\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage[T1]{fontenc}
\usepackage[top=3cm,bottom=3cm,left=2cm,right=2cm]{geometry}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{stmaryrd}
\usepackage{graphicx}
\usepackage{amsthm}
\usepackage{fancyhdr}
\usepackage{faktor}
\usepackage{dsfont}
\usepackage{pgf,tikz,pgfplots}
\usepackage{mathrsfs}
\usepackage{enumitem}
\usepackage{centernot}
\usepackage{float}
\usepackage{xurl}

\pgfplotsset{compat=1.17}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes}

\author{Yohann D'ANELLO}

\pagestyle{fancy}
\lfoot{Yohann D'ANELLO}
\rfoot{M2 DS, Université Paris-Saclay}

\setlength{\headheight}{14pt}

\renewcommand{\headrulewidth}{1pt}
\renewcommand{\footrulewidth}{1pt}

\newtheoremstyle{mystyle}% name
  {\topsep}%Space above
  {\topsep}%Space below
  {}%Body font
  {0pt}%Indent amount
  {\bfseries}% Theorem head font
  {}%Punctuation after theorem head
  {2pt}%Space after theorem head 2
  {\underline{\thmname{#1}~\thmnumber{#2}\thmnote{~(#3)}.}}%Theorem head spec (can be left empty, meaning ‘normal’)

\theoremstyle{mystyle}

\newenvironment{preuve}{\noindent\textit{\underline{\proofname.}}~\newline\text{}}{\hfill $\square$\bigskip}

\newtheorem{definition}{Définition}
\newenvironment{defi}[1][]{\begin{definition}[#1]~\newline\text{}}{\end{definition}\bigskip}

\newtheorem{theorem}[definition]{Théorème}
\newenvironment{thm}[1][]{\begin{theorem}[#1]~\newline\text{}}{\end{theorem}\bigskip}

\newtheorem{proposition}[definition]{Proposition}
\newenvironment{prop}[1][]{\begin{proposition}[#1]~\newline\text{}}{\end{proposition}\bigskip}

\newtheorem{corrolary}[definition]{Corollaire}
\newenvironment{cor}[1][]{\begin{corrolary}[#1]~\newline\text{}}{\end{corrolary}\bigskip}

\newtheorem{lemma}[definition]{Lemme}
\newenvironment{lemme}[1][]{\begin{lemma}[#1]~\newline\text{}}{\end{lemma}\bigskip}

\newtheorem{example}[definition]{Exemple}
\newenvironment{ex}[1][]{\begin{example}[#1]~\newline\text{}}{\end{example}\bigskip}

\newtheorem{exercise}{Exercice}
\newenvironment{exo}[1][]{\begin{exercise}[#1]~\newline\text{}}{\end{exercise}\bigskip}

\newtheorem{remark}[definition]{Remarque}
\newenvironment{rem}[1][]{\begin{remark}[#1]~\newline\text{}}{\end{remark}\bigskip}

\newtheorem{question}{Question}
\newenvironment{q}{\begin{question}~\newline\text{}}{\end{question}\bigskip}

\let\rawl\{
\let\rawr\}
\renewcommand{\{}{\left\rawl}
\renewcommand{\}}{\right\rawr}

\renewcommand{\le}{\leqslant}
\renewcommand{\ge}{\geqslant}
\newcommand{\dx}{\, \mathrm{d}x}
\newcommand{\dy}{\, \mathrm{d}y}
\newcommand{\dz}{\, \mathrm{d}z}
\newcommand{\dt}{\, \mathrm{d}t}
\newcommand{\dmu}{\, \mathrm{d}\mu}
\newcommand{\dP}{\, \mathrm{d}\bbP}
\newcommand{\bbP}{\mathbb{P}}
\newcommand{\calP}{\mathcal{P}}
\newcommand{\calF}{\mathcal{F}}
\newcommand{\frakF}{\mathfrak{F}}
\newcommand{\bbE}{\mathbb{E}}
\newcommand{\calE}{\mathcal{E}}
\newcommand{\calL}{\mathcal{L}}
\newcommand{\calO}{\mathcal{O}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Rbar}{\overline{\R}}
\newcommand{\calR}{\mathcal{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\calC}{\mathcal{C}}
\newcommand{\Cbar}{\overline{\C}}
\newcommand{\K}{\mathbb{K}}
\newcommand{\intset}[2][1]{\left\llbracket {#1} , \, {#2} \right\rrbracket}
\newcommand{\Card}{\mathrm{Card}}
\newcommand{\A}{\mathcal{A}}
\newcommand{\B}{\mathcal{B}}
\renewcommand{\Re}{\mathfrak{Re}}
\renewcommand{\Im}{\mathfrak{Im}}
\newcommand{\dsum}{\displaystyle\sum}
\newcommand{\dprod}{\displaystyle\prod}
\newcommand{\dint}{\displaystyle\int}
%\newcommand{\dbinom}{\displaystyle\binom}
\newcommand{\doublebinom}[2]{\displaystyle\left(\!\!\binom{#1}{#2}\!\!\right)}
\newcommand{\tend}[2]{\underset{#1 \to #2}{\longrightarrow}}
\newcommand{\brkt}[1]{\left\langle {#1} \right\rangle}
\newcommand{\scal}[2]{\left\langle {#1} \middle, {#2} \right\rangle}
\newcommand{\bigslant}[2]{{\raisebox{.2em}{$#1$}\left/\raisebox{.2em}{$#2$}\right.}}
\newcommand{\op}{_{\mathrm{op}}}
\newcommand{\md}{\mathrm{d}}
\newcommand{\fL}{\mathfrak{L}}
\newcommand{\id}{\mathrm{id}}

%\renewcommand{\thesection}{\Roman{section} --}
%\renewcommand{\thesubsection}{\arabic{subsection} --}
%\renewcommand{\thesubsubsection}{\arabic{subsection}.\arabic{subsubsection} --}

\setlength\parindent{0pt}