\usepackage{braket}
\usepackage{polynom}
\usepackage{amsthm}
\usepackage{csquotes}
\usepackage{svg}
\usepackage{environ}
\usepackage{tikz,pgfplots}
\usepackage{titleps}
\usepackage{tcolorbox}

\pgfplotsset{width=10cm,compat=1.15}
\usepgfplotslibrary{external}
\usetikzlibrary{calc,trees,positioning,arrows,fit,shapes}
%\tikzexternalize
\setcounter{MaxMatrixCols}{20}

\newpagestyle{main}{\sethead{\toptitlemarks\thesection\quad\sectiontitle}{}{\thepage}\setheadrule{.4pt}}
\pagestyle{main}

\newtcolorbox{defi-box}{colback=gray!5!white,arc=0pt,outer arc=0pt,colframe=gray!60!black}
\newtcolorbox{bsp-box}{colback=orange!5!white,arc=0pt,outer arc=0pt,colframe=orange!60!black}
\newtcolorbox{visu-box}{colback=cyan!5!white,arc=0pt,outer arc=0pt,colframe=cyan!60!black}
\NewEnviron{splitty}{\begin{displaymath}\begin{split}\BODY\end{split}\end{displaymath}}

\newcommand\N{\mathbb{N}}
\newcommand\R{\mathbb{R}}
\newcommand\Z{\mathbb{Z}}
\newcommand\Q{\mathbb{Q}}
\newcommand\C{\mathbb{C}}
\renewcommand\P{\mathbb{P}}
\renewcommand\O{\mathcal{O}}
\newcommand\pot{\mathcal{P}}
\newcommand{\cupdot}{\mathbin{\mathaccent\cdot\cup}}
\newcommand{\bigcupdot}{\dot{\bigcup}}

\newcommand\refiff[1]{\stackrel{\text{#1}}{\iff}}
\newcommand\refimp[1]{\stackrel{\text{#1}}{\implies}}
\newcommand\refeq[1]{\stackrel{\text{#1}}{=}}
\newcommand\refless[1]{\stackrel{\text{#1}}{<}}