Done tasks of day 5

Day_5/Tasks_day_5.jl

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+### A Pluto.jl notebook ###
+# v0.18.4
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ b11b2fda-b13e-11ec-0b00-13a7cf45371c
+md"""
+# Four vectors
+We want to define our own struct in Julia to deal with four vectors in physics.
+
+Implement the following four vector operators by completing the code in the next cell in the `begin` block:
+
+$v =
+\begin{pmatrix} 
+ct \\
+x \\
+y \\
+z
+\end{pmatrix}$
+
+$u =
+\begin{pmatrix} 
+ct' \\
+x' \\
+y' \\
+z'
+\end{pmatrix}$
+
+$v + u =
+\begin{pmatrix} 
+ct + ct' \\
+x + x' \\
+y + y' \\
+z + z'
+\end{pmatrix}$
+
+$-v =
+\begin{pmatrix} 
+-ct \\
+-x \\
+-y \\
+-z
+\end{pmatrix}$
+
+$v - u =
+\begin{pmatrix} 
+ct - ct' \\
+x - x' \\
+y - y' \\
+z - z'
+\end{pmatrix}$
+
+$v * u = ct * ct' - x * x' - y * y' - z * z'$
+
+$|v|^2 = ct^2 - x^2 - y^2 - z^2$
+
+You should implement $|v|^2$ as a function called `length_squared`.
+"""
+
+# ╔═╡ 04c7c619-e770-415b-ad52-37e0e0e2d2f4
+begin
+	mutable struct FourVector
+		# Add fields here
+	end
+
+	# To override a predefined function of a package, the function has to be imported
+	# In this case, the functions are from the package `Base` which has Julia's builtin functions
+	import Base: +, -, *, ^
+	
+	(+)(v::FourVector, u::FourVector) = FourVector(
+		v.ct + u.ct,
+		v.x + u.x,
+		v.y + u.y,
+		v.z + u.z
+	)
+	
+	#(-)(v::FourVector) = ?
+	
+	#(-)(v::FourVector, u::FourVector) = ?
+
+	#(*)(v::FourVector, u::FourVector) = ?
+end
+
+# ╔═╡ 4b8da4d9-c880-405e-859e-81f5884d29bf
+md"""
+After defining everything above successfully, the cells below would not give you any error.
+"""
+
+# ╔═╡ 22590bad-ff7e-4189-b816-cb5b6e7232c4
+v = FourVector(1.0, 1.0, 1.0, 1.0)
+
+# ╔═╡ e49637f2-e174-4c82-923d-7caf37e5e41a
+u = FourVector(2.0, 3.0, 4.0, 5.0)
+
+# ╔═╡ 3a89512a-30a8-4cf6-9d8a-b090cee2e8a7
+v == u
+
+# ╔═╡ ab360d3d-0ec4-4718-a3b3-a6b90a167f6b
+v == FourVector(1.0, 1.0, 1.0, 1.0)
+
+# ╔═╡ 7fa11520-93a4-48bf-96fa-0f6e134deb96
+v + u
+
+# ╔═╡ 0353376b-94d6-40cf-9b28-18287c75ec69
+v * u
+
+# ╔═╡ 83be3070-c556-4c3d-aaca-93063ac91c64
+-v
+
+# ╔═╡ 8c1ca9ef-6ca4-4a3a-9ffb-8d8f39c9ee48
+v - u
+
+# ╔═╡ 5bee57cf-9c34-4e5c-974f-fcd2636f1300
+length_squared(v)
+
+# ╔═╡ 4a69ccd4-576c-4d31-b75b-8caa9c7159fa
+md"""
+# Chess matrices
+Implement a function that takes an integer `n` as an arguement and returns a `n × n` matrix with a chess pattern using `1` and `0`.
+
+The matrix elements have to be integers.
+
+Example:
+
+$n = 3 \rightarrow \begin{pmatrix} 
+0 & 1 & 0 \\
+1 & 0 & 1 \\
+0 & 1 & 0 \\
+\end{pmatrix}$
+
+If you want to have more fun, implement the function again, but this time with the emojies ⬜️ and ⬛️ instead of 0 and 1 😹
+"""
+
+# ╔═╡ 070e9dc2-884c-4a3b-873a-9a9ebf40c7c6
+# Your code starts here
+
+
+# ╔═╡ 61970ee5-bb70-465a-a940-257a5437574a
+md"""
+# Parsing Pauli matrices
+In the directory `resources`, there are three files:
+- `Matrix_1.txt`
+- `Matrix_2.txt`
+- `Matrix_3.txt`
+
+These are the pauli matrices.
+
+Implement a function that parses these three files and returns the three matrices.
+
+Verify that for all matrices the trace is 0 and the determinant is -1.
+
+#### Hints:
+- You don't need `CSV` or `DataFrames`!
+
+- Instead of
+
+```julia
+lines = open(FILEPATH, "r") do io
+	return readlines(io)
+end
+```
+
+you can just use this shortcut:
+
+```julia
+lines = readlines(FILEPATH)
+```
+
+- You should use
+
+```julia
+parse(Complex{Float64}, STRING)
+```
+
+for parsing a complex number with real and imaginary parts of type `Float64`.
+
+- You should use
+
+```julia
+zeros(Complex{Float64}, (2, 2))
+```
+
+to generate a `2 × 2` matrix with complex numbers with real and imaginary parts as 0 with type `Float64`.
+
+- The package `LinearAlgebra.jl` might be helpful.
+"""
+
+# ╔═╡ eccf0ed9-fe65-4872-8e11-e94a49e642d2
+# Your code starts here
+
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+"""
+
+# ╔═╡ 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]
+"""
+
+# ╔═╡ Cell order:
+# ╟─b11b2fda-b13e-11ec-0b00-13a7cf45371c
+# ╠═04c7c619-e770-415b-ad52-37e0e0e2d2f4
+# ╟─4b8da4d9-c880-405e-859e-81f5884d29bf
+# ╠═22590bad-ff7e-4189-b816-cb5b6e7232c4
+# ╠═e49637f2-e174-4c82-923d-7caf37e5e41a
+# ╠═3a89512a-30a8-4cf6-9d8a-b090cee2e8a7
+# ╠═ab360d3d-0ec4-4718-a3b3-a6b90a167f6b
+# ╠═7fa11520-93a4-48bf-96fa-0f6e134deb96
+# ╠═0353376b-94d6-40cf-9b28-18287c75ec69
+# ╠═83be3070-c556-4c3d-aaca-93063ac91c64
+# ╠═8c1ca9ef-6ca4-4a3a-9ffb-8d8f39c9ee48
+# ╠═5bee57cf-9c34-4e5c-974f-fcd2636f1300
+# ╟─4a69ccd4-576c-4d31-b75b-8caa9c7159fa
+# ╠═070e9dc2-884c-4a3b-873a-9a9ebf40c7c6
+# ╟─61970ee5-bb70-465a-a940-257a5437574a
+# ╠═eccf0ed9-fe65-4872-8e11-e94a49e642d2
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002