Awesome

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% Author:       Léo RACLET
% File:         main.tex
% Description:  LaTeX main document
% License:      MIT
% Version:      v1.0
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\documentclass[12pt, french]{report}
\input{preamble.tex}

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% DOCUMENT                                                 %
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\begin{document}

\begin{titlepage}
  \begin{center}
    \vspace{10cm}
    {\Large \itshape 2023-2024}\\
    \vspace{3cm}
    \pgfornament[width=10cm]{88}\\
    \vspace{2mm}
    \vspace{0.5cm}
    {\huge Mathématiques}\\
    \vspace{0.5cm}
    {\huge FISE 1}\\
    \vspace{0.5cm}
    \pgfornament[width=10cm]{88}\\
    \vfill
    Léo {\sc Raclet}\\
  \end{center}
\end{titlepage}

\tableofcontents
\addcontentsline{toc}{chapter}{Table des matières}
\listoffigures
\addcontentsline{toc}{chapter}{Table des figures}
\listoftables
\addcontentsline{toc}{chapter}{Liste des tableaux}

\etocsettocstyle{
  \section*{Sommaire}
  \hrule
  \bigskip
  \begin{minipage}{.95\linewidth}
  }
  {
  \end{minipage}
  \bigskip
  \hrule
}

\unbchap{Avant-propos}
\chap{Les fondamentaux}
\localtableofcontents

\section{Mathématiques}

\subsection{Blocs de couleurs}

\begin{theorem}[Théorème de Pythagore (oui)]{thm:pythagoras}
  In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the catheti.
  $$a^2+b^2=c^2$$
\end{theorem}
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem (see theorem \ref{thm:pythagoras}), is a relation in Euclidean geometry among the three sides of a right triangle.

\begin{proof}{proof:pythagoras}
  If $x=y=\sqrt{2}$ is an example, then we are done; otherwise $\sqrt{2}^{\sqrt{2}}$ is irrational, in which case taking $x=\sqrt{2}^{\sqrt{2}}$ and $y=\sqrt{2}$ gives us:
  \[\bigg(\sqrt{2}^{\sqrt{2}}\bigg)^{\sqrt{2}}=\sqrt{2}^{\sqrt{2}\sqrt{2}}=\sqrt{2}^{2}=2.\]
\end{proof}

\newpage

\begin{lemma}[Identité de Bézout]{lemma:bezout}
  Let $a$ and $b$ be nonzero integers and let $d$ be their greatest common divisor. Then there exist integers $x$ and $y$ such that:
  \[ax+by=d\]
\end{lemma}

\begin{definition}[]{def:one}
  If we want dummy text in our document then we generally search for lorem ipsum text generators and copy-paste those texts/paragraphs in our document.
\end{definition}

\begin{example}[]{exaple:one}
  In LaTeX, we don't need to do such copy and paste thing. LaTeX has different packages which automatically generates dummy text in our document. You can generate them with just a few lines of code.
\end{example}

\begin{remark}[]{remark:one}
  In the example below, lipsum package is used to print dummy text below chapter title. lipsum[2-4] prints lorem ipsum text from paragraph 2 to paragraph 4
\end{remark}

\begin{property}[]{property:one}
  Every line in your source code must end with otherwise your algorithm will continue on the same line of text in the output.
\end{property}

\begin{lstlisting}[language=Python]
# libraries:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt  # creating the variables:
x = np.linspace(0,100)
y = x**2  # plotting
plt.plot(x, y, '-b')
\end{lstlisting}

\begin{algorithm}
  \caption{An algorithm with caption}
  \KwData{$n \geq 0$}
  \KwResult{$y = x^n$}
  $y \gets 1$\;
  $X \gets x$\;
  $N \gets n$\;
  \While{$N \neq 0$}{
    \eIf{$N$ is even}{
      $X \gets X \times X$\;
      $N \gets \frac{N}{2}$ \Comment*[r]{This is a comment}
    }{\If{$N$ is odd}{
        $y \gets y \times X$\;
        $N \gets N - 1$\;
      }
    }
  }
\end{algorithm}

\begin{important}[]{imp:one}
  If we want dummy text in our document then we generally search for lorem ipsum text generators and copy-paste those texts/paragraphs in our document.
\end{important}

\newpage

\begin{exercise}[]{ex:one}
  If we want dummy text in our document then we generally search for lorem ipsum text generators and copy-paste those texts/paragraphs in our document.
\end{exercise}

\begin{contour}[]{con:one}
  If we want dummy text in our document then we generally search for lorem ipsum text generators and copy-paste those texts/paragraphs in our document.
\end{contour}

\begin{multicols}{2}
  \begin{synthese}[Rappel]{syn:one}
    If we want dummy text in our document then we generally search for lorem ipsum text generators and copy-paste those texts/paragraphs in our document.
  \end{synthese}
  \begin{synthese}[Ordre bien fondé]{syn:two}
    Un ordre est bien fondé s'il n'existe pas
    de suite infiniment strictement décrois-
    sante, i.e. toute partie non vide de E ad-
    met un élément minimal.
    \smallskip

    Un ordre est bien fondé s'il n'existe pas
    de suite infiniment strictement décrois-
    sante, i.e. toute partie non vide de E ad-
    met un élément minimal.
  \end{synthese}
\end{multicols}

\begin{figure}[ht]
  \centering
  \begin{tikzpicture}
    \begin{scope}[every node/.style={circle,thick,draw}]
      \node (A) at (0,0) {A};
      \node (B) at (0,3) {B};
      \node (C) at (2.5,4) {C};
      \node (D) at (2.5,1) {D};
      \node (E) at (2.5,-3) {E};
      \node (F) at (5,3) {F} ;
    \end{scope}
    \begin{scope}[>={Stealth[black]},
        every node/.style={fill=white,circle},
      every edge/.style={draw=red,very thick}]
      \path [->] (A) edge node {$5$} (B);
      \path [->] (B) edge node {$3$} (C);
      \path [->] (A) edge node {$4$} (D);
      \path [->] (D) edge node {$3$} (C);
      \path [->] (A) edge node {$3$} (E);
      \path [->] (D) edge node {$3$} (E);
      \path [->] (D) edge node {$3$} (F);
      \path [->] (C) edge node {$5$} (F);
      \path [->] (E) edge node {$8$} (F);
      \path [->] (B) edge[bend right=60] node {$1$} (E);
    \end{scope}
  \end{tikzpicture}
  \caption{This is a real beautiful figure of a graph}
\end{figure}

\begin{figure}[ht]
  \centering
  \begin{tikzpicture}[domain=0:4]
    \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);

    \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
    \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};

    \draw[color=red]    plot (\x,\x)             node[right] {$f(x) =x$};
    % \x r means to convert '\x' from degrees to _r_adians:
    \draw[color=blue]   plot (\x,{sin(\x r)})    node[right] {$f(x) = \sin x$};
    \draw[color=orange] plot (\x,{0.05*exp(\x)}) node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
  \end{tikzpicture}
\end{figure}

\begin{draw}[my angle/.style={draw, ->, angle eccentricity=1.3, angle radius=9mm}]{Trigonometric circle}
  % coordinate axis
  \draw[-] (-2.0,0) -- (2.0,0);
  \draw[-] (0,-2.0) -- (0,2.0);
  % circle
  \draw (0,0) circle (2cm);
  % coordinates
  \coordinate[label=right:{$( 1,0)$}] (A)  at ( 2,0);
  \coordinate[label=above:{$(0, 1)$}] (B)  at ( 0,2);
  \coordinate[label=left:{$(-1,0)$}] (C)  at (-2,0);
  \coordinate[label=below:{$(0,-1)$}] (D)  at (0,-2);
  %
  \coordinate[label=above:M]  (M) at (60:2);
  \coordinate                 (O) at ( 0:0);
  % angles
  \draw[thick]    (M) -- (C)  (M) -- (O);
  \pic[my angle, "$t$"]      {angle = A--C--M};
  \pic[my angle, "$\theta$"] {angle = A--O--M};
\end{draw}

\clearpage
\end{document}

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