\ProvidesPackage{init}

\usepackage{import}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}
\usepackage[english]{babel}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage{hyperref}
\usepackage{cancel}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{relsize}
\usepackage{listings}
\graphicspath{ {./images/} }
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage[left=2cm, right=2.5cm, top=2.5cm, bottom=2.5cm]{geometry}
\usepackage{enumitem}
\usepackage{mathrsfs}

% Math Functions
\newcommand{\limx}[2]{\displaystyle\lim\limits_{#1 \to #2}}
\newcommand{\st}{\ \text{s.t.}\ }
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\dotp}{\dot{\mathcal{P}}}
\newcommand{\dotq}{\dot{\mathcal{Q}}}
\newcommand{\Int}[1]{\text{int}\left(#1\right)}
\newcommand{\cl}[1]{\text{cl}\left(#1\right)}
\newcommand{\bd}[1]{\text{bd}\left(#1\right)}
\newcommand{\lr}[1]{\langle #1 \rangle)}
\newcommand{\lspan}[1]{\text{span}\left(#1\right)}
\newcommand{\ldim}[1]{\text{dim}\left(#1\right)}
\newcommand{\nullity}[1]{\text{nullity}\left(#1\right)}
\newcommand{\rank}[1]{\text{rank}\left(#1\right)}
\newcommand{\ldet}[1]{\text{det}\left(#1\right)}
\newcommand{\ltr}[1]{\text{tr}\left(#1\right)}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\DeclareMathOperator{\sign}{sgn}
\renewcommand{\qedsymbol}{$\blacksquare$}

% Special Sets
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\F}{\mathbb{F}}

% Theorem Styles
\newtheoremstyle{break}% name
{}%         Space above, empty = `usual value'
{}%         Space below
{}% Body font
{}%         Indent amount (empty = no indent, \parindent = para indent)
{\bfseries}% Thm head font
{}%        Punctuation after thm head
{\newline}% Space after thm head: \newline = linebreak
{}%         Thm head spec
\makeatletter
\def\thmhead@plain#1#2#3{%
	\thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2} }%
	\thmnote{{\the\thm@notefont\bfseries\itshape#3}}}
\let\thmhead\thmhead@plain
\makeatother
\newtheoremstyle{case}{}{}{}{}{}{:}{ }{}
\theoremstyle{case}
\newtheorem{case}{Case}
\theoremstyle{break}
\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem*{lem}{Lemma}
\newtheorem*{remark}{Remark }
\newtheorem*{aside}{}
\newtheorem*{example}{Example}

% Formatting
\setlist[enumerate]{font=\bfseries}