course_notes/notes.sty at master · kkjcheng/course_notes · GitHub

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\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{enumerate}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{verbatim}
\usepackage{tikz}
\usepackage{geometry}
\usepackage{hyperref}
\usepackage{nameref}
\usepackage{tocloft}
\usepackage{mathtools}
\usepackage{indentfirst}
\usepackage{etoolbox}
\usepackage[super]{nth}
\usepackage[object=vectorian]{pgfornament}
\usepackage{enumitem}
\usepackage{bookmark}
\usepackage{thmtools}
\usepackage[noabbrev,capitalize,nameinlink]{cleveref}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\geometry{letterpaper, portrait, margin=1in}
\everymath{\displaystyle}

%% Helper macros for tikz image

\newcommand\pgfmathsinandcos[3]{%
  \pgfmathsetmacro#1{sin(#3)}%
  \pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
  \tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % latitude
  \pgfmathsetmacro\yshift{\cosEl*\sint}
  \tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][1]{
  \LongitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1}}
   % angle of "visibility"
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
  \draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][1]{
  \LatitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1}}
  \pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
  % angle of "visibility"
  \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
  \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
  \draw[current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}
\newcommand{\globe}{\begin{figure}[!h]
\centering
\begin{tikzpicture} % Title page sphere
\def\R{1} % sphere radius
\def\angEl{35} % elevation angle
\filldraw[ball color=white] (0,0) circle (\R);
\foreach \t in {-80,-60,...,80} {\DrawLatitudeCircle[\R]{\t}}
\foreach \t in {-5,-35,...,-175} {\DrawLongitudeCircle[\R]{\t}}
\end{tikzpicture}
\end{figure}}

\newcommand{\sectionline}
{\noindent
  \begin{center}
  {\resizebox{0.5\linewidth}{1ex}
  {{{\begin{tikzpicture}
  \node (C) at (0,0){};
  \node (D) at (9,0){};
  \path (C) to [ornament=85] (D);
  \end{tikzpicture}}}}}
  \end{center}
}

\newcommand{\splitatcommas}[1]{%
  \begingroup
  \ifnum\mathcode`,="8000
  \else
    \begingroup\lccode`~=`, \lowercase{\endgroup
      \edef~{\mathchar\the\mathcode`, \penalty0 \noexpand\hspace{0pt plus 1em}}%
    }\mathcode`,="8000
  \fi
  #1%
  \endgroup
}

\makeatletter
\patchcmd{\upbracefill}{\m@th}{\scriptstyle\m@th}{}{}
\patchcmd{\upbracefill}{$\braceld$}{$\scriptstyle\braceld$}{}{}
\patchcmd{\upbracefill}{\bracelu}{\bracelu\mkern-1mu}{}{}
\patchcmd{\upbracefill}{\hfill\braceru}{\hfill\mkern-1mu\braceru}{}{}
\makeatother

\declaretheoremstyle[
spaceabove=6pt, spacebelow=6pt,
headfont=\normalfont\bfseries,
notefont=\mdseries, notebraces={(}{)},
bodyfont=\normalfont\itshape]{exstyle}

\newtheorem{theorem}{Theorem}
\newtheorem{prop}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem*{theorem*}{Theorem}
\newtheorem*{lemma*}{Lemma}
\newtheorem*{claim}{Claim}

\theoremstyle{definition}
\newtheorem{definition}{Definition}[subsection]
\newtheorem{example}[definition]{Example}
\declaretheorem[name=Exercise,
style=exstyle]{exercise}

\theoremstyle{remark}
\newtheorem*{remark}{Remark}

\foreach \theoremenv in
{theorem,theorem*,lemma,claim,prop,corollary,proof,exercise} {
    \AtBeginEnvironment{\theoremenv}{%
        \setlist[enumerate]{label*={(\arabic*)}}
        \setlist[enumerate,2]{label={(\arabic{enumi}.\arabic*)}}
  }
}

\setlist[enumerate]{label*={\arabic*.}}

\renewcommand{\bf}{\bfseries}
\renewcommand{\sc}{\scshape}
\renewcommand{\it}{\itshape}

\renewcommand\cftsecfont{\bf\sc}
\renewcommand\cftsecpagefont{\normalfont}
\renewcommand{\cftsecleader}{\cftdotfill{\cftdotsep}}
\renewcommand\cftsecdotsep{\cftdot}
\renewcommand\cftsubsecdotsep{\cftdot}

\renewcommand{\bar}[1]{\mkern 1.5mu\overline{\mkern-1.5mu#1\mkern-1.5mu}\mkern 1.5mu}
\renewcommand{\tilde}[1]{\widetilde{#1}}

\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\fact}{!}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}

\DeclareRobustCommand\iff{\;\Longleftrightarrow\;}