prreamble.sty

% Ryan Rueger, 2022
%
% Slogan: Preamble by Ryan Rueger, hence "pRReamble"
%
% Originally adopted from Manfred Einsiedler and Andreas Wieser's Analysis
% script. Many changes and features have come since then, and so is perhaps not
% so recognisable any more.
%
% For a not very up-to-date version of the documentation visit
%
%   https://rueg.re/prreamble.pdf
%

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{prreamble}[2022/11/18 A preamble for mathematics]

% Options {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% These packages are required for managing the options within this package.
% Provides \ifdef, \*toggle* commmmands
\RequirePackage{etoolbox}
% Provides \ifluatex, \ifxetex
\RequirePackage{iftex}
% Provides \NewDocumentCommand
\RequirePackage{xparse}

\newtoggle{debug}
\DeclareOption{debug}{\toggletrue{debug}}

\newtoggle{nobreaks}
\DeclareOption{nobreaks}{\toggletrue{nobreaks}}

\newtoggle{printlinks}
\DeclareOption{printlinks}{\toggletrue{printlinks}}

\newtoggle{print}
\DeclareOption{print}{%
  \PassOptionsToPackage{draft}{hyperref}
  \toggletrue{print}
  \toggletrue{printlinks}
}

\newtoggle{centertitles}
\DeclareOption{centertitles}{%
  \toggletrue{centertitles}
  \PassOptionsToPackage{center}{titlesec}
}

\newtoggle{centerstacktitles}
\DeclareOption{centerstacktitles}{\toggletrue{centerstacktitles}}

\newtoggle{concroman}
\DeclareOption{concroman}{\toggletrue{concroman}}

\newtoggle{concmath}
\DeclareOption{concmath}{\toggletrue{concmath} \toggletrue{concroman}}

\newtoggle{concbold}
\DeclareOption{concbold}{\toggletrue{concbold} \toggletrue{concroman}}

\newtoggle{euler}
\DeclareOption{euler}{\toggletrue{euler}}

\newtoggle{scdefs}
\DeclareOption{scdefs}{\toggletrue{scdefs}}

\newtoggle{scdefobjs}
\DeclareOption{scdefobjs}{\toggletrue{scdefobjs}}

\newtoggle{uldefs}
\DeclareOption{uldefs}{\toggletrue{uldefs}}

\newtoggle{uldefobjs}
\DeclareOption{uldefobjs}{\toggletrue{uldefobjs}}

\newtoggle{scthms}
\DeclareOption{scthms}{\toggletrue{scthms}}

\newtoggle{ulthms}
\DeclareOption{ulthms}{\toggletrue{ulthms}}

\newtoggle{scemph}
\DeclareOption{scemph}{\toggletrue{scemph}}

\newtoggle{milne}
\DeclareOption{milne}{\toggletrue{milne}}

% Original
\newtoggle{original}
\DeclareOption{original}{%
  \toggletrue{original}
  \toggletrue{concroman}
  \toggletrue{euler}
}

% Classic
\newtoggle{classic}
\DeclareOption{classic}{%
  \toggletrue{classic}
  \toggletrue{concbold}
  \toggletrue{concroman}
  \toggletrue{concmath}

  \toggletrue{scdefobjs}
  \toggletrue{scemph}
  \toggletrue{uldefs}
  \toggletrue{ulthms}

  \toggletrue{centertitles}
  \PassOptionsToPackage{center}{titlesec}
}

% Modern
\newtoggle{modern}
\DeclareOption{modern}{%
  \toggletrue{modern}
  \toggletrue{concroman}
  \toggletrue{concmath}
}

\newtoggle{beamer}
\DeclareOption{beamer}{\toggletrue{beamer}}

\newtoggle{nomath}
\DeclareOption{nomath}{\togglefalse{nomath}}

\newtoggle{noletters}
\DeclareOption{noletters}{\toggletrue{noletters}}

\DeclareOption*{\PackageWarning{prreamble}{Unknown '\CurrentOption'}}
\ProcessOptions\relax

\iftoggle{ulthms}{\iftoggle{scthms}{%
  \PackageWarning{prreamble}{Both ulthms and scthms was specified}
}{}}{}

\iftoggle{uldefs}{\iftoggle{scdefs}{%
    \PackageWarning{prreamble}{Both uldefs and scdefs was specified}
}{}}{}

\iftoggle{uldefobjs}{\iftoggle{scdefobjs}{%
  \PackageWarning{prreamble}{Both uldefobjs and scdefobjs was specified}
}{}}{}

\iftoggle{concmath}{\iftoggle{euler}{%
  \PackageWarning{prreamble}{Cannot use concmath and euler together}
}{}}{}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Context {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This preamble was initially developed by Andreas Wieser, Prof. Manfred
% Einsiedler and a host of others
%
% To generate a ``clean'' version of this preamble, it can be piped through
% `sed`
%
% This clean version will not have any comments
%
% $ sed -e '/^%/d' -e '/^\s*$/d' -e 's/\s*%.*$//' preamble.tex > clean-preamble.tex
%
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% How to use this package {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Here is a boilerplate example for using this preamble.
%
% The \documentclass is purposely _not_ defined in this preamble, and thus must
% be defined in the document before \inputting the preamble.
%
% \documentclass[11pt,a4paper,oneside]{article}
% \input{preamble}
% \begin{document}
% ...
% \end{document}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default packages and configurations {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Descriptions obtained from CTAN

\newtoggle{geometryloadedbefore}
\ifdef{\newgeometry}{\toggletrue{geometryloadedbefore}}{}

\AtEndPreamble{%
  % If geometry is loaded
  \ifdef{\newgeometry}{%
    % But it wasn't loaded before prreamble
    \nottoggle{geometryloadedbefore}{%
      \PackageWarning{prreamble}{geometry was loaded after prreamble}
    }{}
  }{}
}

\ifluatex \else \ifxetex \else
    \RequirePackage[utf8]{inputenc}
    % Standard package for selecting font encodings
    % https://www.ctan.org/pkg/fontenc
    % Including Cyrllic encodings (T2{A,B,C}) later comes into conflict with the
    % \C command.
    \RequirePackage[T1]{fontenc}
\fi \fi

% Standard mathematics packages
\RequirePackage{amsmath}
\RequirePackage{amscd}
\RequirePackage{amsfonts}
\RequirePackage{amsthm}
% Pre-defined colors
% https://www.ctan.org/pkg/xcolor
\RequirePackage{xcolor}
\definecolor{maroon}{cmyk}{0, 0.87, 0.68, 0.32}
\colorlet{ochre}{brown}
\newcommand{\purple}[1]{{\color{violet} #1}}
\newcommand{\violet}[1]{{\color{violet} #1}}
\newcommand{\green}[1]{{\color{teal} #1}}
\newcommand{\teal}[1]{{\color{teal} #1}}
\newcommand{\red}[1]{{\color{red} #1}}
\newcommand{\ochre}[1]{{\color{ochre} #1}}
\newcommand{\maroon}[1]{{\color{maroon} #1}}
\newcommand{\blue}[1]{{\color{blue} #1}}
\nottoggle{beamer}{%
  % Hyperref - Extensive support for hypertext in LaTeX
  % Needs to be included _before_ amsrefs!
  \RequirePackage[
    hidelinks,
    colorlinks=true,
    allcolors=maroon,
    unicode,
  ]{hyperref}
}{}
% AMS alternative to bibtex. Allows for bibliography in the same source file as
% the main file.
\RequirePackage[lite,backrefs]{amsrefs}

% Mathtools - Mathematical tools to use with amsmath
% Must be loaded _before_ unicode-math
% Provides: \hookrightarrow, ...
% https://www.ctan.org/pkg/mathtools
\RequirePackage{mathtools}
\PassOptionsToPackage{warnings-off={mathtools-colon,mathtools-overbracket}}{unicode-math}

% Fontspec - Advanced font selection in XeLaTeX and LuaLaTeX
% https://ctan.org/pkg/fontspec
\iftoggle{milne}{%
  \RequirePackage{newtx}
}{%
  \RequirePackage{fontspec}
}

\iftoggle{concroman}{%
  % concroman
  \iftoggle{concmath}{%
    \iftoggle{concbold}{%
      % concmath and concbold
      \RequirePackage[math-style=ISO]{concmath-otf}
    }{%
      % concmath and !concbold
      \RequirePackage{unicode-math}
      \setmathfont{Concrete Math}[math-style=ISO]
      \setmainfont{cmunorm.otf}[
        BoldFont=lmroman9-bold.otf,
        ItalicFont=cmunoti.otf,
        BoldItalicFont=cmunobi.otf
      ]
    }
    % Steal the \setminus command from Asana-Math
    % Needs to come after getting concmath font from concmath-otf
    \setmathfont{Asana-Math.otf}[range={"029F5}]
  }{%
    \iftoggle{concbold}{%
        % !concmath and concbold
        \setmainfont{cmunorm.otf}[
          BoldFont=cmunobx.otf,
          ItalicFont=cmunoti.otf,
          BoldItalicFont=cmunobi.otf
        ]
      }{%
        % !concmath and !concbold
        \setmainfont{cmunorm.otf}[
          BoldFont=lmroman9-bold.otf,
          ItalicFont=cmunoti.otf,
          BoldItalicFont=cmunobi.otf
        ]
    }
  }
  \newcommand{\graffito}[1]{%
    \marginpar{\fontspec{ccslc9.tfm}\raggedright\footnotesize\color{maroon}#1}
  }
}{%
  % !concroman
  \newcommand{\graffito}[1]{%
    \marginpar{\fontspec{lmmonoltcond10-oblique.otf}\raggedright\footnotesize\color{maroon}#1}
  }
  \nottoggle{milne}{%
    \RequirePackage{amssymb}
  }{}
}

\iftoggle{euler}{%
  \RequirePackage{euler-math}
  \setmathfont{STIXTwoMath-Regular.otf}[range=sfup,Scale=MatchUppercase]
}{}

% If the scemph option is configured, use schape instead of bold.
\iftoggle{scemph}{%
  \renewcommand{\textbf}{\textsc}
}{}

% Macros supporting the Mathematics of Physics
% Provides: \evaluated
\RequirePackage{physics}
% Typeset mathematical double stroke symbols
% Provides: \mathbb, \mathds
% https://www.ctan.org/tex-archive/fonts/doublestroke
\RequirePackage{dsfont}
% Enumerate with redefinable labels
% Provides: \enumerate
% https://www.ctan.org/pkg/enumerate
\RequirePackage{enumerate}
% Extensive control of page headers and footers
% https://www.ctan.org/pkg/fancyhdr
\nottoggle{beamer}{%
  \RequirePackage{fancyhdr}
  \AtBeginDocument{\addtolength{\headheight}{1ex}}
  % Indent first paragraph after section header
  % (Default is to indent all but the first)
  % https://www.ctan.org/pkg/indentfirst
  % \RequirePackage{indentfirst}
  % Print text verbatim (useful for code snippet)
  % https://ctan.org/pkg/indentfirst?lang=en
}{}
\RequirePackage{verbatim}
\nottoggle{beamer}{%
  % Enhanced support for graphics
  % https://www.ctan.org/pkg/graphicx
  \RequirePackage[final]{graphicx}
}{}
% Create PostScript and PDF graphics
% Include after: graphicx, xcolor
% https://www.ctan.org/pkg/pgf
\RequirePackage{tikz}
\usetikzlibrary{angles,arrows,calc,decorations.pathmorphing,matrix,shapes}
% Create commutative diagrams with TikZ
% https://ctan.org/pkg/tikz-cd
\RequirePackage{tikz-cd}
% Select any font size in LaTeX
% https://ctan.org/pkg/anyfontsize
% This essentially fixes 'Font shape ... not available in size ...' errors
\RequirePackage{anyfontsize}
\nottoggle{beamer}{%
  % A package for producing multiple indexes
  \RequirePackage{imakeidx}
  \indexsetup{firstpagestyle=empty}
  % Change index for larger index items
  \renewcommand{\@idxitem}{\par\hangindent 10\p@}
  % Ensure the index is created
  \makeindex
}{}
% Force footnotes to the bottom of the page
% https://www.ctan.org/pkg/footmisc
\RequirePackage[bottom]{footmisc}
% https://www.ctan.org/pkg/soul
% Hyphenation for letterspacing, underlining, and more
\RequirePackage{soul}
% Override \underline with more robust underlining
% Standard \underline cannot perform line breaks
\let\defaultunderline\underline
\renewcommand{\underline}{\ul}
% Intermix single and multiple columns
% https://www.ctan.org/pkg/multicol
% For breaking long calculations into columns
\RequirePackage{multicol}
% Typeset source code listings using LaTeX
% https://www.ctan.org/pkg/listings
\RequirePackage{listings}
\definecolor{codegreen}{rgb}{0,0.6,0}
\definecolor{codegray}{rgb}{0.5,0.5,0.5}
\definecolor{codepurple}{rgb}{0.58,0,0.82}
\definecolor{backcolour}{rgb}{0.98,0.98,0.98}
\lstdefinestyle{mystyle}{%
    backgroundcolor=\color{backcolour},
    commentstyle=\color{codegreen},
    keywordstyle=\color{magenta},
    numberstyle=\tiny\color{codegray},
    stringstyle=\color{codepurple},
    basicstyle=\ttfamily,
    breakatwhitespace=false,
    breaklines=true,
    captionpos=b,
    keepspaces=true,
    numbers=left,
    numbersep=5pt,
    showspaces=false,
    showstringspaces=false,
    showtabs=false,
    tabsize=2,
}
\lstset{style=mystyle}

% Framed environments that can split at page boundaries
% Used for defining new environments
% https://www.ctan.org/pkg/mdframed
\RequirePackage{mdframed}
\newmdenv[
  topline=false,
  bottomline=false,
  rightline=false,
  skipabove=\topsep,
  skipbelow=\topsep,
  innertopmargin=1pt,
  innerbottommargin=1pt,
]{siderules}
\newmdenv[
  topline=true,
  bottomline=true,
  rightline=true,
  leftline=true,
  skipabove=\topsep,
  skipbelow=\topsep,
  innertopmargin=1ex,
  innerbottommargin=1ex,
]{fullrules}

% Honourable mentions for packages which have been used in this preamble at some
% point in time.
%
% \RequirePackage{caption}
% \RequirePackage{comment}
% \RequirePackage{faktor}
% \RequirePackage{float}
% \RequirePackage{import}
% \RequirePackage{pdfpages}
% \RequirePackage{subcaption}
% \RequirePackage{transparent}
% \RequirePackage{url}
% \RequirePackage{xifthen}
% \RequirePackage{xspace}
% \RequirePackage{pgfplots}
% \pgfplotsset{width=12cm,compat=1.9}
% \usepgfplotslibrary{external}
% \RequirePackage{wasysym}

% The 'quotes' tikzlibrary, i.e. \usetikzlibrary{...,quotes}.

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Page Layout: Setting white space {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{setspace}
\iftoggle{concroman}{%
  \iftoggle{classic}{%
    \setstretch{1.75}
  }{%
    \setstretch{1.15}
  }
}{%
  \setstretch{1.1}
}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Page Layout: Geometry (deprecated) {{{{{
% Dynamically set margins for different page sizes.
% \newcommand\papersize[1]{%
%   TT\fi
%   \uppercase{\ifdim\csname #1@PAPER\endcsname}=\paperheight
% }
%
% \makeatletter
% \@namedef{A4@PAPER}{297mm}
% \@namedef{A5@PAPER}{210mm}
% \@namedef{B5@PAPER}{250mm}
% \@namedef{LETTER@PAPER}{11in}
% \@namedef{LEGAL@PAPER}{14in}
% \@namedef{EXECUTIVE@PAPER}{10.5in}
% \makeatother

% \if\papersize{a4}
%   % Required to be able to set the page size
%   \RequirePackage[
%     left=1.35in,
%     right=1.35in,
%     top=1.35in,
%     bottom=1.35in,
%     headheight=20pt,
%     headsep=0.3in,
%     footskip=0.5in
%   ]{geometry}
% \fi

% \if\papersize{a5}
%   % Required to be able to set the page size
%   \RequirePackage[
%     left=0.6in,
%     top=0.575in,
%     right=.6in,
%     bottom=0.55in,
%     headheight=20pt,
%     headsep=0.1in,
%     footskip=0.15in
%   ]{geometry}
% \fi
% }}}}}
% Page Layout: Title page {{{{{
% horizontal double rule top
\newcommand{\hdrulet}{\vspace{3ex}\rule{\textwidth}{1.6pt}\vspace*{-\baselineskip}\vspace*{2pt}\newline\rule{\textwidth}{0.4pt} \\ \vspace{1ex}}
% horizontal double rule bottom
\newcommand{\hdruleb}{\vspace{1ex}\rule{\textwidth}{0.4pt}\vspace*{-\baselineskip}\vspace{3.2pt}\newline\rule{\textwidth}{1.6pt} \\ \vspace{3ex}}
% horizontal (single) rule top
\newcommand{\hrulet}{\vspace{3ex}\rule{\textwidth}{1.6pt} \\ \vspace{1ex}}
% horizontal (single) rule bottom
\newcommand{\hruleb}{\vspace{1ex}\rule{\textwidth}{1.6pt} \\ \vspace{3ex}}
% Double ruled title
\newcommand{\dTitle}[1]{~\\\hdrulet{\Large\textbf{#1}\\}\hdruleb~\\}

\newcommand{\PlainTitleLogo}[5]{%
  \AtBeginDocument{%
    \thispagestyle{empty}
    \begin{center}
      \includegraphics{#1} \\
      \vspace{27.1728ex}
      \iftoggle{concroman}{ { \MakeUppercase{#2} \\ } }{ #2 }
      \vspace{12ex}
      \, #3 \\
      \vspace{10ex}
      \iftoggle{concroman}{ {\large \MakeUppercase{#4}  \\ } }{ {\large #4 \\ } }
    \end{center}
    \vfill
    {\large \raggedright \parindent0pt #5 \vspace{10ex}}
  }
}

\newcommand{\PlainTitleLogoExtra}[6]{%
  \AtBeginDocument{%
    \thispagestyle{empty}
    \begin{center}
      \includegraphics{#1} \\
      \vspace{12.1728ex}
      \iftoggle{concroman}{ { \MakeUppercase{#2} \\ } }{ #2 }
      \vspace{12.1728ex}
      #5
      \vspace{12ex}
      \, #3 \\
      \vspace{10ex}
      \iftoggle{concroman}{ {\large \MakeUppercase{#4}  \\ } }{ {\large #4 \\ } }
    \end{center}
    \vfill
    {\large \raggedright \parindent0pt #6 \vspace{6ex}}
  }
}

\newcommand{\PlainTitleName}[5]{%
  \iftoggle{concroman}{%
    \AtBeginDocument{%
      \thispagestyle{empty}
      \begin{center}
        {\LARGE #1} \\
        \vspace{12.1728ex}
        {\Huge #2 \\ }
        \vspace{12ex}
        \, #3 \\
        \vspace{10ex}
        {\LARGE #4\\ }
      \end{center}
      \vfill
      {\large \parindent0pt \begin{flushleft} \iftoggle{concroman}{\iftoggle{classic}{\setstretch{1.75}}{\setstretch{1.1}}}{\setstretch{1.1}} #5 \end{flushleft} \vspace{10ex}}
    }
  }{}
}

\newcommand{\PlainTitle}[4]{%
  \iftoggle{concroman}{%
    \AtBeginDocument{%
      \thispagestyle{empty}
      \begin{center}
        \vspace{12.1728ex}
        {\Huge #1 \\ }
        \vspace{12ex}
        \, #2 \\
        \vspace{10ex}
        {\LARGE #3\\ }
      \end{center}
      \vfill
      {\large \parindent0pt \begin{flushleft} \iftoggle{concroman}{\iftoggle{classic}{\setstretch{1.75}}{\setstretch{1.1}}}{\setstretch{1.1}} #4 \end{flushleft} \vspace{10ex}}
    }
  }{}
}

\newcommand{\PlainTitleShort}[4]{%
  \AtBeginDocument{%
    \thispagestyle{empty}
    \begin{center}

      \vspace{10.36ex}

      #1

      \vspace{3.456ex}

      {\bfseries #2}

      \vspace{3.456ex}

      #3

      \vspace{5.184ex}

      #4
    \end{center}
  }
}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Page Layout: Justification rules {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \doublehyphendemerits=10000    % No consecutive line hyphens.
% \brokenpenalty=10000           % No broken words across columns/pages.
% \widowpenalty=9999             % Almost no widows at bottom of page.
% \clubpenalty=9999              % Almost no orphans at top of page.
% \interfootnotelinepenalty=9999 % Almost never break footnotes.
% \binoppenalty=9999             % Almost never break binary operators.
% \relpenalty=9999               % Almost never break binary relations.
\iftoggle{nobreaks}{}{%
  \let\defaultldots\ldots
  \renewcommand{\ldots}{\allowbreak\defaultldots\allowbreak}
}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nottoggle{beamer}{%
% Page Layout: Headers and footers {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Set pagestyle to be fancy as default in whole of document
\pagestyle{fancy}
% Clear old settings for headers and footers
\fancyhf{}
% Set headers and footers in document with
% \lhead{} \chead{} \rhead{}
% \lfoot{} \cfoot{} \rfoot{}
% Set line width for header and footer
\AtBeginDocument{\renewcommand{\headrulewidth}{0.5pt}}
\AtBeginDocument{\renewcommand{\footrulewidth}{0.5pt}}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
}{}
% Page Layout: Titles {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nottoggle{beamer}{%
  \RequirePackage{titlesec}
  \iftoggle{centerstacktitles}{%
    \titleformat{\section}[display]{\Large\filcenter}{\thesection}{0.5ex}{\bfseries}
  }{}
}{}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Page Layout: Whitespace around align (display) environments {{{{{
\AtBeginDocument{\addtolength{\abovedisplayskip}{-1.25ex}}
\AtBeginDocument{\addtolength{\belowdisplayskip}{-1ex}}
\AtBeginDocument{\addtolength{\abovedisplayshortskip}{-1.25ex}}
\AtBeginDocument{\addtolength{\belowdisplayshortskip}{-1ex}}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Page Layout: Whitespace around center environments {{{{{
\let\defaultcenter\center
\let\defaultendcenter\endcenter
\renewenvironment{center}{\setlength\topsep{0.2em}\defaultcenter}{\defaultendcenter}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Generic tools {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% When referencing lists, often we need two write things such as
% "\textit{(iii)}" which is long. This macro "enumerated reference" makes it
% easier.
% Usage: \eref{<n>}
% Example: \eref{3}
\newcommand{\eref}[1]{(\romannumeral#1)}

% Using this macro allows us to change our mind on the style of definitions
% after the fact. For example, one could easily switch from italic to bold text.
% Usage: \define[[index]]{<text>}
% Example: A map is \define{continuous} if ...
% Example: A polynomial is \define[homogeneous polynomial]{homogeneous} if ...
\iftoggle{uldefobjs}{%
  \NewDocumentCommand\define{o m}{%
    \IfNoValueTF{#1}{\underline{#2}\index{#2}}{\underline{#2}\index{#1}}}
}{%
  \iftoggle{scdefobjs}{%
    \NewDocumentCommand\define{o m}{%
      \IfNoValueTF{#1}{{\normalfont \textsc{#2}}\index{#2}}{\textsc{#2}\index{#1}}}
  }{%
    \iftoggle{milne}{%
      \NewDocumentCommand\define{o m}{%
        \IfNoValueTF{#1}{\textbf{\emph{#2}}\index{#2}}{\textbf{\emph{#2}}\index{#1}}}
    }{%
      \NewDocumentCommand\define{o m}{%
        \IfNoValueTF{#1}{\emph{#2}\index{#2}}{\emph{#2}\index{#1}}}
    }
  }
}

% Middle Text Ascii Tilde. The default is too high, an appears above the
% character.
\iftoggle{concroman}{%
  \newcommand{\mtextasciitilde}{\raisebox{-0.75ex}{\textasciitilde}}
}{%
  \newcommand{\mtextasciitilde}{\textasciitilde}
}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nottoggle{beamer}{%
% Maths Environments {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 1. \newtheorem{<Internal name>}{<External name>}[<env>]
%    Is counted after <env>. e.g.
%    \newtheorem{corollary}{Corollary}[theorem]
%    Theorem 1 is succeeded by Corollary 1.2
% 2. \newtheorem{<Internal name>}[<env>]{<External name>}[<env>]
%    \newtheorem{corollary}[theorem]{Corollary}
%    Is shares counter with <env>. i.e. Theorem 1 is succeeded by Corollary 2

% Declare a new theoremstyle
% \newtheoremstyle{mystyle}%
%    {3pt}                   % Space above
%    {3pt}                   % Space below
%    {\itshape\color{red}}   % Body font
%    {}                      % Indent amount
%    {\bfseries\color{blue}} % Theorem head font
%    {.}                     % Punctuation after theorem head
%    {.5em}                  % Space after theorem head
%    {}                      % Theorem head spec (can be left empty, meaning 'normal')
%
% Numbering of environments example
% If we define
%
%   \newtheorem*{proposition*}{Proposition}
%   \newtheorem{proposition-extra}{Proposition*}
%
% then calling
%
%   \begin{proposition*}
%     ...
%   \end{proposition*}
%
% Will create a non-numbered proposition (e.g. for a famous named theorem that
% will never be referenced to by a number: When 'The Heine-Borel' theorem will
% always be said, and not 'Theorem 3.14').
%
% and calling
%
%   \begin{proposition-extra}
%      ...
%   \end{proposition-extra}
%
% will create a numbered proposition that is printed with a star (e.g. for
% extracurricular material).

% \underline is actually \ul from the soul package
% soul does not allow expanding text as an argument, unless it is wrapped in an
% \mbox call
\newtheoremstyle{ultheorem}%
   {3pt}        % Space above
   {3pt}        % Space below
   {\itshape}   % Body font
   {}           % Indent amount
   {}           % Theorem head font
   {.}          % Punctuation after theorem head
   {.5em}       % Space after theorem head
   {\underline{\mbox{\thmname{#1}\thmnumber{ #2}}}\thmnote{ (#3)}} % Theorem head spec (can be left empty, meaning 'normal')

\newtheoremstyle{sctheorem}%
   {3pt}        % Space above
   {3pt}        % Space below
   {\itshape}   % Body font
   {}           % Indent amount
   {\scshape}   % Theorem head font
   {.}          % Punctuation after theorem head
   {.5em}       % Space after theorem head
   {} % Theorem head spec (can be left empty, meaning 'normal')

% \underline is actually \ul from the soul package
% soul does not allow expanding text as an argument, unless it is wrapped in an
% \mbox call
\newtheoremstyle{uldefinition}%
   {3pt}        % Space above
   {3pt}        % Space below
   {}           % Body font
   {}           % Indent amount
   {}           % Theorem head font
   {.}          % Punctuation after theorem head
   {.5em}       % Space after theorem head
   {\underline{\mbox{\thmname{#1}\thmnumber{ #2}}}\thmnote{ (#3)}} % Theorem head spec (can be left empty, meaning 'normal')

\newtheoremstyle{scdefinition}%
   {3pt}        % Space above
   {3pt}        % Space below
   {}           % Body font
   {}           % Indent amount
   {\scshape}   % Theorem head font
   {.}          % Punctuation after theorem head
   {.5em}       % Space after theorem head
   {} % Theorem head spec (can be left empty, meaning 'normal')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Theorems
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\iftoggle{ulthms}{%
  \theoremstyle{ultheorem}
}{%
  \iftoggle{scthms}{%
    \theoremstyle{sctheorem}
  }{%
    \theoremstyle{plain}
  }
}

% Base number off chapter if documentclass 'book' is selected, else use
% sections.
% This is crudely done by checking if the command '\chapter' exists.

% For some reason, if one tries to do this via
% \ifdef{\chapter} ...
% the compilation fails

\ifundef{\chapter}{%
  \newtheorem{theorem}{Theorem}[section]
  \numberwithin{equation}{section}
  \numberwithin{figure}{section}
}{%
  \newtheorem{theorem}{Theorem}[chapter]
  \numberwithin{equation}{chapter}
  \numberwithin{figure}{chapter}
}

\newtheorem*{theorem*}{Theorem}
\newtheorem{theorem-extra}{Theorem*}

% Number propositions after theorems
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{counterexample}[theorem]{Counterexample}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{generic-corollary}[theorem]{Corollary}
\newtheorem{important-exercise}[theorem]{Important Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{construction}[theorem]{Construction}
\newtheorem{propose}[theorem]{Propose}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{reminder}[theorem]{Reminder}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{important-remark}[theorem]{Remark}

% Numbered, but starred
\newtheorem{propose-extra}[theorem]{Propose*}
\newtheorem{proposition-extra}[theorem]{Proposition*}
\newtheorem{lemma-extra}[theorem]{Lemma*}

% Non-numbered
\newtheorem*{corollary*}{Corollary}
\newtheorem*{counterexample*}{Counterexample}
\newtheorem*{example*}{Example}
\newtheorem*{exercise*}{Exercise}
\newtheorem*{fact}{Fact}
\newtheorem*{fact*}{Fact}
\newtheorem*{lemma*}{Lemma}
\newtheorem*{propose*}{Propose}
\newtheorem*{proposition*}{Proposition}
\newtheorem*{construction*}{Construction}
\newtheorem*{important-remark*}{Remark}

% Always return to plain
\theoremstyle{plain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Remarks
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{remark}

% Numbered remark (for referencing)
\newtheorem{nremark}[theorem]{Remark}
\newtheorem*{remark}{Remark}
\newtheorem*{Metaremark}{Thesis remark}

% Always return to plain
\theoremstyle{plain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\iftoggle{uldefs}{%
  \theoremstyle{uldefinition}
}{%
  \iftoggle{scdefs}{%
    \theoremstyle{scdefinition}
  }{%
    \theoremstyle{definition}
  }
}

% Numbered after theorem
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{defining}[theorem]{Defining}
\newtheorem{definition-define}[theorem]{Define}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{definition-extra}[theorem]{Definition*}
\newtheorem{notation}[theorem]{Notation}

% Non-numbered
\newtheorem*{definition*}{Definition}
\newtheorem*{definition-extra*}{Definition*}

% Always return to plain
\theoremstyle{plain}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Lecture counter {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Create a lecture counter that can be invoked to create a note in the margin
% listing the lecture number and the date.
% Usage: \lecture{<Date>}
% Example: \lecture{1970.01.01}
\newcounter{lecture}
\newcommand{\lecture}[1]{%
  \stepcounter{lecture}
  \marginpar{\color{orange}\flushleft{\footnotesize Lecture: \thelecture{} #1}}
}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
}{}
% Printable links {{{{{
\newcommand{\phref}[2]{\iftoggle{printlinks}{\href{#1}{#2}\footnote{#1}}{\href{#1}{#2}}}
% }}}}}

% Mathematical notation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nottoggle{noletters}{
% Special Letters {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% For faster typesetting of the blackboard letters
\newcommand{\bA}{\mathbb{A}}
\newcommand{\bB}{\mathbb{B}}
\newcommand{\bC}{\mathbb{C}}
\newcommand{\bD}{\mathbb{D}}
\newcommand{\bE}{\mathbb{E}}
\newcommand{\bF}{\mathbb{F}}
\newcommand{\bG}{\mathbb{G}}
\newcommand{\bH}{\mathbb{H}}
\newcommand{\bI}{\mathbb{I}}
\newcommand{\bJ}{\mathbb{J}}
\newcommand{\bK}{\mathbb{K}}
\newcommand{\bL}{\mathbb{L}}
\newcommand{\bM}{\mathbb{M}}
\newcommand{\bN}{\mathbb{N}}
\newcommand{\bO}{\mathbb{O}}
\newcommand{\bP}{\mathbb{P}}
\newcommand{\bQ}{\mathbb{Q}}
\newcommand{\bR}{\mathbb{R}}
\newcommand{\bS}{\mathbb{S}}
\newcommand{\bT}{\mathbb{T}}
\newcommand{\bU}{\mathbb{U}}
\newcommand{\bV}{\mathbb{V}}
\newcommand{\bW}{\mathbb{W}}
\newcommand{\bX}{\mathbb{X}}
\newcommand{\bY}{\mathbb{Y}}
\newcommand{\bZ}{\mathbb{Z}}

% For faster typesetting of the calligraphic letters
\newcommand{\cA}{\mathcal{A}}
\newcommand{\cB}{\mathcal{B}}
\newcommand{\cC}{\mathcal{C}}
\newcommand{\cD}{\mathcal{D}}
\newcommand{\cE}{\mathcal{E}}
\newcommand{\cF}{\mathcal{F}}
\newcommand{\cG}{\mathcal{G}}
\newcommand{\cH}{\mathcal{H}}
\newcommand{\cI}{\mathcal{I}}
\newcommand{\cJ}{\mathcal{J}}
\newcommand{\cK}{\mathcal{K}}
\newcommand{\cL}{\mathcal{L}}
\newcommand{\cM}{\mathcal{M}}
\newcommand{\cN}{\mathcal{N}}
\newcommand{\cO}{\mathcal{O}}
\newcommand{\cP}{\mathcal{P}}
\newcommand{\cQ}{\mathcal{Q}}
\newcommand{\cR}{\mathcal{R}}
\newcommand{\cS}{\mathcal{S}}
\newcommand{\cT}{\mathcal{T}}
\newcommand{\cU}{\mathcal{U}}
\newcommand{\cV}{\mathcal{V}}
\newcommand{\cW}{\mathcal{W}}
\newcommand{\cX}{\mathcal{X}}
\newcommand{\cY}{\mathcal{Y}}
\newcommand{\cZ}{\mathcal{Z}}

% For faster typesetting of the fraction letters
\newcommand{\fa}{\mathfrak{a}}
\newcommand{\fb}{\mathfrak{b}}
\newcommand{\fc}{\mathfrak{c}}
\newcommand{\fd}{\mathfrak{d}}
\newcommand{\fe}{\mathfrak{e}}
\newcommand{\ff}{\mathfrak{f}}
\newcommand{\fg}{\mathfrak{g}}
\newcommand{\fh}{\mathfrak{h}}
% \newcommand{\fi}{\mathfrak{i}}
\newcommand{\fj}{\mathfrak{j}}
\newcommand{\fk}{\mathfrak{k}}
\newcommand{\fl}{\mathfrak{l}}
\newcommand{\fm}{\mathfrak{m}}
\newcommand{\fn}{\mathfrak{n}}
\newcommand{\fo}{\mathfrak{o}}
\newcommand{\fp}{\mathfrak{p}}
\newcommand{\fq}{\mathfrak{q}}
\newcommand{\fr}{\mathfrak{r}}
\newcommand{\fs}{\mathfrak{s}}
\newcommand{\ft}{\mathfrak{t}}
\newcommand{\fu}{\mathfrak{u}}
\newcommand{\fv}{\mathfrak{v}}
\newcommand{\fw}{\mathfrak{w}}
\newcommand{\fx}{\mathfrak{x}}
\newcommand{\fy}{\mathfrak{y}}
\newcommand{\fz}{\mathfrak{z}}

\newcommand{\fA}{\mathfrak{A}}
\newcommand{\fB}{\mathfrak{B}}
\newcommand{\fC}{\mathfrak{C}}
\newcommand{\fD}{\mathfrak{D}}
\newcommand{\fE}{\mathfrak{E}}
\newcommand{\fF}{\mathfrak{F}}
\newcommand{\fG}{\mathfrak{G}}
\newcommand{\fH}{\mathfrak{H}}
\newcommand{\fI}{\mathfrak{I}}
\newcommand{\fJ}{\mathfrak{J}}
\newcommand{\fK}{\mathfrak{K}}
\newcommand{\fL}{\mathfrak{L}}
\newcommand{\fM}{\mathfrak{M}}
\newcommand{\fN}{\mathfrak{N}}
\newcommand{\fO}{\mathfrak{O}}
\newcommand{\fP}{\mathfrak{P}}
\newcommand{\fQ}{\mathfrak{Q}}
\newcommand{\fR}{\mathfrak{R}}
\newcommand{\fS}{\mathfrak{S}}
\newcommand{\fT}{\mathfrak{T}}
\newcommand{\fU}{\mathfrak{U}}
\newcommand{\fV}{\mathfrak{V}}
\newcommand{\fW}{\mathfrak{W}}
\newcommand{\fX}{\mathfrak{X}}
\newcommand{\fY}{\mathfrak{Y}}
\newcommand{\fZ}{\mathfrak{Z}}

% For faster typesetting of the monospace letters
\newcommand{\mA}{\texttt{A}}
\newcommand{\mB}{\texttt{B}}
\newcommand{\mC}{\texttt{C}}
\newcommand{\mD}{\texttt{D}}
\newcommand{\mE}{\texttt{E}}
\newcommand{\mF}{\texttt{F}}
\newcommand{\mG}{\texttt{G}}
\newcommand{\mH}{\texttt{H}}
\newcommand{\mI}{\texttt{I}}
\newcommand{\mJ}{\texttt{J}}
\newcommand{\mK}{\texttt{K}}
\newcommand{\mL}{\texttt{L}}
\newcommand{\mM}{\texttt{M}}
\newcommand{\mN}{\texttt{N}}
\newcommand{\mO}{\texttt{O}}
\newcommand{\mP}{\texttt{P}}
\newcommand{\mQ}{\texttt{Q}}
\newcommand{\mR}{\texttt{R}}
\newcommand{\mS}{\texttt{S}}
\newcommand{\mT}{\texttt{T}}
\newcommand{\mU}{\texttt{U}}
\newcommand{\mV}{\texttt{V}}
\newcommand{\mW}{\texttt{W}}
\newcommand{\mX}{\texttt{X}}
\newcommand{\mY}{\texttt{Y}}
\newcommand{\mZ}{\texttt{Z}}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
}{}
\nottoggle{nomath}{
% Sets {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\one}{\mathds{1}} % Set-Characteristic function

\AtBeginDocument{\renewcommand{\subset}{\subseteq}} % Override the default subset command
\AtBeginDocument{\renewcommand{\supset}{\supseteq}} % Override the default supset command

\providecommand{\complement}{}
\AtBeginDocument{\renewcommand{\complement}[1]{{#1}^{c}}} % Set complement

\providecommand{\closure}{}
\AtBeginDocument{\renewcommand{\closure}[1]{\overline{#1}}} % Topological closure

\newcommand{\interior}[1]{\mathring{#1}}                       % Topological interior
\newcommand{\card}[1]{\left\vert#1\right\vert}                 % Cardinality
\newcommand{\until}{,\allowbreak \ldots,\allowbreak}           % Listing a, ..., b

\newcommand{\set}[1]{\left\lbrace#1\right\rbrace}              % Set
\newcommand{\cset}[2]{\left\lbrace#1\,\mid\,#2\right\rbrace}   % Set with conditions (vertical line)
\newcommand{\csetc}[2]{\left\lbrace#1\,:\,#2\right\rbrace}   % Set with conditions (vertical line)
\newcommand{\bigset}[1]{\bigl\lbrace#1\bigr\rbrace}            % Big Set
\newcommand{\bigcset}[2]{\bigl\lbrace#1\,\mid\,#2\bigr\rbrace} % Big Set with conditions (vertical line)
\newcommand{\bigcsetc}[2]{\bigl\lbrace#1\,:\,#2\bigr\rbrace} % Big Set with conditions (vertical line)
\newcommand{\tup}[1]{\left(#1\right)}                          % Tuple

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Topology {{{{{
\newcommand{\homot}[1][]{\overset{#1}{\simeq}}
% }}}}}
% Probability {{{{{
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\Cov}{Cov}
\DeclareMathOperator{\Leb}{Leb}
\DeclareMathOperator{\Vol}{Vol}
% }}}}}
% Trigonometric functions {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\DeclareMathOperator{\arsinh}{arsinh}
\DeclareMathOperator{\arcosh}{arcosh}
\DeclareMathOperator{\artanh}{artanh}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Analysis {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Derivatives
\DeclareMathOperator{\De}{\thinspace{\mathrm{D}}}    % Derivative
\DeclareMathOperator{\boldpartial}{\pmb{\partial}}   % (Bold) partial derivative
% \DeclareMathOperator{\de}{\thinspace{\mathrm{d}}}    % Derivative
\DeclareMathOperator{\de}{\mathrm{d}}                % Derivative
\DeclareMathOperator{\dvol}{\,\operatorname{dvol}}   % Volumetric integration
\newcommand{\euler}{\operatorname{e}}       % Euler's constant
\DeclareMathOperator{\graph}{\operatorname{graph}}   % Graph
\DeclareMathOperator{\im}{im}                        % Image / Imaginary Part
\newcommand{\laplace}{\Delta}                        % Laplace operator
\DeclareMathOperator{\metric}{\operatorname{d}}      % Metric
\DeclareMathOperator{\re}{Re}                        % Real part
\DeclareMathOperator{\rot}{rot}                      % Rotation/ curl
\DeclareMathOperator{\vol}{vol}                      % Volumetric integration
\DeclareMathOperator{\ind}{ind}                      % Winding number

% Don't make this an operator. It will mess up the spacing
\newcommand{\ii}{\iota}                              % Imaginary unit
\newcommand{\ceiling}[1]{\left\lceil#1\right\rceil}  % Ceiling function
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}  % Floor function
\newcommand{\restr}[2]{\ensuremath{#1|_{#2}}}        % Restriction
\newcommand{\bigrestr}[2]{\ensuremath{#1\big|_{#2}}} % Restriction
\newcommand{\at}[1]{\ensuremath{\big|_{#1}}}         % At
\newcommand{\support}[1][]{\operatorname{supp}_{#1}} % [Named] Support
\newcommand{\vc}[1]{\mathbf{#1}}                     % Vector
\newcommand{\weak}{\textsuperscript*}                % Weak decoration

\let\physicsdivergence\divergence                    % Override the \divergence command from the physics package
\renewcommand{\divergence}{\mathrm{div}}             % Divergence

\DeclareMathOperator{\Per}{Per}                      % Set of periods of a function
\newcommand{\conjugate}[1]{\overline{#1}} % Complex conjuage

\DeclareMathOperator{\sign}{\operatorname{sign}}     % sign function

\DeclareMathOperator{\res}{res}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Algebra {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\DeclareMathOperator{\Adj}{Adj}                      % Adjunct matrix
\DeclareMathOperator{\Aut}{Aut}                      % Automorphism
\DeclareMathOperator{\End}{End}                      % Endomorphism
\DeclareMathOperator{\Char}{char}                    % (Field) Characteristic
\DeclareMathOperator{\Frac}{Frac}                    % Fraction field
\DeclareMathOperator{\Der}{Der}                      % Derivation
\DeclareMathOperator{\Gal}{Gal}                      % Galois group
\DeclareMathOperator{\Hom}{Hom}                      % Homomorphisms
\DeclareMathOperator{\Mat}{Mat}                      % Matrices
\DeclareMathOperator{\Obj}{Obj}                      % Object
\DeclareMathOperator{\Orb}{Orb}                      % Orbit
\DeclareMathOperator{\Stab}{Stab}                    % Stabiliser
\DeclareMathOperator{\Rank}{Rank}                    % Rank
\DeclareMathOperator{\Null}{Null}                    % Null
\DeclareMathOperator{\Nullity}{Nullity}              % Null
\DeclareMathOperator{\Sym}{Sym}                      % Symmetric
\DeclareMathOperator{\coker}{coker}                  % Cokernel
\DeclareMathOperator{\compose}{\circ}                % Composition
\DeclareMathOperator{\Span}{Span}                    % Span/Linear hull
\DeclareMathOperator{\id}{id}                        % Identity
\DeclareMathOperator{\jac}{Jac}                      % Jacobson Radical
\DeclareMathOperator{\krulldim}{\dim_\mathrm{Krull}} % Krull dimension
\DeclareMathOperator{\codim}{codim}                  % Codimension
\DeclareMathOperator{\lcm}{lcm}                      % Lowest common denominator
\DeclareMathOperator{\nil}{nil}                      % Nilradical
\DeclareMathOperator{\ord}{ord}                      % Order
\DeclareMathOperator{\rad}{rad}                      % Jacobson Radical
\DeclareMathOperator{\sgn}{sgn}                      % Sign
\DeclareMathOperator{\tor}{tor}                      % Torsion
\DeclareMathOperator{\Tor}{Tor}                      % Torsion (capitalised)
\DeclareMathOperator{\Eig}{Eig}                      % Eigenspace
\DeclareMathOperator{\Class}{Cl}                     % Class group
\DeclareMathOperator{\Cl}{Cl}                        % Class group
\DeclareMathOperator{\Ell}{Ell}                      % Elliptic curves
\DeclareMathOperator{\Spm}{Spm}                      % Spm functor (milne)
\newcommand{\subgroup}{\leqslant}                    % Subgroup

\let\physicsev\ev                                    % Override \ev from the physics package
\renewcommand{\ev}{\mathrm{ev}}                      % Evaluation
\let\physicseval\eval                                % Override \eval from the physics package
\renewcommand{\eval}{\mathrm{eval}}                  % Evaluation

\newcommand{\Ass}[1][]{\operatorname{Ass}_{#1}}                          % Associated prime
\newcommand{\Bil}[1][]{\operatorname{Bil}_{#1}}                          % Bilinear maps
\newcommand{\Tens}[1][]{\mathbin{\bigotimes_{\scriptscriptstyle{#1}}}}   % Tensor Product
\newcommand{\Ann}[1][]{\operatorname{Ann}_{#1}}                          % Annihilator
\newcommand{\cl}[1]{\overline{#1}}                                       % Class of representatives
\newcommand{\height}[1][]{\operatorname{ht}_{#1}}                        % Prime ideal height
\newcommand{\nHom}[4]{\Hom_{(#1-\mathrm{#2})} \left(#3,\, #4 \right)}    % Named homomorphisms
\newcommand{\scalarprod}[2]{\ensuremath{\left\langle#1,#2\right\rangle}} % Scalar product
\newcommand{\hull}[1]{\ensuremath{\left\langle\,#1\,\right\rangle}}      % Span
\newcommand{\tens}[1][]{\otimes_{\scriptscriptstyle{#1}}}                % Tensor product
\newcommand{\trdeg}[1][]{\operatorname{trdeg}_{#1}}                      % Transcendence degree
\newcommand{\field}[1]{#1}                                               % Field

% Styled arrows
\renewcommand{\to}[1][]{\xrightarrow{#1}}                                 % Overloaded \to for named arrow
\newcommand{\into}[1][]{\xhookrightarrow{#1}}                             % Injection/ into map
\newcommand{\onto}[1][]{\xrightarrow{#1}\mathrel{\mkern-14mu}\rightarrow} % Surjection/ onto map
\newcommand{\isoto}{\xrightarrow{\sim}}                                   % Isomorpism map

% Fractions
% Dynamically decide whether to place elements in fraction above each other or
% next to each other based on whether in display mode or not.
\let\defaultfrac\frac
\renewcommand{\frac}[2]{\mathchoice{\defaultfrac{#1}{#2}}{#1/#2}{#1/#2}{#1/#2}}
\newcommand{\ifrac}[2]{#1/#2}

% Quotients
% Tool for moving maths expressions
\makeatletter
\newcommand{\raisemath}[1]{\mathpalette{\raisemAth{#1}}}
\newcommand{\raisemAth}[3]{\raisebox{#1}{$#2#3$}}
\makeatother
% Dynamically decide how much space should be left between operands and how much
% they should be raised, based on whether in display mode or not.
% \newcommand{\quot}[2]{%
%   \mathchoice
%     {\raisemath{0.4ex}{#1} \big/ \raisemath{-0.4ex}{#2}}%
%     {\scalebox{0.9}{$\raisemath{0.1ex}{#1}/\raisemath{-0.3ex}{#2}$}}%
%     {#1/#2}%
%     {#1/#2}%
% }
\newcommand{\quot}[2]{%
  \mathchoice
    {\raisemath{0.4ex}{#1} \big/ \raisemath{-0.4ex}{#2}}%
    {\raisemath{0.1ex}{#1}/\raisemath{-0.3ex}{#2}}%
    {#1/#2}%
    {#1/#2}%
}
\newcommand{\q}[2]{\quot{#1}{#2}} % Quotients

\newcommand{\quotl}[2]{%
  \mathchoice
    {\raisemath{-0.4ex}{#2} \big\backslash \raisemath{0.4ex}{#1}}%
    {\raisemath{-0.1ex}{#2}\backslash\raisemath{0.3ex}{#1}}%
    {#2\backslash#1}%
    {#2\backslash#1}%
}
\newcommand{\ql}[2]{\quotl{#1}{#2}} % Quotients

\newcommand{\divides}{\mid}
\newcommand{\ndivides}{\not\mid}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Number Theory {{{{{
\DeclareMathOperator{\li}{li}
\DeclareMathOperator{\Div}{Div}
\DeclareMathOperator{\Cusps}{Cusps}
% Bit of a hack using negative space
\newcommand{\jacobi}[2]{%
  \mathchoice
  {\left(\mkern-8mu\left(\defaultfrac{#1}{#2}\right)\mkern-8mu\right)}%
  {\left(\mkern-0mu\left(#1/#2\right)\mkern-0mu\right)}%
  {\left(\mkern-3mu\left(#1/#2\right)\mkern-3mu\right)}%
  {\left(\mkern-3mu\left(#1/#2\right)\mkern-3mu\right)}%
}
\newcommand{\slashby}[2]{|_{#1}#2}
\DeclareMathOperator{\Reg}{Reg} % Field regulator
\DeclareMathOperator{\disc}{disc} % Field discriminant
% }}}}}
% Rings, Fields and Groups {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\Poly}{Poly}
\newcommand{\A}{\mathbb{A}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\D}{\mathbb{D}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\F}{\mathbb{F}}
\let\defaultH\H
\renewcommand{\H}{\mathbb{H}}
\newcommand{\K}{\mathbb{K}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\NZ}{\mathbb{N}_0}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Zn}{\quot{\mathbb{Z}}{n\mathbb{Z}}}
\newcommand{\Zp}{\quot{\mathbb{Z}}{p\mathbb{Z}}}

\DeclareMathOperator{\Rk}{\mathbb{R}^k}
\DeclareMathOperator{\Rm}{\mathbb{R}^m}
% \DeclareMathOperator{\Rn}{\mathbb{R}^n}

\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\PSL}{PSL}
\DeclareMathOperator{\SO}{SO}

\let\defaultP\P % Override the default \P command
\renewcommand{\P}{\mathbb{P}}

\newcommand{\algclosure}[1]{{#1}^{\textrm{al}}}
% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Computing {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Problems
\DeclareMathOperator{\SAT}{SAT}
\DeclareMathOperator{\CLIQUE}{CLIQUE}

% Time-complexity
\DeclareMathOperator{\Time}{Time}
\DeclareMathOperator{\TIME}{TIME}

% Memory-complexity
\DeclareMathOperator{\Space}{Space}
\DeclareMathOperator{\SPACE}{SPACE}

% Complexity classes
\DeclareMathOperator{\PTIME}{P}
\DeclareMathOperator{\NPTIME}{NP}
\DeclareMathOperator{\DLOG}{DLOG}
\DeclareMathOperator{\PSPACE}{PSPACE}
\DeclareMathOperator{\EXPTIME}{EXPTIME}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% General Typesetting {{{{{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\til}[1]{\widetilde{#1}}
\newcommand{\defeq}{\overset{\scriptscriptstyle\mathrm{def.}}{=}}
\newcommand{\qefed}{\overset{\reflectbox{$\scriptscriptstyle\mathrm{def.}$}}{=}}
\newcommand{\exeq}{\overset{\scriptscriptstyle\mathrm{!}}{=}}
\newcommand{\absleq}{\overset{\abs{\cdot}}{\leq}}
\newcommand{\normleq}{\overset{\norm{\cdot}}{\leq}}

% }}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Algebraic Geometry {{{{{
% Birational maps
\newcommand{\birational}{\mathbin{\tikz [baseline=-0.25ex,-latex, ->, densely dashed] \draw [->, densely dashed] (0pt,0.5ex) -- (1.3em,0.5ex); }}
% Category of irreducible $k$-varieties and rational maps between them
\DeclareMathOperator{\Rat}{Rat}
\DeclareMathOperator{\Bir}{Bir}
\DeclareMathOperator{\Bl}{Bl} % Blow up
\DeclareMathOperator{\Spec}{Spec} % Blow up
\DeclareMathOperator{\Sing}{Sing} % Singular locus
\DeclareMathOperator{\Pic}{Pic} % Picard group
\let\defaultsp\sp
\renewcommand{\sp}{\mathrm{sp}} % Underlying topological space of a scheme
\newcommand{\opp}{\mathrm{opp}}
% }}}}}
% Algebraic Topology {{{{{
\newcommand{\bound}{\partial}
\newcommand{\face}[2]{\ensuremath{#1}|_{#2}}    % Restriction
\DeclareMathOperator{\diam}{diam}
% }}}}}
}{}

% Debug {{{{{
\iftoggle{debug}{%
  \AtBeginDocument{%
    {% Must be inside {} to ensure settings are local

    \pagestyle{empty}

    \begin{mdframed}

      \setlength{\parindent}{0cm}

      \section*{prreamble Debugging Information}

      Configured options

      \begin{center}
        \setlength{\tabcolsep}{2em}
        \begin{tabular}{l | l}
          nobreaks     & \iftoggle{nobreaks}{\green{True}}{\red{False}}     \\
          print        & \iftoggle{print}{\green{True}}{\red{False}}        \\
          scdefs       & \iftoggle{scdefs}{\green{True}}{\red{False}}       \\
          scthms       & \iftoggle{scthms}{\green{True}}{\red{False}}       \\
          uldefobjs    & \iftoggle{uldefobjs}{\green{True}}{\red{False}}    \\

          concmath         & \iftoggle{concmath}{\green{True}}{\red{False}}     \\
          ~~~~concroman    & \iftoggle{concroman}{\green{True}}{\red{False}}    \\
          ~~~~centertitles & \iftoggle{centertitles}{\green{True}}{\red{False}} \\
          ~~~~scdefobjs    & \iftoggle{scdefobjs}{\green{True}}{\red{False}}    \\
          ~~~~scemph       & \iftoggle{scemph}{\green{True}}{\red{False}}       \\
          ~~~~uldefs       & \iftoggle{uldefs}{\green{True}}{\red{False}}       \\
          ~~~~ulthms       & \iftoggle{ulthms}{\green{True}}{\red{False}}       \\
        \end{tabular}
      \end{center}

      \vspace{3ex} \hrule \vspace{3ex}

      \begin{theorem*}
        This is an (unnumbered) example theorem.
      \end{theorem*}

      \begin{definition*}[Example]
        This is an (unnumbered) example definition, defining \define{something}.
      \end{definition*}

      \begin{remark}
        This is an example remark.
      \end{remark}

      \vspace{3ex} \hrule \vspace{3ex}

      \texttt{{\textbackslash}textbf\{This is bold face text\}}

      \textbf{This is bold face text}.

      \vspace{1ex}

      \texttt{{\textbackslash}textit\{This is italic text\}}

      \textit{This is italic text}.

      \vspace{1ex}

      \texttt{{\textbackslash}emph\{This is emphasised text\}}

      \emph{This is emphasised text}.

      \vspace{1ex}

      \texttt{{\textbackslash}texit\{This is {\textbackslash}emph\{emphasised\}
      text inside italic text\}}

      \textit{This is \emph{emphasised} text inside italic text}.

      \vspace{1ex}

      \texttt{{\textbackslash}textbf\{This is {\textbackslash}emph\{emphasised\} text inside bold text\}.}

      \textbf{This is \emph{emphasised} text inside bold text}.

      \vspace{3ex} \hrule \vspace{3ex}

      This is an example link colour \href{https://tug.org}{https://tug.org}.

      \vspace{3ex} \hrule \vspace{3ex}

      \iftoggle{geometryloadedbefore}{%
        \green{Geometry was loaded before prreamble}
      }{%
        \ifdef{\newgeometry}{%
          \red{Geometry was loaded after prreamble}
        }{%
          \green{Geometry was not loaded}
        }
      }
    \end{mdframed}
    }
    \setcounter{page}{0}
  }
}{}
% }}}}}

\newcommand{\email}[1]{\href{mailto:#1}{#1}}
\newcommand{\emailtt}[1]{\href{mailto:#1}{\texttt{#1}}}

\newcommand{\sectionnn}[1]{
\section*{#1}
\phantomsection
\addcontentsline{toc}{section}{\protect\numberline{}#1}
}

\endinput