\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}

% Spacing functions
\newcommand{\thmfill}{\hfill\\}

% 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
\declaretheorem[numberwithin=chapter, style=definition]{theorem, definition, notation, lemma, corollary, remark}

% Formatting
\setlist[enumerate]{font=\bfseries}
\newcounter{alphasect}
\def\alphainsection{0}

\let\oldsection=\section
\def\section{%
	\ifnum\alphainsection=1%
	\addtocounter{alphasect}{1}
	\fi%
	\oldsection}%

\renewcommand\thesection{%
	\ifnum\alphainsection=1% 
	\Alph{alphasect}
	\else%
	\arabic{section}
	\fi%
}%

\newenvironment{alphasection}{%
	\ifnum\alphainsection=1%
	\errhelp={Let other blocks end at the beginning of the next block.}
	\errmessage{Nested Alpha section not allowed}
	\fi%
	\setcounter{alphasect}{0}
	\def\alphainsection{1}
}{%
	\setcounter{alphasect}{0}
	\def\alphainsection{0}
}%