main.tex

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% \documentclass[UTF8,fontset=none,leqno]{ctexart}

% Make sure you have installed the fonts I use. If not, just remember to
% make some modifications.
\documentclass[UTF8,fontset=none,twoside,leqno,12pt,a4paper]{ctexart}
% \documentclass[UTF8,twoside,leqno]{ctexart}

\usepackage{amssymb}
\usepackage{amsmath}
% Add hyperlinks to the table of contents
\usepackage[hidelinks]{hyperref}
\usepackage{bookmark}
\usepackage{xcolor}
\xeCJKsetup{CJKmath=true}
\def\period{。}
% \definecolor{bb}{RGB}{251,114,153}

% \usepackage{lipsum}

% Enable unicode-math? If this is enabled, many font packages will not work.
% However, if this is enabled, the symbols look better.
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\setmathfont{TeX Gyre Termes Math}[range=bb/{latin,Latin}]

\providecommand{\newsection}{}
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% \renewcommand{\newsection}{\cleardoublepage \thispagestyle{plain}}

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% Set the fonts. You can use whatever you like, or simply remove this part
% and remove the option "fontset=none".

\def\heiti{\CJKfontspec{Sarasa Mono SC Light}}
\def\songti{\CJKfontspec{Source Han Serif CN}}
\def\kaishu{\CJKfontspec{Sarasa Mono SC Light}}
\def\fangsong{\CJKfontspec{Sarasa Mono SC Light}}
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\setCJKmonofont{Sarasa Mono SC Light}
\setCJKmainfont[ItalicFont=Sarasa Mono SC Light]{Source Han Serif CN}
\setCJKsansfont{Sarasa Mono SC Light}
% I use Sarasa Mono SC instead of Kaishu or Fangsong.
% The operating system I use do not have the 4 fonts:
% Heiti, Songti, Kaishu, Fangsong.

% ================================================================================

% Punctuation style: narrow some punctuation symbols
\punctstyle{kaiming}

% Footnote
% Footnotes per page
\usepackage[perpage]{footmisc}
% Define a new set of footnote symbols
\DefineFNsymbols*{myFootnoteStyle}{
    % If unicode-math is not enabled, the dollar signs can be removed.
    {$\dagger$}{$\ddagger$}{$\S$}{$\P$}{$\parallel$}{$\dagger\dagger$}{$\ddagger\ddagger$}
}
\setfnsymbol{myFootnoteStyle}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}

% My own footnote command
\providecommand{\myFN}{}
\renewcommand{\myFN}[1]{\footnote{\sffamily \ #1}}

% Proof and solution style
\usepackage{amsthm}
% Use \nopunct to remove the dot: https://tex.stackexchange.com/questions/268912/can-i-change-the-dot-to-a-colon-after-proof-in-amsthm
% Use \vspace{-\topsep} to remove extra line: https://tex.stackexchange.com/questions/59755/space-before-proof
\newenvironment{pf}{\begin{proof}[\indent\bf 证 \hspace{-.1em}\hspace{-\labelsep}\hspace{1em}\nopunct]}{\end{proof}}

\newtheoremstyle{exer} % ⟨name⟩
{} % ⟨Space above⟩
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{} % ⟨Body font⟩
{\parindent} % ⟨Indent amount⟩
{\bfseries} % ⟨Theorem head font⟩
{.} % ⟨Punctuation after theorem head⟩
{.5em} % ⟨Space after theorem head⟩
{} % ⟨Theorem head spec (can be left empty, meaning 'normal')⟩
\theoremstyle{exer}
\newtheorem{exercise}{}[subsection]

\newtheoremstyle{exer*} % ⟨name⟩
{} % ⟨Space above⟩
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{} % ⟨Body font⟩
{\parindent} % ⟨Indent amount⟩
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{0em} % ⟨Space after theorem head⟩
{} % ⟨Theorem head spec (can be left empty, meaning 'normal')⟩
\theoremstyle{exer*}
\newtheorem*{exercise*}{}

\newtheoremstyle{remarkStyle} % ⟨name⟩
{} % ⟨Space above⟩
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{} % ⟨Body font⟩
{\parindent} % ⟨Indent amount⟩
{\bfseries} % ⟨Theorem head font⟩
{} % ⟨Punctuation after theorem head⟩
{1em} % ⟨Space after theorem head⟩
{} % ⟨Theorem head spec (can be left empty, meaning 'normal')⟩
\theoremstyle{remarkStyle}
\newtheorem*{proposition}{命题}
\newtheorem*{definition}{定义}
\newtheorem*{example}{例}
\newtheorem*{remark}{评注}

% https://oomake.com/question/175655
\renewcommand{\theexercise}{\arabic{exercise}}

% Use some special characters.
\usepackage{pifont}

% Allow page breaks in display formulae
\allowdisplaybreaks[3]

\def\CC{\mathbb{C}}
\def\RR{\mathbb{R}}
\def\QQ{\mathbb{Q}}
\def\ZZ{\mathbb{Z}}
\def\NN{\mathbb{N}}
\def\FF{\mathbb{F}}
\def\ii{\mathrm{i}}
\def\myStar{\ding{72}}
\def\ellipsis{\dots}
\def\qedsymbol{\ding{44}}
\newcommand{\term}[1]{(\textit{#1})}

\makeatletter
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% \renewcommand{\leqnomode}{\tagsleft@true\let\veqno\@@leqno}
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% \renewcommand{\reqnomode}{\tagsleft@false\let\veqno\@@eqno}

% Clear even-numbered pages
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        \else \thispagestyle{empty} \ \clearpage\fi\fi}

% For two-sided documents
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    \let\@mkboth\markboth
    \def\sectionmark##1{%
        \markboth {{%
                    \ifnum \c@secnumdepth >\z@
                        \thesection\quad
                    \fi
                    ##1}}{}}%
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\makeatother

% ============================================================
% The document begins.
% ============================================================

\begin{document}

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% \pagestyle{empty}

\pagestyle{empty}

\ \

\vfill

\begin{center}
    \sffamily

    \textbf{\huge Delving into Polynomials}

    \vspace{2ex}

    \textit{\large A \ding{200}\myFN{\ding{200} implies stupidity in the two-dimensional culture.} article written by a \ding{200} person}
\end{center}

\vfill

\ \

\vfill

\ \

\clearpage

\ \
\clearpage

\title{}
\date{}
\author{}
\ctexset{today=old}
\pagestyle{plain}
\pagenumbering{roman}
\renewcommand{\contentsname}{Table of Contents}
\renewcommand{\abstractname}{Abstract}

\pagestyle{plain}
\thispagestyle{empty}
\tableofcontents

\newsection
\input{contents/License Notice.tex}

\newsection
\input{contents/Preface.tex}

\newsection
\pagestyle{headings}
\setcounter{page}{1}
\pagenumbering{arabic}

\section*{Delving into Polynomials}
\addcontentsline{toc}{section}{Delving into Polynomials}
\markboth{Delving into Polynomials}{}

Out of boredom, I wrote the article.

    % This is used to occupy some space.
    {
        \vfill \itshape \sffamily \small
        \begin{center}
            \begin{tabular}{l}
                Gohan ni suru? Ofuro ni suru? Sore tomo\ellipsis \ wa ta shi? \\
                (Would you like dinner? Would you like a bath? Or\ellipsis \ would you like me?)
            \end{tabular}
        \end{center}
    }

\clearpage
\input{contents/Prerequisites.tex}

\clearpage
\input{contents/Definition of Polynomials.tex}

\clearpage
\input{contents/Division Algorithm.tex}

\clearpage
\input{contents/Polynomial Equality.tex}

\clearpage
\input{contents/Derivatives.tex}

\clearpage
\input{contents/Roots of Polynomials.tex}

\clearpage
\input{contents/Polynomials over F.tex}

\clearpage
\input{contents/Interpolation.tex}

\clearpage
\input{contents/Generalized Binomial Coefficients.tex}

\clearpage
\input{contents/Summation Formulae.tex}

\clearpage
\input{contents/Derivatives Revisited.tex}

\clearpage
\input{contents/Introduction to Differential Calculus on Polynomials.tex}

\cleardoublepage
% \thispagestyle{empty}
\pagestyle{empty}

\end{document}