikā. Tomēr, nav jāizmanto obligāti, lai atibldētu uz uzdevumiem. 

Uzdevumus varat iesniegt veidā, kas Jums vissērtāk. Rekomendēju vai nu rakstīt atbildes MS Word dokumentā, papildinot ar skrīnšotiem, kad tas palīdz, vai arī papildināt šo klādi un eksportēt to PDF formātā. Atbildes lūdzu iesniegt Moodle vidē, lai būtu vieglāk labot un sniegt atzīmes. 
"""


# ╔═╡ 2927037b-5d51-4167-a11f-185404a4ab8b
md"""
#### Uzdevums 1 ####
Šajā uzdevumā jūs izmantosiet melnā ķermeņa spektra simulāciju, lai izpētītu, kā objektu emitētā elektromagnētiskā starojuma spektru ietekmē objektu temperatūra. Šajā simulācijā jūs varat ievadīt temperatūru un novērot izstarotā starojuma spektru. Jūs varat arī izmantot [interaktīvu rīku PHET mājas lapā](https://phet.colorado.edu/en/simulations/blackbody-spectrum) ja jums nepatīk šī klāde.

a) Visuma zvaigžņu temperatūra mainās atkarībā no zvaigznes veida un vecuma. Aplūkojot zvaigznes izstarotās gaismas spektra formu, mēs varam kaut ko pateikt par tās vidējo virsmas temperatūru.
i) Ja mēs novērojam zvaigznes spektru un konstatējam, ka maksimālā jauda ir uz sarkanās un infrasarkanās gaismas robežas, kāda ir aptuvenā zvaigznes virsmas temperatūra? (C grādos) 

ii) Ja mēs novērojam zvaigznes spektru un konstatējam, ka maksimālā jauda ir uz robežas starp zilo un ultravioleto gaismu, kāda ir zvaigznes virsmas temperatūra? (C grādos) 

b) Spuldzes darbojas 2500 °C temperatūrā.
i) Kāds ir viļņa garums, pie kura tiek izstarota vislielākā jauda, ja spuldze darbojas 2500 C temperatūrā?

ii) Paskaidrojiet, kāpēc parastās kvēlspuldzes patērē daudz enerģijas. Noteikti miniet savu pamatojumu. 

c) Izpētiet, kā novērotais spektrs reaģē uz temperatūras izmaiņām. Ņemiet vērā, ka šeit varat mainīt tikai temperatūru, bet apsveriet, kā mainītos spektrs (jauda pret krāsu), ja mainītu citas objekta īpašības. Domājot par apgalvojumiem (i)--(iii), pasakiet vai apgalvojums ir patiess vai maldīgs:
  (i) Ja vienīgā izmaiņa, ko veicat, ir objekta temperatūras samazināšana, tad dažos gadījumos pie 1000 nm izstarotās jaudas daudzums palielināsies. 

  (ii) Ja vienīgā izmaiņa, ko veicat, ir objekta temperatūras samazināšana, kopējais izstarotās jaudas daudzums samazinās visos gadījumos. 

  (iii) Ja palielinātu spuldzes kvēlspuldzes virsmas laukumu, bet tās temperatūra paliktu nemainīga, tad lielāka daļa no kopējās emitētās jaudas tiktu emitēta kā infrasarkanais starojums . 


Translated with www.DeepL.com/Translator (free version)
"""

# ╔═╡ b12508b9-083f-4347-93ff-59bfe98995e7
md"""
#### Uzdevums 2 ####
Tagad izmantosiet mūsu arpēķina klādi vai [interaktīvu rīku PHET mājas lapā](https://phet.colorado.edu/en/simulations/blackbody-spectrum), lai izpetītu Viņa pārbīdes likumu.
1. Pie dažādām temperatūrām, nosakiet viļņa garumu, pie kura emisijas spektram ir maksimums. 
2. Rakstiet temperatūras viena vektorā, piemēram Tvertibas=\[200, 300, 400, 500, 600, 700, 800, 1000\] un lambda_max=\[l1, l2, l3,.... \]. Uzmaniet, ka abiem vektoriem ir vienāds garums. 
3. Veidojiet grafiku ar Jūsu mērījumiem. 
4. Veidojiet modeli, ņēmot vērā Vīna pārbīdes likumu. 
5. Veidojiet fitu, lai atrastu modeļa parametrus. 
Jūs varat izmantot jebkuru rīku, kas Jums liekas piemērots, bet lūdzu iesniedziet nepieciešamos datus, lai varētu izvērtēt Jūsu darbu: grafikus, kodu fragmentus, dati.
"""

# ╔═╡ 9581f784-6110-4c0d-80b2-73d4da9bd9cf
md"""
#### Uzdevums 3 ####
Tagad izmantosiet mūsu aprēķina klādi vai [interaktīvu rīku PHET mājas lapā](https://phet.colorado.edu/en/simulations/blackbody-spectrum), lai izpetītu Stefāna-Bolcmaņa likumu.
1. Pie dažādām temperatūrām, nosakiet integrālo emisiju. 
2. Veidojiet vektorus ar $T$ vērtībām un integrālās emisijas vērtībām. 
3. Veidojiet grafiku. 
4. Veidojiet modeli, ņēmot vērā Stefāna-Bolcmaņa likumu. 
5. Veidojiet fitu, lai atrastu modeļa parametrus.
Jūs varat izmantot jebkuru rīku, kas Jums liekas piemērots, bet lūdzu iesniedziet nepieciešamos datus, lai varētu izvērtēt Jūsu darbu: grafikus, kodu fragmentus, dati.
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Interact = "c601a237-2ae4-5e1e-952c-7a85b0c7eef1"
LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
UnitfulRecipes = "42071c24-d89e-48dd-8a24-8a12d9b8861f"

[compat]
Interact = "~0.10.4"
LsqFit = "~0.12.1"
Plots = "~1.27.4"
PlutoUI = "~0.7.38"
QuadGK = "~2.4.2"
Unitful = "~1.11.0"
UnitfulRecipes = "~1.5.3"
"""

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

julia_version = "1.7.2"
manifest_format = "2.0"

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

[[deps.Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.3"

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

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git-tree-sha1 = "b649200e887a487468b71821e2644382699f1b0f"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.11.0"

[[deps.UnitfulRecipes]]
deps = ["RecipesBase", "Unitful"]
git-tree-sha1 = "2f61bddb66a5a563b5e67c336577f1af1e650f7b"
uuid = "42071c24-d89e-48dd-8a24-8a12d9b8861f"
version = "1.5.3"

[[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 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.WebIO]]
deps = ["AssetRegistry", "Base64", "Distributed", "FunctionalCollections", "JSON", "Logging", "Observables", "Pkg", "Random", "Requires", "Sockets", "UUIDs", "WebSockets", "Widgets"]
git-tree-sha1 = "c9529be473e97fa0b3b2642cdafcd0896b4c9494"
uuid = "0f1e0344-ec1d-5b48-a673-e5cf874b6c29"
version = "0.8.17"

[[deps.WebSockets]]
deps = ["Base64", "Dates", "HTTP", "Logging", "Sockets"]
git-tree-sha1 = "f91a602e25fe6b89afc93cf02a4ae18ee9384ce3"
uuid = "104b5d7c-a370-577a-8038-80a2059c5097"
version = "1.5.9"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "505c31f585405fc375d99d02588f6ceaba791241"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.5"

[[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.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:
# ╠═3ea3f970-b03d-11ec-1934-d3426ffdd91e
# ╟─39c34251-82b2-439e-ba92-d47d69ac7ce4
# ╟─c28038a8-8933-4bbc-bf82-f1777773a589
# ╟─1c657f2f-c40f-4295-bb89-7bcf5205c0b4
# ╠═b7e0aa75-2faa-4282-a057-92fd1c2097ad
# ╟─2aa42dfd-c7e5-47eb-8096-1b225a8deb8f
# ╠═5813f691-7c35-447d-bd2a-c2984c9528a4
# ╟─b675b485-5200-49f8-9ce3-b7668966fed1
# ╠═3512adef-5b11-4933-95ff-f65cf0e9f52b
# ╟─1d5f5fe5-7c5f-4d0e-88af-7abc51108204
# ╠═fa795d58-9108-4ac5-8a82-df7ab6cfa569
# ╟─0d15db70-91cc-4a77-b04b-446c99c03225
# ╠═f7cb975f-1499-49d3-b000-5fe3be3b2ad2
# ╟─688cfd30-022f-4cb3-bfa1-85ff36dc3cbc
# ╠═282e816a-81a6-42a4-997d-a9a576fbfe4d
# ╠═473bdf0d-2921-4693-9cdf-4f7a01e955e2
# ╟─f439534b-7730-4098-aa02-82f4cfd242e5
# ╠═156102f5-5a08-40ce-98a3-75a506c36802
# ╟─67f54312-4965-449c-977b-892dc3c04811
# ╟─2927037b-5d51-4167-a11f-185404a4ab8b
# ╟─b12508b9-083f-4347-93ff-59bfe98995e7
# ╟─9581f784-6110-4c0d-80b2-73d4da9bd9cf
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
