17 Commits
v3.02 ... v3.06

Author SHA1 Message Date
EthanDeng
68b212d756 remove ctan uploading 2019-02-25 01:13:46 +08:00
EthanDeng
bd5d1aaa31 renew readme.md 2019-02-25 01:13:11 +08:00
EthanDeng
baf92783b1 renew 3.06 2019-02-25 00:55:40 +08:00
EthanDeng
a6617a8259 remove old tutorial 2019-02-18 20:10:34 +08:00
EthanDeng
1e722f465f renew theorem method 2019-02-18 20:07:44 +08:00
EthanDeng
8b00ca1d47 add new xelatex pdf 2019-02-08 22:16:53 +08:00
EthanDeng
f715507d47 renew guide book 2019-02-08 21:48:14 +08:00
EthanDeng
f987bae98f change the titlepage 2019-02-07 23:33:09 +08:00
EthanDeng
aa50aed13c readme typo 2019-02-05 12:04:13 +08:00
EthanDeng
ec7ff38b37 add license 2019-02-05 08:53:26 +08:00
EthanDeng
515a05dd0d renew readme 2019-02-03 15:19:19 +08:00
EthanDeng
c9fbc62984 change the font setting for XeLaTeX-Cn 2019-01-22 19:19:44 +08:00
EthanDeng
d3ddd4f232 add readme file 2019-01-17 00:58:12 +08:00
EthanDeng
7d4c6673ad date 2019-01-15 18:36:00 +08:00
EthanDeng
8f09be2d61 format 2019-01-15 18:19:15 +08:00
EthanDeng
d79866f1cb v3.04 2019-01-15 17:24:28 +08:00
EthanDeng
ec862e0bf6 v3.03 2019-01-15 15:18:42 +08:00
18 changed files with 2042 additions and 2278 deletions

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## Core latex/pdflatex auxiliary files:
*.aux
*.lof
*.log
*.lot
*.fls
*.out
*.toc
*.fmt
*.fot
*.cb
*.cb2
.*.lb
## Intermediate documents:
*.dvi
*.xdv
*-converted-to.*
# these rules might exclude image files for figures etc.
# *.ps
# *.eps
# *.pdf
## Generated if empty string is given at "Please type another file name for output:"
.pdf
## Bibliography auxiliary files (bibtex/biblatex/biber):
*.bbl
*.bcf
*.blg
*-blx.aux
*-blx.bib
*.run.xml
## Build tool auxiliary files:
*.fdb_latexmk
*.synctex
*.synctex(busy)
*.synctex.gz
*.synctex.gz(busy)
*.pdfsync
## Auxiliary and intermediate files from other packages:
# algorithms
*.alg
*.loa
# achemso
acs-*.bib
# amsthm
*.thm
# beamer
*.nav
*.pre
*.snm
*.vrb
# changes
*.soc
# cprotect
*.cpt
# elsarticle (documentclass of Elsevier journals)
*.spl
# endnotes
*.ent
# fixme
*.lox
# feynmf/feynmp
*.mf
*.mp
*.t[1-9]
*.t[1-9][0-9]
*.tfm
#(r)(e)ledmac/(r)(e)ledpar
*.end
*.?end
*.[1-9]
*.[1-9][0-9]
*.[1-9][0-9][0-9]
*.[1-9]R
*.[1-9][0-9]R
*.[1-9][0-9][0-9]R
*.eledsec[1-9]
*.eledsec[1-9]R
*.eledsec[1-9][0-9]
*.eledsec[1-9][0-9]R
*.eledsec[1-9][0-9][0-9]
*.eledsec[1-9][0-9][0-9]R
# glossaries
*.acn
*.acr
*.glg
*.glo
*.gls
*.glsdefs
# gnuplottex
*-gnuplottex-*
# gregoriotex
*.gaux
*.gtex
# htlatex
*.4ct
*.4tc
*.idv
*.lg
*.trc
*.xref
# hyperref
*.brf
# knitr
*-concordance.tex
# TODO Comment the next line if you want to keep your tikz graphics files
*.tikz
*-tikzDictionary
# listings
*.lol
# makeidx
*.idx
*.ilg
*.ind
*.ist
# minitoc
*.maf
*.mlf
*.mlt
*.mtc[0-9]*
*.slf[0-9]*
*.slt[0-9]*
*.stc[0-9]*
# minted
_minted*
*.pyg
# morewrites
*.mw
# nomencl
*.nlg
*.nlo
*.nls
# pax
*.pax
# pdfpcnotes
*.pdfpc
# sagetex
*.sagetex.sage
*.sagetex.py
*.sagetex.scmd
# scrwfile
*.wrt
# sympy
*.sout
*.sympy
sympy-plots-for-*.tex/
# pdfcomment
*.upa
*.upb
# pythontex
*.pytxcode
pythontex-files-*/
# thmtools
*.loe
# TikZ & PGF
*.dpth
*.md5
*.auxlock
# todonotes
*.tdo
# easy-todo
*.lod
# xmpincl
*.xmpi
# xindy
*.xdy
# xypic precompiled matrices
*.xyc
# endfloat
*.ttt
*.fff
# Latexian
TSWLatexianTemp*
## Editors:
# WinEdt
*.bak
*.sav
# Texpad
.texpadtmp
# Kile
*.backup
# KBibTeX
*~[0-9]*
# auto folder when using emacs and auctex
./auto/*
*.el
# expex forward references with \gathertags
*-tags.tex
# standalone packages
*.sta
# generated if using elsarticle.cls
*.spl

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The LaTeX Project Public License
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PREAMBLE
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Defining What Constitutes the Work
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the Work.

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<!-- Author : Dongsheng Deng & Liam Huang-->
<!-- Program Email: elegantlatex2e@gmail.com -->
# ElegantBook
[Homepage](https://elegantlatex.org/) | [Github](https://github.com/ElegantLaTeX/ElegantBook) | [CTAN](https://ctan.org/pkg/elegantbook) | [Download](https://github.com/ElegantLaTeX/ElegantBook/releases) | [Wiki](https://github.com/ElegantLaTeX/ElegantBook/wiki) | [Weibo](https://weibo.com/elegantlatex)
![License](https://img.shields.io/ctan/l/elegantbook.svg)
![CTAN Version](https://img.shields.io/ctan/v/elegantbook.svg)
![Github Version](https://img.shields.io/github/release/ElegantLaTeX/ElegantBook.svg)
![Repo Size](https://img.shields.io/github/repo-size/ElegantLaTeX/ElegantBook.svg)
ElegantBook is designed for books. Just enjoy it! If you have any questions, suggestions or bug reports, you can create issues, pull requests or contact us at elegantlatex2e@gmail.com.
如果你有其他问题、建议或者报告 bug可以提交 issues 或者给我们发邮件elegantlatex2e@gmail.com。
# License
This work is released under the LaTeX Project Public License, v1.3c or later.
本模板发布遵循 LaTeX 项目公共许可证 1.3 c 或更高版本。

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%% tikz setting
\tikzset{x=1pt,y=1pt}
\tikzset{elegant/.style={fill=main,draw=main},
null/.style={fill=white,draw=none}}
%% the triangle shape
\newcommand{\triz}[2]{
\begin{scope}[xshift=#1,rotate=#2]
\draw[elegant] (0,0) -- (105,6) .. controls (119,21) and (132,13) .. (135,12) .. controls (124,15) and (110,8) .. (107,-12) -- cycle;
\draw[null] (40,-0.5) -- (101,-4) -- (103,1)--cycle;
\end{scope}
}
%% the ellipse shape +127
\newcommand{\ellz}[1]{
\begin{scope}[xshift=#1,yshift=3]
\draw[elegant,rotate around={60:(0,-3)}](0,-3) ellipse (10.5 and 8.5);
\draw[null](-3,-10) .. controls (-10,-6) and (-2,6) .. (4.5,4) .. controls (0,3) and (-4,-6) .. (-3,-10)--cycle;
\end{scope}
}
%% the integration shape+147
\newcommand{\intz}[1]{
\begin{scope}[xshift=#1,yshift=2]
\draw[elegant,draw=none,very thin] (-31,-14.5) .. controls (-17,-21) and (-9,-8) .. (-3,0) .. controls (10,19) and (22,17) .. (29,9) .. controls (21,13) and (13,13) .. (3,-1) .. controls (-4,-11) and (-18,-27) .. (-31,-14.5) -- cycle ;
\end{scope}
}

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\documentclass[cn]{elegantbook}
\title{ElegantBook优美的 \LaTeX{} 书籍模板}
\subtitle{Elegant\LaTeX{} 经典之作}
\author{Ethan Deng \& Liam Huang}
\institute{Elegant\LaTeX{} Program}
\date{\today}
\version{3.06}
\equote{Victory won\rq t come to us unless we go to it. --- M. Moore}
\logo{logo.png}
\cover{cover.jpg}
\begin{document}
\maketitle
\tableofcontents
\clearpage
\thispagestyle{empty}
\mainmatter
\hypersetup{pageanchor=true}
\chapter{Elegant\LaTeX{} 系列模板介绍}
值此版本发行之际,我们 Elegant\LaTeX{} 项目组向大家重新介绍一下我们的工作我们致力于打造一系列美观、优雅、简便的模板方便用户使用。Elegant\LaTeX{} 系列模板目前由 \href{https://github.com/ElegantLaTeX/ElegantNote}{ElegantNote}\href{https://github.com/ElegantLaTeX/ElegantBook}{ElegantBook}\href{https://github.com/ElegantLaTeX/ElegantPaper}{ElegantPaper} 组成,分别用于排版笔记,书籍和工作论文。这些子项目的名词是一体的,请在使用这些名词的时候不要将其断开(如 Elegant Note 是不正确的写法。并且Elegant\LaTeX{} Book 指的即是 ElegantBook。
最新版本下载地址:\href{https://github.com/ElegantLaTeX/ElegantBook/releases}{Github:ElegantBook/releases}。本文将介绍本模板的一些设置内容以及基本使用方法。如果您在使用此模板,欢迎把您使用此模板制作的成品发一份给我们,谢谢!如果您有其他问题,建议或者意见,欢迎联系我们。
\section{ElegantBook 更新说明}
在这几年间,我们收到了很多用户的反馈,主要的问题涉及到字体安装,编码支持,定理浮动,定理跨页,交叉引用等等。我们思前想后,原先让用户安装字体以追求视觉上的美观并不完美,用户陷入了巨大的麻烦,这违背了我们的模板初衷。因此我们在新版中删除了这部分,用户无需安装任何字体。让我们来看下此次 ElegantBook 模板 3.x 更新的主要内容有:
\begin{enumerate}
\item 删除了自定义字体设置,改用 \lstinline{ctex} 宏包或者系统默认字体;
\item 模板拆分为中英文模式(\lstinline{lang=cn/en}
\item \lstinline{PDFLaTeX}\lstinline{XeLaTeX} 支持;
\item 使用 \lstinline{tcolorbox} 宏包改写定理类环境,可跨页;
\item 定理类环境名字更新,修复定理环境交叉引用;
\item 颜色名字更新,统一链接颜色;
\item 重新绘制 Elegant\LaTeX{} 的 Logo
\item 更新封面与装饰物,删除水印;
\item 修正附录相关内容;
\item 增加灰色主题 \lstinline{color=plain}
\item 增加代码高亮;
\item 美化列表环境。
\end{enumerate}
\chapter{ElegantBook 设置说明}
\section{编译方式}
本模板基于基础的 book 文类,所以 book 的选项对于本模板也是有效的。默认编码为 UTF-8推荐使用 \TeX{} Live 编译。本文编写环境为 Win10 (64bit) + \TeX{} Live 2018支持 \lstinline{PDFLaTeX} 以及 \lstinline{XeLaTeX} 编译。
\subsection[选择 PDFLaTeX 编译]{选择 \lstinline{PDFLaTeX} 编译}
如果你使用 \lstinline{PDFLaTeX} 编译,默认的 Computer Modern 字体被换成了 \lstinline{newtx} 系列字体,默认的字体字号是 12 pt。关于字体设置的宏包主要用到了
\begin{itemize}
\item \lstinline{newtxtext} 用于文档正文字体,类似于 Times New Roman 字体。
\item \lstinline{newtxmath} 用于数学字体,搭配 \lstinline{newtxtext} 非常合适。
\item \lstinline{FiraMono} 用于打字机字体,并使用了 \lstinline{scale=0.7} 选项。
\item \lstinline{ctex} 用于中文字体设置,并使用了 \lstinline{scheme=plain} 选项。
\end{itemize}
一次完整的编译:\lstinline[breaklines]{PDFLaTeX -> BibTeX -> PDFLaTeX*2}
\subsection[选择 XeLaTeX 编译]{选择 \lstinline{XeLaTeX} 编译}
如果你选择 \lstinline{XeLaTeX} 编译的话,那么设置字体的宏包为 \lstinline{fontspec}\lstinline{xeCJK}。由于模板中使用的字体是 Windows 中的字体,所以如果你使用其他操作系统,比如 Linux 或者 Mac OS那么你需要把所用字体替换为你系统中的字体。设置字体的命令
\begin{lstlisting}[frame=single]
\RequirePackage{fontenc}
\RequirePackage[no-math]{fontspec}
\setmainfont{Times New Roman}[NFSSFamily=ntxtlf]
\setsansfont{Arial}
%\setmonofont[Scale=0.7]{Courier New}
\RequirePackage{xeCJK}
\RequirePackage{xunicode}
\setCJKmainfont[BoldFont={SimHei},ItalicFont={KaiTi}]{SimSun}
\setCJKsansfont[BoldFont={SimHei},ItalicFont={KaiTi}]{KaiTi}
\setCJKmonofont[BoldFont={SimHei},ItalicFont={KaiTi},Scale=0.7]{Microsoft YaHei}
\XeTeXlinebreaklocale "zh"
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt
\RequirePackage{newtxmath}
\end{lstlisting}
一次完整的编译:\lstinline[breaklines]{XeLaTeX -> BibTeX -> XeLaTeX*2}
\section{语言模式}
本模板内含两套语言环境,改变语言环境会改变图表标题的引导词(图,表),文章结构词(比如目录,参考文献等),以及定理环境中的引导词(比如定理,引理等)。不同语言模式的启用如下:
\begin{lstlisting}[frame=single]
\documentclass[cn]{elegantbook}
\documentclass[lang=cn]{elegantbook}
\documentclass[en]{elegantbook}
\documentclass[lang=en]{elegantbook}
\end{lstlisting}
\begin{remark}
不管选用中文环境(\lstinline{lang=cn})还是英文环境(\lstinline{lang=en})均可输入中文。另外如果在笔记中使用了抄录环境(\lstinline{lstlisting}),并且其中包括了中文,请务必使用 \lstinline{XeLaTeX} 编译。
\end{remark}
\section{颜色主题}
本模板内置 4 组颜色主题,分别为 \textcolor{main1}{\lstinline{green}}(默认)、\textcolor{main2}{\lstinline{cyan}}\textcolor{main3}{\lstinline{blue}}\textcolor{gray}{\lstinline{plain}},另外还有一个自定义的选项 \lstinline{nocolor}。调用颜色主题 \lstinline{green} 的方法为
\begin{lstlisting}[frame=single]
\documentclass[green]{elegantbook} %or
\documentclass[color=green]{elegantbook}
\end{lstlisting}
其中 \textcolor{gray}{plain} 主题为全灰色。如果需要自定义颜色的话请选择 \lstinline{nocolor} 选项或者使用 \lstinline{color=none},然后在导言区定义 main、second、third 颜色,具体方法如下:
\begin{lstlisting}[frame=single]
\definecolor{main}{RGB}{70,70,70}
\definecolor{second}{RGB}{115,45,2}
\definecolor{third}{RGB}{0,80,80}
\end{lstlisting}
\begin{table}[htp]
\caption{ElegantBook 模板中的颜色主题\label{tab:color thm}}
\centering
\begin{tabular}{ccccc}
\toprule
& \textcolor{main1}{green} & \textcolor{main2}{cyan} & \textcolor{main3}{blue} & 主要使用的环境\\
\midrule
main & \makecell{{\color{main1}\rule{1cm}{1cm}}}& \makecell{{\color{main2}\rule{1cm}{1cm}}}&\makecell{ {\color{main3}\rule{1cm}{1cm}}}& definition \\
second &\makecell{ {\color{second1}\rule{1cm}{1cm}}}& \makecell{{\color{second2}\rule{1cm}{1cm}}}&\makecell{ {\color{second3}\rule{1cm}{1cm}}}&theorem \ lemma \ corollary\\
third &\makecell{ {\color{third1}\rule{1cm}{1cm}}}& \makecell{{\color{third2}\rule{1cm}{1cm}}}&\makecell{ {\color{third3}\rule{1cm}{1cm}}}&proposition\\
\bottomrule
\end{tabular}
\end{table}
\section{章标题显示风格}
本模板内置 2 套\textit{章标题显示风格},包含 \lstinline{hang}(默认)与 \lstinline{display} 两种风格,区别在于章标题单行显示(\lstinline{hang})与双行显示(\lstinline{display}),本说明使用了 \lstinline{hang}。调用方式为
\begin{lstlisting}[frame=single]
\documentclass[hang]{elegantbook} %or
\documentclass[titlestyle=hang]{elegantbook}
\end{lstlisting}
\section{数学环境简介}
在我们这个模板中,定义了四大类环境
\begin{itemize}
\item \textit{定理类环境},包含标题和内容两部分,全部定理类环境的编号均以章节编号。根据格式的不同分为 3 种
\begin{itemize}
\item \textcolor{main}{\textbf{definition}} 环境,颜色为 \textcolor{main}{main}
\item \textcolor{second}{\textbf{theorem、lemma、corollary}} 环境,颜色为 \textcolor{second} {second}
\item \textcolor{third}{\textbf{proposition}} 环境,颜色为 \textcolor{third}{third}
\end{itemize}
\item \textit{示例类环境},有 \textbf{example、exercise、problem} 环境(对应于例,练习,例题),自动编号,编号以章节为单位。
\item \textit{证明类环境},有 \textbf{proof、note} 环境,特点是,有引导符或者结尾符,\textbf{note} 环境有引导符号,\textbf{proof} 环境有证明完毕符号。
\item \textit{结论类环境},有 \textbf{conclusion、assumption、propertyremark、solution} 环境,三者均以粗体的引导词为开头,和普通段落格式一致。
\end{itemize}
\subsection{定理类环境的使用}
由于本模板使用了 \lstinline{tcolorbox} 宏包来定制定理类环境,所以和普通的定理环境的使用有些许区别,定理的使用方法如下:
\begin{lstlisting}[frame=single]
\begin{theorem}{<theorem name>}{<label>}
The content of theorem.
\end{theorem}
\end{lstlisting}
第一个必选项 \lstinline{<theorem name>} 是定理的名字,第二个必选项 \lstinline{<label>} 是交叉引用时所用到的标签,交叉引用的方法为 \verb|\ref{thm:label}|。请注意,交叉引用时必须加上前缀 \lstinline{thm:}。效果如下:
\begin{theorem}{<theorem name>}{<label>}
The content of theorem.
\end{theorem}
其他相同用法的定理类环境有:
\begin{table}[htbp]
\centering
\caption{定理类环境}
\begin{tabular}{llll}
\toprule
环境名 & 标签名 & 前缀 & 交叉引用 \\
\midrule
definition & label & def & \lstinline|\ref{def:label}| \\
theorem & label & thm & \lstinline|\ref{thm:label}| \\
lemma & label & lem & \lstinline|\ref{lem:label}| \\
corrlary & label & cor & \lstinline|\ref{cor:label}| \\
proposition & label & pro & \lstinline|\ref{pro:label}| \\
\bottomrule
\end{tabular}%
\label{tab:theorem-class}%
\end{table}%
\subsection{其他数学环境的使用}
其他三种数学环境因为没有选项,可以直接使用,比如 \lstinline{example} 环境的使用:
\begin{lstlisting}[frame=single]
\begin{example}
This is the content of example environment.
\end{example}
\end{lstlisting}
效果如下:
\begin{example}
This is the content of example environment.
\end{example}
这几个都是同一类环境,区别在于
\begin{itemize}
\item 示例环境example、练习exercise与例题problem章节自动编号
\item 注意note环境有提醒引导符证明proof环境有证明结束符
\item 结论conclusion等环境都是普通段落环境引导词加粗。
\end{itemize}
\section{封面和徽标}
本模板使用的封面图片来源于 \href{https://pixabay.com/en/tea-time-poetry-coffee-reading-3240766/}{pixabay.com}\footnote{感谢 China\TeX{} 提供免费图源网站,另外还推荐 \href{https://www.pexels.com/}{pexels.com}},图片完全免费,可用于任何场景。封面图片的尺寸为 $1280 \times 1024$, 更换图片的时候请\textbf{严格}按照封面图片尺寸进行裁剪。推荐一个免费的在线图片裁剪网站 \href{https://www.befunky.com/create/crop-photo/}{befunky.com}
本文用到的 Logo 比例为 1:1也即正方形图片在更换图片的时候请选择合适的图片进行替换。
\section{列表环境}
本模板借助于 \lstinline{tikz} 定制了 \lstinline{itemize}\lstinline{enumerate} 环境,其中 \lstinline{itemize} 环境修改了 3 层嵌套,而 \lstinline{enumerate} 环境修改了 4 层嵌套(仅改变颜色)。示例如下\\[2ex]
\begin{minipage}[b]{0.49\textwidth}
\begin{itemize}
\item first item of nesti;
\item second item of nesti;
\begin{itemize}
\item first item of nestii;
\item second item of nestii;
\begin{itemize}
\item first item of nestiii;
\item second item of nestiii.
\end{itemize}
\end{itemize}
\end{itemize}
\end{minipage}
\begin{minipage}[b]{0.49\textwidth}
\begin{enumerate}
\item first item of nesti;
\item second item of nesti;
\begin{enumerate}
\item first item of nestii;
\item second item of nestii;
\begin{enumerate}
\item first item of nestiii;
\item second item of nestiii.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{minipage}
\section{参考文献}
此模板使用了 Bib\TeX{} 来生成参考文献默认使用的文献样式bib style\lstinline{aer}。参考文献示例:~\cite{Chen2018} 使用了中国一个大型的 P2P 平台(人人贷)的数据来检验男性投资者和女性投资者在投资表现上是否有显著差异。
你可以在谷歌学术MendeleyEndnote 中获得文献条目bib item然后把它们添加到 \lstinline{reference.bib} 中。在文中引用的时候引用它们的键值bib key即可。注意需要在编译的过程中添加 Bib\TeX{} 编译。如果你想在参考文献中添加未引用的文献,可以使用
\section{添加序章}
如果你想在第一章前面添加序章,不改变原本章节序号,你可以在第一章内容前面使用
\begin{lstlisting}[frame=single]
\chapter*{序章}
\addcontentsline{toc}{chapter}{序章}
\markboth{序章}{}
序章的内容。
\end{lstlisting}
\chapter{ElegantBook 写作示例}
\section{Lebesgue 积分}
在前面各章做了必要的准备后,本章开始介绍新的积分。在 Lebesgue 测度理论的基础上建立了 Lebesgue 积分,其被积函数和积分域更一般,可以对有界函数和无界函数统一处理。正是由于 Lebesgue 积分的这些特点,使得 Lebesgue 积分比 Riemann 积分具有在更一般条件下的极限定理和累次积分交换积分顺序的定理,这使得 Lebesgue 积分不仅在理论上更完善,而且在计算上更灵活有效。
Lebesgue 积分有几种不同的定义方式。我们将采用逐步定义非负简单函数,非负可测函数和一般可测函数积分的方式。
由于现代数学的许多分支如概率论、泛函分析、调和分析等常常用到一般空间上的测度与积分理论,在本章最后一节将介绍一般的测度空间上的积分。
\subsection{积分的定义}
我们将通过三个步骤定义可测函数的积分。首先定义非负简单函数的积分。以下设 $E$$\mathcal{R}^n$ 中的可测集。
\begin{definition}{可积性}{int}
$ f(x)=\sum\limits_{i=1}^{k} a_i \chi_{A_i}(x)$$E$ 上的非负简单函数,其中 $\{A_1,A_2,\ldots,A_k\}$$E$ 上的一个可测分割,$a_1,a_2,\ldots,a_k$ 是非负实数。定义 $f$$E$ 上的积分为
\begin{equation}
\label{inter}
\int_{E} f dx = \sum_{i=1}^k a_i m(A_i) .
\end{equation}
一般情况下 $0 \leq \int_{E} f dx \leq \infty$。若 $\int_{E} f dx < \infty$,则称 $f$$E$ 上可积。
\end{definition}
一个自然的问题是Lebesgue 积分与我们所熟悉的 Riemann 积分有什么联系和区别?在 4.4 在我们将详细讨论 Riemann 积分与 Lebesgue 积分的关系。这里只看一个简单的例子。设 $D(x)$ 是区间 $[0,1]$ 上的 Dirichlet 函数。即 $D(x)=\chi_{Q_0}(x)$,其中 $Q_0$ 表示 $[0,1]$ 中的有理数的全体。根据非负简单函数积分的定义,$D(x)$$[0,1]$ 上的 Lebesgue 积分为
\begin{equation}
\label{inter2}
\int_0^1 D(x)dx = \int_0^1 \chi_{Q_0} (x) dx = m(Q_0) = 0
\end{equation}
$D(x)$$[0,1]$ 上是 Lebesgue 可积的并且积分值为零。但 $D(x)$$[0,1]$ 上不是 Riemann 可积的。
有界变差函数是与单调函数有密切联系的一类函数。有界变差函数可以表示为两个单调递增函数之差。与单调函数一样,有界变差函数几乎处处可导。与单调函数不同,有界变差函数类对线性运算是封闭的,它们构成一线空间。练习题 \ref{exer:43} 是一个性质的证明。
\begin{exercise}\label{exer:43}
$f\in L(\mathcal{R}^1)$$g$$\mathcal{R}^1$ 上的有界可测函数。证明函数
\begin{equation}
\label{ex:1}
I(t) = \int_{\mathcal{R}^1} f(x+t)g(x)dx \quad t \in \mathcal{R}^1
\end{equation}
$\mathcal{R}^1$ 上的连续函数。
\end{exercise}
\begin{theorem}{Fubini 定理}{fubi}
1$f(x,y)$$\mathcal{R}^p\times\mathcal{R}^q$ 上的非负可测函数,则对几乎处处的 $x\in \mathcal{R}^p$$f(x,y)$ 作为 $y$ 的函数是 $\mathcal{R}^q$ 上的非负可测函数,$g(x)=\int_{\mathcal{R}^q}f(x,y) dy$$\mathcal{R}^p$ 上的非负可测函数。并且
\begin{equation}
\label{eq:461}
\int_{\mathcal{R}^p\times\mathcal{R}^q} f(x,y) dxdy=\int_{\mathcal{R}^p}\left(\int_{\mathcal{R}^q}f(x,y)dy\right)dx.
\end{equation}
2$f(x,y)$$\mathcal{R}^p\times\mathcal{R}^q$ 上的可积函数,则对几乎处处的 $x\in\mathcal{R}^p$$f(x,y)$ 作为 $y$ 的函数是 $\mathcal{R}^q$ 上的可积函数,并且 $g(x)=\int_{\mathcal{R}^q}f(x,y) dy$$\mathcal{R}^p$ 上的可积函数。而且~\ref{eq:461} 成立。
\end{theorem}
\begin{note}
在本模板中引理lemma推论corollary )的样式和定理~\ref{thm:fubi} 的样式一致,包括颜色,仅仅只有计数器的设置不一样。
\end{note}
我们说一个实变或者复变量的实值或者复值函数是在区间上平方可积的,如果其绝对值的平方在该区间上的积分是有限的。所有在勒贝格积分意义下平方可积的可测函数构成一个希尔伯特空间,也就是所谓的 $L^2$ 空间,几乎处处相等的函数归为同一等价类。形式上,$L^2$ 是平方可积函数的空间和几乎处处为 0 的函数空间的商空间。
\begin{proposition}{最优性原理}{max}
如果 $u^*$$[s,T]$ 上为最优解,则 $u^*$$[s,T]$ 任意子区间都是最优解,假设区间为 $[t_0,t_1]$ 的最优解为 $u^*$ ,则 $u(t_0)=u^{*}(t_0)$,即初始条件必须还是在 $u^*$ 上。
\end{proposition}
我们知道最小二乘法可以用来处理一组数据,可以从一组测定的数据中寻求变量之间的依赖关系,这种函数关系称为经验公式。本课题将介绍最小二乘法的精确定义及如何寻求点与点之间近似成线性关系时的经验公式。假定实验测得变量之间的 $n$ 个数据,则在平面上,可以得到 $n$ 个点,这种图形称为 “散点图”,从图中可以粗略看出这些点大致散落在某直线近旁, 我们认为其近似为一线性函数,下面介绍求解步骤。
\begin{figure}[htbp]
\centering
\includegraphics[width=0.6\textwidth]{scatter.pdf}
\caption{散点图示例 $\hat{y}=a+bx$ \label{fig:scatter}}
\end{figure}
以最简单的一元线性模型来解释最小二乘法。什么是一元线性模型呢?监督学习中,如果预测的变量是离散的,我们称其为分类(如决策树,支持向量机等),如果预测的变量是连续的,我们称其为回归。回归分析中,如果只包括一个自变量和一个因变量,且二者的关系可用一条直线近似表示,这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量,且因变量和自变量之间是线性关系,则称为多元线性回归分析。对于二维空间线性是一条直线;对于三维空间线性是一个平面,对于多维空间线性是一个超平面。
\begin{property}
柯西列的性质
\begin{enumerate}
\item $\{x_k\}$ 是柯西列,则其子列 $\{x_k^i\}$ 也是柯西列。
\item $x_k\in \mathcal{R}^n$$\rho(x,y)$ 是欧几里得空间,则柯西列收敛,$(\mathcal{R}^n,\rho)$ 空间是完备的。
\end{enumerate}
\end{property}
\begin{conclusion}
回归分析regression analysis) 是确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法。运用十分广泛,回归分析按照涉及的变量的多少,分为一元回归和多元回归分析;按照因变量的多少,可分为简单回归分析和多重回归分析;按照自变量和因变量之间的关系类型,可分为线性回归分析和非线性回归分析。
\end{conclusion}
\nocite{EINAV2010,Havrylchyk2018}
\bibliography{reference}
\appendix
\chapter{基本数学工具}
本附录包括了计量经济学中用到的一些基本数学,我们扼要论述了求和算子的各种性质,研究了线性和某些非线性方程的性质,并复习了比例和百分数。我们还介绍了一些在应用计量经济学中常见的特殊函数,包括二次函数和自然对数,前 4 节只要求基本的代数技巧,第 5 节则对微分学进行了简要回顾;虽然要理解本书的大部分内容,微积分并非必需,但在一些章末附录和第 3 篇某些高深专题中,我们还是用到了微积分。
\section{求和算子与描述统计量}
\textbf{求和算子} 是用以表达多个数求和运算的一个缩略符号,它在统计学和计量经济学分析中扮演着重要作用。如果 $\{x_i: i=1, 2, \ldots, n\}$ 表示 $n$ 个数的一个序列,那么我们就把这 $n$ 个数的和写为:
\begin{equation}
\sum_{i=1}^n x_i \equiv x_1 + x_2 +\cdots + x_n
\end{equation}
\chapter{最小示例}
\begin{lstlisting}[frame=single]
\documentclass{elegantbook}
% title info
\title{Title}
\subtitle{Subtitle is here}
% bio info
\author{Your Name}
\institute{XXX University}
\date{\today}
% extra info
\version{1.00}
\equote{Victory won\rq t come to us unless we go to it. --- M. Moore}
\logo{logo.png}
\cover{cover.jpg}
\begin{document}
\maketitle
\tableofcontents
\mainmatter
\hypersetup{pageanchor=true}
% add preface chapter here if needed
\chapter{Example Chapter Title}
The content of chapter one.
\bibliography{reference}
\appendix
\chapter{Appendix Chapter Title}
The content of appendix 1.
\end{document}
\end{lstlisting}
\end{document}

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\documentclass{elegantbook}
\title{An Elegant \LaTeX{} Template for Books}
\subtitle{Classic Elegant\LaTeX{} Template}
\author{Ethan Deng \& Liam Huang}
\institute{Elegant\LaTeX{} Program}
\date{\today}
\version{3.06}
\equote{Victory won\rq t come to us unless we go to it. --- M. Moore}
\logo{logo.png}
\cover{cover.jpg}
\begin{document}
\maketitle
\tableofcontents
\clearpage
\thispagestyle{empty}
\mainmatter
\hypersetup{pageanchor=true}
\chapter{Elegant\LaTeX{} Templates}
On the occasion of this release, we, Elegant\LaTeX{} Program, want to reintroduce our work to you. We are committed to creating a series of beautiful, elegant, easy to use \LaTeX{} templates for users. The Elegant\LaTeX{} is currently composed of \href{https://github.com/ElegantLaTeX/ElegantNote}{ElegantNote}, \href{https://github.com/ElegantLaTeX/ElegantBook}{ElegantBook}, \href{https://github.com/ElegantLaTeX/ElegantPaper}{ElegantPaper} for typesetting notes, books, and working papers respectively.
The latest version is available on \href{https://github.com/ElegantLaTeX/ElegantBook/releases}{Github:ElegantBook/releases}. This guide describes some settings of this template and how to use it. If you have any other questions, suggestions or comments, please feel free to contact us.
\section{ElegantBook Updates}
Over these years, we've received a lot of feedback from users, with major issues related to font installation, coding support, theorem class environments floats, theorem cross-page, cross-references, and etc. We really think about these problems, it wasn't elegant to let the user install the font for visual beauty since users got into a lot of trouble, which went against the concept of our template. So we've removed that from the new version, users don't have to install any fonts. Let's take a look at the ElegantBook template 3.x updates:
\begin{enumerate}
\item Remove custom font settings and use the \lstinline{ctex} package or system font instead;
\item Add English and Chinese modes\lstinline{lang=cn/en});
\item \lstinline{PDFLaTeX}\lstinline{XeLaTeX} Support;
\item Use the \lstinline{tcolorbox} package to re-written the theorem class environments, which can span over pages;
\item Theorem class environments name updated, and cross-references fixed;
\item Color name updated, link color unified;
\item New Elegant\LaTeX{} Logo;
\item New cover and decorations, remove the watermark;
\item Fix appendix;
\item Add gray theme: \lstinline{color=plain};
\item Add code highlighting;
\item Beautify the list environment.
\end{enumerate}
\chapter{ElegantBook Settings}
\section{Compilation Methods}
This template is based on the Standard LaTeX book class, so the options of book class also work. The default encoding is UTF-8, and \TeX{} Live is recommended. The test environment is Win10 + \TeX{} Live 2018.
\subsection[Compile with PDFLaTeX]{Compile with \lstinline{PDFLaTeX}}
If you choose \lstinline{PDFLaTeX} to process your book, the default article font computer modern has changed to \lstinline{newtx} series, and the default font size is set to \lstinline{11pt}. The fonts are settings with:
\begin{itemize}
\item \lstinline{newtxtext} package for text fonts, similar to times new roman font.
\item \lstinline{newtxmath} package for math fonts, close to \lstinline{times} package.
\item \lstinline{FiraMono} package for typewriter fonts, with option \lstinline{scale=0.7}.
\item \lstinline{ctex} package for Chinese fonts, with option \lstinline{scheme=plain}.
\end{itemize}
A full compilation chain\lstinline[breaklines]{PDFLaTeX -> BibTeX -> PDFLaTeX*2}.
\subsection[Compile with XeLaTeX]{Compile with \lstinline{XeLaTeX}}
If you choose \lstinline{XeLaTeX} to process your book, we use \lstinline{fontspec} package and \lstinline{xeCJK} package. we used fonts available in Windows, if you are using Linux or Mac OS, please substitute these fonts with that of your system.
\begin{lstlisting}[frame=single]
\RequirePackage{fontenc}
\RequirePackage[no-math]{fontspec}
\setmainfont{Times New Roman}[NFSSFamily=ntxtlf]
\setsansfont{Arial}
%\setmonofont[Scale=0.7]{Courier New}
\RequirePackage{xeCJK}
\RequirePackage{xunicode}
\setCJKmainfont[BoldFont={SimHei},ItalicFont={KaiTi}]{SimSun}
\setCJKsansfont[BoldFont={SimHei},ItalicFont={KaiTi}]{KaiTi}
\setCJKmonofont[BoldFont={SimHei},ItalicFont={KaiTi},Scale=0.7]{Microsoft YaHei}
\XeTeXlinebreaklocale "zh"
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt
\RequirePackage{newtxmath}
\end{lstlisting}
A full compilation chain\lstinline[breaklines]{XeLaTeX -> BibTeX -> XeLaTeX*2}.
\section{Languages}
We defined one option named \lstinline{lang}, this option has two alternative values, \lstinline{lang=en} (default) or \lstinline{lang=cn}. \lstinline{lang=cn} will make the caption of figure/table, abstract name, refname etc. Chinese, while \lstinline{lang=en} will keep all these stuff English, as the default article class sets. You can use this option as
\begin{lstlisting}[frame=none]
\documentclass[cn]{elegantbook}
\documentclass[lang=cn]{elegantbook}
\documentclass[en]{elegantbook}
\documentclass[lang=en]{elegantbook}
\end{lstlisting}
\begin{remark}
You can input Chinese Character in either \lstinline{lang=en} or \lstinline{lang=cn}. If you are using (\lstinline{lstlisting}) environment, and it contains Chinese characters, please use \lstinline{XeLaTeX}.
\end{remark}
\section{Color Themes}
This template contains 4 color themes,they are \textcolor{main1}{\lstinline{green}} (default), \textcolor{main2}{\lstinline{cyan}}, \textcolor{main3}{\lstinline{blue}}, \textcolor{gray}{\lstinline{plain}}, and there is a customization color option \lstinline{nocolor}. You can choose \lstinline{green} with
\begin{lstlisting}[frame=single]
\documentclass[green]{elegantbook} %or
\documentclass[color=green]{elegantbook}
\end{lstlisting}
where \textcolor{gray}{plain} theme is gray for all theorem class environments and paper structures. If you want to customize the colors, please select \lstinline{nocolor} or use \lstinline{color=none} , then define the main, second, and third colors in the preamble section as follows:
\begin{lstlisting}[frame=single]
\definecolor{main}{RGB}{70,70,70}
\definecolor{second}{RGB}{115,45,2}
\definecolor{third}{RGB}{0,80,80}
\end{lstlisting}
\begin{table}[htp]
\caption{ElegantBook Themes\label{tab:color thm}}
\centering
\begin{tabular}{ccccc}
\toprule
& \textcolor{main1}{green} & \textcolor{main2}{cyan} & \textcolor{main3}{blue} & Main Environments\\
\midrule
main & \makecell{{\color{main1}\rule{1cm}{1cm}}}& \makecell{{\color{main2}\rule{1cm}{1cm}}}&\makecell{ {\color{main3}\rule{1cm}{1cm}}}& definition \\
second &\makecell{ {\color{second1}\rule{1cm}{1cm}}}& \makecell{{\color{second2}\rule{1cm}{1cm}}}&\makecell{ {\color{second3}\rule{1cm}{1cm}}}&theorem \ lemma \ corollary\\
third &\makecell{ {\color{third1}\rule{1cm}{1cm}}}& \makecell{{\color{third2}\rule{1cm}{1cm}}}&\makecell{ {\color{third3}\rule{1cm}{1cm}}}&proposition\\
\bottomrule
\end{tabular}
\end{table}
\section{Chapter Title Display Styles}
This template contains 2 sets of \textit{title display styles},which including \lstinline{hang}(default) and \lstinline{display} style,
The difference is that the chapter heading is displayed on a single line (\lstinline{hang}) and on a double line (\lstinline{display}) , and this guide uses \lstinline{hang} . To change display style
\begin{lstlisting}[frame=single]
\documentclass[hang]{elegantbook} %or
\documentclass[titlestyle=hang]{elegantbook}
\end{lstlisting}
\section{Theorem Class Environments}
In this template, we defined four categories of theorem class environments
\begin{itemize}
\item \textit{Theorem Environment}, including title and contents, numbering within chapter. There are three types depending on the format
\begin{itemize}
\item \textcolor{main}{\textbf{definition}} environment, the color is \textcolor{main}{main};
\item \textcolor{second}{\textbf{theorem, lemma, corollary}} environment, the color is \textcolor{second} {second};
\item \textcolor{third}{\textbf{proposition}} environment, the color is \textcolor{third}{third}.
\end{itemize}
\item \textit{Example Environments}, including \textbf{example, exercise, problem} environment, auto numering within chapter.
\item \textit{Proof Environment}, including \textbf{proof, note} environment, they contain introductory symbol (\textbf{note} environment) or ending symbol (\textbf{proof} environment).
\item \textit{Conclusion Environments}, including \textbf{conclusion, assumption, property, remark, solution} environment, all of these begin with boldfaced words, and the contents are the same as a normal paragraph.
\end{itemize}
\subsection{Theorem Class Environments}
The template uses the \lstinline{tcolorbox} package to customize the theorem class environments, it is slightly different from the normal theorem environments. The usage is as follows:
\begin{lstlisting}[frame=single]
\begin{theorem}{<theorem name>}{<label>}
The content of theorem.
\end{theorem}
\end{lstlisting}
The first parameter \lstinline{<theorem name>} is the name of the theorem, and the second parameter \lstinline{label} is the label used in cross-reference with \verb|ref{thm:label}|. Note that cross-references must be prefixed with \lstinline{thm:}. The effect is as follows:
\begin{theorem}{<theorem name>}{<label>}
The content of theorem.
\end{theorem}
Other theorem class environments with the same usage are:
\begin{table}[htbp]
\centering
\caption{Theorem Class Environments}
\begin{tabular}{llll}
\toprule
Environment & Label text & Prefix & Cross-reference \\
\midrule
definition & label & def & \lstinline|\ref{def:label}| \\
theorem & label & thm & \lstinline|\ref{thm:label}| \\
lemma & label & lem & \lstinline|\ref{lem:label}| \\
corrlary & label & cor & \lstinline|\ref{cor:label}| \\
proposition & label & pro & \lstinline|\ref{pro:label}| \\
\bottomrule
\end{tabular}%
\label{tab:theorem-class}%
\end{table}%
\subsection{Other Customized Environments}
The other three math environments can be used directly since there are no options for them, the \lstinline{example} environment usage:
\begin{lstlisting}[frame=single]
\begin{example}
This is the content of example environment.
\end{example}
\end{lstlisting}
The effect is as follows:
\begin{example}
This is the content of example environment.
\end{example}
These are all the same environments, except that
\begin{itemize}
\item example, exercise, problem environments numbering within chapter;
\item note with introductory symbol, proof with ending symbol;
\item conclusion environment with boldfaced keywords and normal paragraph content.
\end{itemize}
\section{Cover and Logo}
The cover image used in this template is from \href{https://pixabay.com/en/tea-time-poetry-coffee-reading-3240766/}{pixabay.com}\footnote{Thank China\TeX{} for providing free image source site, and \href{https://www.pexels.com/}{pexels.com} is also recommended.}. The image is completely free and can be used in any circumstance. The cover image size is $1280 \times 1024$, when changing the cover, please crop it according to the size of the cover picture strictly. Here is a free online image clipping site: \href{https://www.befunky.com/create/crop-photo/}{befunky.com}.
This Logo ratio is 1:1, that is square picture. In the replacement of the picture, please choose the appropriate picture to replace.
\section{List Environments}
This template uses \lstinline{tikz} to customize \lstinline{itemize} and \lstinline{enumerate} environments, the \lstinline{itemize} environment customized to the third depth, and \lstinline{enumerate} environment customized to fourth depth. The effect is as follows\\[2ex]
\begin{minipage}[b]{0.49\textwidth}
\begin{itemize}
\item first item of nesti;
\item second item of nesti;
\begin{itemize}
\item first item of nestii;
\item second item of nestii;
\begin{itemize}
\item first item of nestiii;
\item second item of nestiii.
\end{itemize}
\end{itemize}
\end{itemize}
\end{minipage}
\begin{minipage}[b]{0.49\textwidth}
\begin{enumerate}
\item first item of nesti;
\item second item of nesti;
\begin{enumerate}
\item first item of nestii;
\item second item of nestii;
\begin{enumerate}
\item first item of nestiii;
\item second item of nestiii.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{minipage}
\section{Bibliography}
This template uses Bib\TeX{} to generate the bibliography, the default bibliography style is \lstinline{aer}. Let's take a glance at the citation effect, ~\cite{Chen2018} use data from a major peer-to-peer lending marketplace in China to study whether female and male investors evaluate loan performance differently.
If you want to use Bib\TeX{}, you must create a file named \lstinline{reference.bib}, and add bib items (from Google Scholar, Mendeley, EndNote, and etc.) to \lstinline{reference.bib} file, and cite the bibkey in the \lstinline{tex} file. The Bib\TeX{} will automatically generate the bibliography for you for the reference you cited. If you want to add some noncited reference to the bibliography, you can use
\begin{lstlisting}
\nocite{EINAV2010, Havrylchyk2018}
\end{lstlisting}
\section{Preface}
If you want to add a preface before the first chapter without changing the number of chapter, you can use it before the first chapter
\begin{lstlisting}[frame=single]
\chapter*{Preface}
\addcontentsline{toc}{chapter}{Preface}
\markboth{Preface}{}
The content of Preface.
\end{lstlisting}
\chapter{ElegantBook Writing Sample}
\lipsum[1]
% source: https://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/Theorems.html
\section{Writing Sample}
We will define the integral of a measurable function in three steps. First, we define the integral of a nonnegative simple function. Let $E$ be the measurable set in $\mathcal{R}^N$.
\begin{definition}{Left Coset}{}
Let $H$ be a subgroup of a group~$G$. A \emph{left coset} of $H$ in $G$ is a subset of $G$ that is of the form $xH$, where $x \in G$ and $xH = \{ xh : h \in H \}$. Similarly a \emph{right coset} of $H$ in $G$ is a subset of $G$ that is of the form $Hx$, where $Hx = \{ hx : h \in H \}$
\end{definition}
\begin{note}
Note that a subgroup~$H$ of a group $G$ is itself a left coset of $H$ in $G$.
\end{note}
\lipsum[2]
\begin{theorem}{Lagrange's Theorem}{}
Let $G$ be a finite group, and let $H$ be a subgroup of $G$. Then the order of $H$ divides the order of $G$.
\end{theorem}
\lipsum[3]
\begin{proposition}{Size of Left Coset}{}
Let $H$ be a finite subgroup of a group $G$. Then each left coset of $H$ in $G$ has the same number of elements as $H$.
\end{proposition}
\begin{proof}
Let $z$ be some element of $xH \cap yH$. Then $z = xa$ for some $a \in H$, and $z = yb$ for some $b \in H$. If $h$ is any element of $H$ then $ah \in H$ and $a^{-1}h \in H$, since $H$ is a subgroup of $G$. But $zh = x(ah)$ and $xh = z(a^{-1}h)$ for all $h \in H$. Therefore $zH \subset xH$ and $xH \subset zH$, and thus $xH = zH$. Similarly $yH = zH$, and thus $xH = yH$, as required.
\end{proof}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.6\textwidth]{scatter.pdf}
\caption{Matplotlib: Scatter Plot Example\label{fig:scatter}}
\end{figure}
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. While there are many types of regression analysis, at their core they all examine the influence of one or more independent variables on a dependent variable. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.
Let's continue using our application training example. In this case, we'd want to measure the historical levels of satisfaction with the events from the past three years or so, as well as any information possible in regards to the independent variables.
\begin{table}[htbp]
\small
\centering
\caption{Auto MPG and Price \label{tab:reg}}
\begin{tabular}{lcc}
\toprule
& (1) & (2) \\
\midrule
mpg & -238.90*** & -49.51 \\
& (53.08) & (86.16) \\
weight & & 1.75*** \\
& & (0.641) \\
constant & 11,253*** & 1,946 \\
& (1,171) & (3,597) \\
obs & 74 & 74 \\
$R^2$ & 0.220 & 0.293 \\
\bottomrule
\multicolumn{3}{l}{\scriptsize Standard errors in parentheses} \\
\multicolumn{3}{l}{\scriptsize *** p<0.01, ** p<0.05, * p<0.1} \\
\end{tabular}%
\end{table}%
\lipsum[1-2]
\begin{itemize}
\item Routing and resource discovery;
\begin{itemize}
\item Language Models
\item Vector Space Models
\end{itemize}
\item Resilient and scalable computer networks;
\item Distributed storage and search.
\end{itemize}
\nocite{EINAV2010,Havrylchyk2018}
\bibliography{reference}
\appendix
\chapter{Mathematical Tools}
This appendix covers some of the basic mathematics used in econometrics. We briefly discuss the properties of summation operators, study the properties of linear and some nonlinear equations, and review the ratios and percentages. We also introduce some special functions that are common in econometrics applications, including quadratic functions and natural logarithms. The first four sections require only basic algebraic techniques. The fifth section briefly reviews differential Calculus Although Calculus is not necessary to understand much of this book, it is used in some of the end-of-chapter appendices and in some of the more advanced topics in part 3.
\section{Summation Operator and Description Statistics}
\textbf{Summation Operator} is an abbreviation used to express the summation of numbers, it plays an important role in statistics and econometrics analysis. If $\{x_i: i=1, 2, \ldots, n\}$ is a sequence of $n$ numbers, the summation of the $n$ numbers is
\begin{equation}
\sum_{i=1}^n x_i \equiv x_1 + x_2 +\cdots + x_n
\end{equation}
\chapter{A Minimal Example}
\begin{lstlisting}[frame=single]
\documentclass{elegantbook}
% title info
\title{Title}
\subtitle{Subtitle is here}
% bio info
\author{Your Name}
\institute{XXX University}
\date{\today}
% extra info
\version{1.00}
\equote{Victory won\rq t come to us unless we go to it. --- M. Moore}
\logo{logo.png}
\cover{cover.jpg}
\begin{document}
\maketitle
\tableofcontents
\mainmatter
\hypersetup{pageanchor=true}
% add preface chapter here if needed
\chapter{Example Chapter Title}
The content of chapter one.
\bibliography{reference}
\appendix
\chapter{Appendix Chapter Title}
The content of appendix 1.
\end{document}
\end{lstlisting}
\end{document}

View File

@@ -1,15 +1,15 @@
%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%
%% start of file `elegantbook.cls'. %% start of file `elegantbook.cls'.
%% Copyright 2013-2019 ElegantLaTeX (ddswhu@126.com) %% Copyright 2013-2019 ElegantLaTeX (elegantlatex2e@gmail.com)
%% %%
%% This work may be distributed and/or modified freely %% This work may be distributed and/or modified freely
%% available at https://ddswhu.me/resource/ %% available at https://github.com/ElegantLaTeX/ElegantBook
% % % %
%% Last Modification 2018-12-31 %% Last Modification 2019-02-25
%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%
% % !Mode:: "TeX:UTF-8" % % !Mode:: "TeX:UTF-8"
\NeedsTeXFormat{LaTeX2e} \NeedsTeXFormat{LaTeX2e}
\ProvidesClass{elegantbook}[2018/12/31 v3.02 ElegantBook document class] \ProvidesClass{elegantbook}[2019/02/24 v3.06 ElegantBook document class]
\RequirePackage{kvoptions} \RequirePackage{kvoptions}
\RequirePackage{etoolbox} \RequirePackage{etoolbox}
@@ -17,13 +17,16 @@
\newcommand{\ekv}[1]{\kvsetkeys{ELEGANT}{#1}} \newcommand{\ekv}[1]{\kvsetkeys{ELEGANT}{#1}}
% ----- Colors ----- % ----- Colors -----
\DeclareStringOption[green]{color}[green] \DeclareStringOption[green]{color}
\DeclareStringOption[en]{lang}
% ----- backward compatibility % ----- backward compatibility
\DeclareVoidOption{green}{\ekv{color = green}} \DeclareVoidOption{green}{\ekv{color = green}}
\DeclareVoidOption{cyan}{\ekv{color = cyan}} \DeclareVoidOption{cyan}{\ekv{color = cyan}}
\DeclareVoidOption{blue}{\ekv{color = blue}} \DeclareVoidOption{blue}{\ekv{color = blue}}
\DeclareVoidOption{plain}{\ekv{color = plain}}
\DeclareVoidOption{nocolor}{\ekv{color = none}} \DeclareVoidOption{nocolor}{\ekv{color = none}}
\DeclareVoidOption{en}{\ekv{lang=en}}
\DeclareVoidOption{cn}{\ekv{lang=cn}}
% ----- Math option ----- % ----- Math option -----
\newcommand\mailto[1]{\href{mailto:#1}{\nolinkurl{#1}}} \newcommand\mailto[1]{\href{mailto:#1}{\nolinkurl{#1}}}
@@ -37,19 +40,62 @@
\ProcessKeyvalOptions*\relax \ProcessKeyvalOptions*\relax
% \ProcessOptions*\relax % \ProcessOptions*\relax
\LoadClass[12pt,a4paper,openany]{book} \LoadClass[12pt,a4paper,oneside,openany]{book}
\RequirePackage{indentfirst}
\usepackage[UTF8,space=auto,scheme=plain]{ctex}
\usepackage{indentfirst}
\setlength\parindent{2em} \setlength\parindent{2em}
% fontsetting
\RequirePackage{ifxetex}
\ifxetex
\RequirePackage{fontenc}
\RequirePackage[no-math]{fontspec}
\setmainfont{Times New Roman}[NFSSFamily=ntxtlf]
\setsansfont{Arial}
%\setmonofont[Scale=0.9]{Courier New}
\RequirePackage{xeCJK}
\RequirePackage{xunicode}
\setCJKmainfont[BoldFont={SimHei},ItalicFont={KaiTi}]{SimSun}
\setCJKsansfont[BoldFont={SimHei},ItalicFont={KaiTi}]{KaiTi}
\setCJKmonofont[BoldFont={SimHei},ItalicFont={KaiTi},Scale=0.7]{Microsoft YaHei}
\XeTeXlinebreaklocale "zh"
\XeTeXlinebreakskip = 0pt plus 1pt minus 0.1pt
\RequirePackage{newtxmath}
%\DeclareSymbolFont{operators}{OT1}{ntxtlf}{m}{n}
%\SetSymbolFont{operators}{bold}{OT1}{ntxtlf}{b}{n}
\setCJKfamilyfont{zhsong}{SimSun}
\setCJKfamilyfont{zhhei}{SimHei}
\setCJKfamilyfont{zhkai}{KaiTi}
\setCJKfamilyfont{zhfs}{FangSong}
\newcommand*{\songti}{\CJKfamily{zhsong}}
\newcommand*{\heiti}{\CJKfamily{zhhei}}
\newcommand*{\kaishu}{\CJKfamily{zhkai}}
\newcommand*{\fangsong}{\CJKfamily{zhfs}}
\else
\RequirePackage{fontenc}
\RequirePackage{newtxtext}
\RequirePackage{newtxmath}
\RequirePackage[UTF8, scheme=plain]{ctex}
\fi
\RequirePackage[scale=0.7]{FiraMono}
%
% font setting for text and math % font setting for text and math
\RequirePackage[T1]{fontenc} % \RequirePackage[T1]{fontenc}
\RequirePackage{newtxtext} % \RequirePackage{newtxtext}
\RequirePackage{newtxmath} % \RequirePackage{newtxmath}
\RequirePackage[scale=0.85]{newtxtt} % \RequirePackage[scale=0.85]{newtxtt}
\RequirePackage{type1cm} \RequirePackage{anyfontsize}
\DeclareSymbolFont{cmlargesymbols}{OMX}{cmex}{m}{n}
\DeclareMathSymbol{\intop}{\mathop}{cmlargesymbols}{"5A}
\def\int{\intop\nolimits}
\DeclareMathSymbol{\ointop}{\mathop}{cmlargesymbols}{"49}
\def\oint{\ointop\nolimits}
\DeclareMathSymbol{\sumop}{\mathop}{cmlargesymbols}{"58}
\let\sum\sumop
\DeclareMathSymbol{\prodop}{\mathop}{cmlargesymbols}{"59}
\let\prod\prodop
% ----- Handle Colors ----- % ----- Handle Colors -----
@@ -57,151 +103,180 @@
\RequirePackage{xcolor} \RequirePackage{xcolor}
\ifdefstring{\ELEGANT@color}{green}{ \ifdefstring{\ELEGANT@color}{green}{
\definecolor{main}{RGB}{0,120,2}% \definecolor{main}{RGB}{0,120,2}%
\definecolor{second}{RGB}{230,90,7}% \definecolor{second}{RGB}{230,90,7}%
\definecolor{third}{RGB}{0,160,152}% \definecolor{third}{RGB}{0,160,152}%
}{\relax} }{\relax}
\ifdefstring{\ELEGANT@color}{cyan}{ \ifdefstring{\ELEGANT@color}{cyan}{
\definecolor{main}{RGB}{0,175,152}% \definecolor{main}{RGB}{0,175,152}%
\definecolor{second}{RGB}{239,126,30}% \definecolor{second}{RGB}{239,126,30}%
\definecolor{third}{RGB}{120,8,13}% \definecolor{third}{RGB}{120,8,13}%
}{\relax} }{\relax}
\ifdefstring{\ELEGANT@color}{blue}{ \ifdefstring{\ELEGANT@color}{blue}{
\definecolor{main}{RGB}{20,50,104}% \definecolor{main}{RGB}{20,50,104}%
\definecolor{second}{RGB}{180,50,131}% \definecolor{second}{RGB}{180,50,131}%
\definecolor{third}{RGB}{7,127,128}% \definecolor{third}{RGB}{7,127,128}%
}{\relax}
\ifdefstring{\ELEGANT@color}{plain}{
\definecolor{main}{RGB}{50,50,50}%
\definecolor{second}{RGB}{50,50,50}%
\definecolor{third}{RGB}{50,50,50}%
}{\relax} }{\relax}
%green color
\definecolor{main1}{RGB}{0,120,2}
\definecolor{second1}{RGB}{230,90,7}
\definecolor{third1}{RGB}{0,160,152}
%cyan color
\definecolor{main2}{RGB}{0,175,152}
\definecolor{second2}{RGB}{239,126,30}
\definecolor{third2}{RGB}{120,8,13}
%blue color
\definecolor{main3}{RGB}{20,50,104}
\definecolor{second3}{RGB}{180,50,131}
\definecolor{third3}{RGB}{7,127,128}
% corlor definition
\definecolor{winered}{rgb}{0.5,0,0} \definecolor{winered}{rgb}{0.5,0,0}
\definecolor{bule}{RGB}{18,29,57}
\AtBeginDocument{
\input{base.tex} \newcommand{\base}[2]{%
\nointerlineskip \vspace{0.1\baselineskip}\hspace{\fill}
{\color{#1}
\resizebox{0.3\linewidth}{1.5ex}
{{%
{\begin{tikzpicture}
\node (C) at (0,0) {};
\node (D) at (4,0) {};
\path (C) to [ornament=#2] (D);
\end{tikzpicture}}}}}%
\hspace{\fill}
\par\nointerlineskip \vspace{0.1\baselineskip}
} }
\providecommand{\base}{
\begin{tikzpicture}[scale=0.2]
\triz{0}{0}
\ellz{128}
\intz{149}
\ellz{170}
\intz{191}
\ellz{212}
\triz{341}{180}
\end{tikzpicture}}
%\newcommand*{\base}{
%}
% ----- Title Style ----- % ----- Title Style -----
\ifdefstring{\ELEGANT@titlestyle}{hang}{\def\style{hang}}{\relax} \ifdefstring{\ELEGANT@titlestyle}{hang}{\def\style{hang}}{\relax}
\ifdefstring{\ELEGANT@titlestyle}{display}{\def\style{display}}{\relax} \ifdefstring{\ELEGANT@titlestyle}{display}{\def\style{display}}{\relax}
\newtoks\zhtitle
\newtoks\entitle
\newtoks\email \newtoks\email
\newtoks\version \newtoks\version
\newtoks\enend \newtoks\institute
\newtoks\zhend \newtoks\subtitle
%%
\RequirePackage{enumerate}
% list/itemize/enumerate setting
\RequirePackage[shortlabels]{enumitem}
\setlist{nolistsep}
%% % caption settings
\renewcommand{\contentsname}{\hspace{2em}} \RequirePackage{caption}
\renewcommand{\figurename}{} \captionsetup{labelfont = bf}
\renewcommand{\tablename}{} \RequirePackage[font=small,labelfont={bf,color=main}]{caption}
\renewcommand{\partname}{} \captionsetup[table]{skip=3pt}
\renewcommand{\listfigurename}{} \captionsetup[figure]{skip=3pt}
\renewcommand{\listtablename}{}
\renewcommand{\bibname}{}
\renewcommand{\appendixname}{\hspace{2em}}
\renewcommand{\indexname}{\hspace{2em}}
% more pretty font %%
\linespread{1.3} \linespread{1.3}
\RequirePackage{microtype} \RequirePackage{microtype}
\RequirePackage{graphicx}
%\RequirePackage{enumerate}
\RequirePackage{amsmath,mathrsfs,amsfonts}
\RequirePackage{booktabs} \RequirePackage{booktabs}
\RequirePackage{multicol} \RequirePackage{multicol}
\RequirePackage{xcolor} \RequirePackage{xcolor}
\RequirePackage{graphicx}
\RequirePackage{fancyvrb} \RequirePackage{fancyvrb}
\graphicspath{{image/}{figure/}{fig/}{img/}} \RequirePackage{makecell,lipsum,texnames,setspace}
%%
\ifdefstring{\ELEGANT@lang}{en}{
\newcommand\figref[1]{\textbf{Figure}~\ref{#1}}
\newcommand\tabref[1]{\textbf{Table}~\ref{#1}}
\renewcommand{\chaptername}{Chapter \thechapter}
}{\relax}
\ifdefstring{\ELEGANT@lang}{cn}{
\renewcommand{\contentsname}{}
\renewcommand{\figurename}{}
\renewcommand{\tablename}{}
\renewcommand{\partname}{ \thepart\; }
\renewcommand{\listfigurename}{}
\renewcommand{\listtablename}{}
\renewcommand{\bibname}{}
\renewcommand{\appendixname}{}
\renewcommand{\indexname}{}
\newcommand\figref[1]{\textbf{}~\ref{#1}}
\newcommand\tabref[1]{\textbf{}~\ref{#1}}
\renewcommand{\chaptername}{ \thechapter\;}
}{\relax}
%%
\RequirePackage{graphicx}
\RequirePackage{enumerate}
\RequirePackage{amsmath,mathrsfs,amsfonts}
\RequirePackage{booktabs}
\linespread{1.3}
\graphicspath{{./figure/}{./figures/}{./image/}{./images/}{./graphics/}{./graphic/}{./pictures/}{./picture/}} \graphicspath{{./figure/}{./figures/}{./image/}{./images/}{./graphics/}{./graphic/}{./pictures/}{./picture/}}
\newcommand*{\myquote}[1]{\def\@myquote{#1}} \RequirePackage{tikz}
\usetikzlibrary{backgrounds,calc,shadows}
\usepackage[object=vectorian]{pgfornament} %%
\newcommand*{\logo}[1]{ \newcommand*{\eitemi}{\tikz \draw [baseline, ball color=main, draw=main] circle (2pt);}
\def\@logo{\includegraphics[width=0.3\textwidth]{#1} \newcommand*{\eitemii}{\tikz \draw [baseline, fill=main,draw=main,circular drop shadow] circle (2pt);}
} \newcommand*{\eitemiii}{\tikz \draw [baseline, fill=main,draw=main] circle (2pt);}
} \setlist[enumerate,1]{label=\color{main}\arabic*.}
\setlist[enumerate,2]{label=\color{main}(\alph*).}
%% \setlist[enumerate,3]{label=\color{main}\Roman*.}
\RequirePackage{wallpaper} \setlist[enumerate,4]{label=\color{main}\Alph*.}
\newcommand*{\cover}[1]{\def\@cover{ \setlist[itemize,1]{label={\eitemi}}
\ThisTileWallPaper{\paperwidth}{\paperheight}{#1} \setlist[itemize,2]{label={\eitemii}}
} \setlist[itemize,3]{label={\eitemiii}}
}
\RequirePackage{natbib}
\setlength{\bibsep}{0.0pt}
\def\bibfont{\footnotesize}
%% %%
\RequirePackage{hyperref}
\AtBeginDocument{
\hypersetup{
pdftitle = {\the\zhtitle\the\zhend},
pdfauthor = {\@author}
}
}
\hypersetup{
breaklinks,
unicode,
bookmarksnumbered=true,
bookmarksopen=true,
pdfsubject=\@author \@title Book,
pdfkeywords={ElegantBook},
pdfcreator={XeLaTeX with ElegantBook class},
colorlinks,
linkcolor=main,
citecolor=winered,
plainpages=false,
pdfstartview=FitH,
pdfborder={0 0 0},
linktocpage
}
\RequirePackage{geometry} \RequirePackage{geometry}
\geometry{ \geometry{
a4paper, a4paper,
left=27mm, %% or inner=23mm % left=27mm, %% or inner=23mm
right=27mm, %% or outer=18mm % right=27mm, %% or outer=18mm
top=25.4mm, bottom=25.4mm, top=25.4mm, bottom=25.4mm,
headheight=2.17cm, headheight=2.17cm,
headsep=4mm, headsep=4mm,
footskip=12mm footskip=12mm
} }
\RequirePackage{hyperref}
\hypersetup{
breaklinks,
unicode,
linktoc=all,
bookmarksnumbered=true,
bookmarksopen=true,
pdfkeywords={ElegantBook},
colorlinks,
linkcolor=winered,
citecolor=winered,
urlcolor = winered,
plainpages=false,
pdfstartview=FitH,
pdfborder={0 0 0},
linktocpage
}
%% %%
\RequirePackage[center,pagestyles]{titlesec} \RequirePackage[center,pagestyles]{titlesec}
\renewcommand{\chaptername}{ \thechapter\;} \RequirePackage{apptools}
\RequirePackage[toc,page]{appendix}
\titleformat{\chapter}[\style]{\bfseries} \titleformat{\chapter}[\style]{\bfseries}
{\filcenter\LARGE\enspace\bfseries{\color{main}\chaptername}\enspace}{1pt}{\bfseries\color{main}\LARGE\filcenter}[\filcenter\base] {\filcenter\LARGE\enspace\bfseries{\color{main}\IfAppendix{\appendixname}{\chaptername}\enspace}}{1pt}{\bfseries\color{main}\LARGE\filcenter}[\filcenter\base{main}{88}]
\titleformat{\section}[hang]{\bfseries} \titleformat{\section}[hang]{\bfseries}
{\hspace{-2.45em}\Large\bfseries{\color{main}\thesection}\enspace}{1pt}{\color{main}\Large\bfseries\filright} {\hspace{-2.45em}\Large\bfseries{\color{main}\thesection}\enspace}{1pt}{\color{main}\Large\bfseries\filright}
@@ -209,34 +284,25 @@
\titleformat{\subsection}[hang]{\bfseries} \titleformat{\subsection}[hang]{\bfseries}
{\hspace{-2.45em}\large\bfseries\color{main}\thesubsection\enspace}{1pt}{\color{main}\large\bfseries\filright} {\hspace{-2.45em}\large\bfseries\color{main}\thesubsection\enspace}{1pt}{\color{main}\large\bfseries\filright}
\titleformat{\subsubsection}[hang]{\bfseries}
{\hspace{-2.45em}\large\bfseries\color{main}\thesubsection\enspace}{1pt}{\color{main}\large\bfseries\filright}
\titlespacing{\chapter}{0pt}{0pt}{1.5\baselineskip} \titlespacing{\chapter}{0pt}{0pt}{1.5\baselineskip}
%\titlespacing{\subsection}{0pt}{0.5\baselineskip}{-\baselineskip} %\titlespacing{\subsection}{0pt}{0.5\baselineskip}{-\baselineskip}
\RequirePackage{caption}
\captionsetup{labelfont = bf}
% list/itemize/enumerate setting % list/itemize/enumerate setting
\RequirePackage[shortlabels]{enumitem} \RequirePackage[shortlabels]{enumitem}
\setlist{nolistsep} \setlist{nolistsep}
% caption settings
\RequirePackage[font=small,labelfont={bf}]{caption}
\captionsetup[table]{skip=3pt}
\captionsetup[figure]{skip=3pt}
\definecolor{bule}{RGB}{18,29,57}
\RequirePackage[most]{tcolorbox} \RequirePackage[most]{tcolorbox}
\tcbset{ \tcbset{
common/.style={ common/.style={
fontupper=\kaishu, fontupper=\itshape,
lower separated=false, lower separated=false,
coltitle=white, coltitle=white,
colback=gray!10, colback=gray!10,
@@ -269,49 +335,99 @@
}, },
} }
\newtcbtheorem[auto counter,number within=chapter]{definition}{}{defstyle}{def} \newtcbtheorem[auto counter,number within=chapter]{definition}{
\newtcbtheorem[auto counter,number within=chapter]{theorem}{}{thmstyle}{thm} \ifdefstring{\ELEGANT@lang}{en}{Definition}{}
\newtcbtheorem[auto counter,number within=chapter]{proposition}{}{propstyle}{prop} }{defstyle}{def}
\newtcbtheorem[auto counter,number within=chapter]{corollary}{}{thmstyle}{cor}
\newtcbtheorem[auto counter,number within=chapter]{lemma}{}{thmstyle}{lemma}
\newtcbtheorem[auto counter,number within=chapter]{theorem}{
\ifdefstring{\ELEGANT@lang}{en}{Theorem}{}
}{thmstyle}{thm}
\newtcbtheorem[auto counter,number within=chapter]{proposition}{
\ifdefstring{\ELEGANT@lang}{en}{Proposition}{}
}{propstyle}{pro}
\newtcbtheorem[auto counter,number within=chapter]{corollary}{
\ifdefstring{\ELEGANT@lang}{en}{Corollary}{}
}{thmstyle}{cor}
\newtcbtheorem[auto counter,number within=chapter]{lemma}{
\ifdefstring{\ELEGANT@lang}{en}{Lemma}{}
}{thmstyle}{lem}
%% Example with counter %% Example with counter
\newcounter{example}[chapter] \newcounter{exam}[chapter]
\renewcommand{\theexample}{\thechapter.\arabic{example}} \setcounter{exam}{0}
\newenvironment{example}{\par\noindent\textbf{\,\refstepcounter{example}\theexample}\color{black!90}}{\par} \renewcommand{\theexam}{\thechapter.\arabic{exam}}
\newenvironment{example}[1][]{
\refstepcounter{exam}\par\medskip\noindent \textbf{\color{main}{
\ifdefstring{\ELEGANT@lang}{en}{Example}{}
}~\theexam #1: }\rmfamily %
}{
\par\medskip\ignorespacesafterend %
}
%% Exercise with counter %% Exercise with counter
\newcounter{exercise}[chapter] \newcounter{exer}[chapter]
\renewcommand{\theexercise}{\thechapter.\arabic{exercise}} \setcounter{exer}{0}
\newenvironment{exercise}{\par\noindent\textbf{\,\refstepcounter{exercise}\theexercise}}{\par} \renewcommand{\theexer}{\thechapter.\arabic{exer}}
\newenvironment{exercise}[1][]{
\refstepcounter{exer}\par\medskip\noindent \textbf{\color{main}{
\ifdefstring{\ELEGANT@lang}{en}{Exercise}{}
}~\theexer #1: }\rmfamily %
}{
\par\medskip\ignorespacesafterend %
}
%% Exercise with counter
\newcounter{prob}[chapter]
\setcounter{prob}{0}
\renewcommand{\theprob}{\thechapter.\arabic{prob}}
\newenvironment{problem}[1][]{
\refstepcounter{prob}\par\medskip\noindent \textbf{\color{main}{
\ifdefstring{\ELEGANT@lang}{en}{Problem}{}
}~\theprob #1: }\rmfamily %
}{
\par\medskip\ignorespacesafterend %
}
%%define the note and proof environment %%define the note and proof environment
\RequirePackage{pifont,manfnt} \RequirePackage{pifont,manfnt}
\newenvironment{note}{\par\noindent{\makebox[0pt][r]{\scriptsize\color{red!90}\textdbend\quad}\textbf{}}\itshape}{\par}
\newenvironment{proof}{\par\noindent\textbf{}\color{black!90}\small}{\hfill$\Box$\quad\par}
\newenvironment{remark}{\noindent\textbf{}}{\par}
\newenvironment{assumption}{\par\noindent\textbf{}}{\par}
\newenvironment{conclusion}{\par\noindent\textbf{}}{\par}
\newenvironment{solution}{\par\noindent\textbf{}}{\par}
\newenvironment{property}{\par\noindent\textbf{}}{\par}
\newenvironment{note}{\par\noindent{\makebox[0pt][r]{\scriptsize\color{red!90}\textdbend\quad}\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Note:}{}
}}\itshape}{\par}
\newenvironment{proof}{\par\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Proof:}{}
}\color{black!90}\small}{\hfill$\Box$\quad\par}
\newenvironment{remark}{\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Remark:}{}
}}{\par}
\newenvironment{assumption}{\par\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Assumption:}{}
}}{\par}
\newenvironment{conclusion}{\par\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Conclusion:}{}
}}{\par}
\newenvironment{solution}{\par\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Solution:}{}
}}{\par}
\newenvironment{property}{\par\noindent\textbf{\color{main}
\ifdefstring{\ELEGANT@lang}{en}{Property:}{}
}}{\par}
% %
\RequirePackage{fancyhdr} \RequirePackage{fancyhdr}
\RequirePackage{lastpage} \RequirePackage{lastpage}
\fancyhf{} \fancyhf{}
\fancyhead[EL,OR]{\color{main}--\thepage/\pageref{LastPage}--} \fancyhead[EL,OR]{\color{main}--\thepage/\pageref*{LastPage}--}
\fancyhead[ER]{\color{main}\em\nouppercase\leftmark{}} \fancyhead[ER]{\color{main}\em\nouppercase\leftmark{}}
\fancyhead[OL]{\color{main}\em\nouppercase\rightmark} \fancyhead[OL]{\color{main}\em\nouppercase\rightmark}
\fancyfoot[c]{\base} \fancyfoot[c]{\base{main}{88}}
\renewcommand{\headrule}{\color{main}\hrule width\textwidth} \renewcommand{\headrule}{\color{main}\hrule width\textwidth}
\pagestyle{fancy} \pagestyle{fancy}
@@ -319,69 +435,76 @@
\renewcommand{\sectionmark}[1]{\markright{\thesection\; #1}{} } \renewcommand{\sectionmark}[1]{\markright{\thesection\; #1}{} }
\renewcommand{\chaptermark}[1]{\markboth{\chaptername \; #1\;}{}} \renewcommand{\chaptermark}[1]{\markboth{\chaptername \; #1\;}{}}
\DeclareSymbolFont{cmlargesymbols}{OMX}{cmex}{m}{n}
\DeclareMathSymbol{\intop}{\mathop}{cmlargesymbols}{"5A}
\def\int{\intop\nolimits}
\DeclareMathSymbol{\ointop}{\mathop}{cmlargesymbols}{"49}
\def\oint{\ointop\nolimits}
\DeclareMathSymbol{\sumop}{\mathop}{cmlargesymbols}{"58}
\let\sum\sumop
\DeclareMathSymbol{\prodop}{\mathop}{cmlargesymbols}{"59}
\let\prod\prodop
\newcommand\figref[1]{\textbf{Figure}~\ref{#1}}
\newcommand\tabref[1]{\textbf{Table}~\ref{#1}}
%% %%
\newcommand*{\equote}[1]{\def\@equote{#1}}
\def\maketitle{% \newcommand*{\logo}[1]{
\thispagestyle{empty} \def\@logo{\includegraphics[width=0.3\textwidth]{#1}
% \@cover }
\vfill }
\vspace*{2cm} \newcommand*{\cover}[1]{
\begin{center} \def\@logo{\includegraphics[width=\linewidth]{cover.jpg}
\color{second} }
\rule{0.8\textwidth}{2pt}\\
\Huge {\color{main} \bfseries \the\entitle } {\color{second} \bfseries \the\enend}\\
{\Huge \bfseries{\color{main} \the\zhtitle } \the\zhend}\\
\rule{0.8\textwidth}{2pt}
\end{center}
\vskip3ex
\begin{figure}[htp]
\centering
\@logo
\end{figure}
\begin{center}
\begin{minipage}{0.65\textwidth}
\indent\centering\color{bule}\@myquote
\end{minipage}
\end{center}
\vfill
\vspace{2cm}
\begin{flushright}
\color{second}
\rule{0.45\textwidth}{1pt}\\
{\color{main}\@author}\\
{\color{main}\today}\\
: \hyperlink{\the\email}{\the\email}\\
\rule{0.45\textwidth}{1pt}
\end{flushright}
\vfill
\begin{center}
\color{second} : \the\version
\end{center}
\vfil\eject
} }
\renewcommand*{\maketitle}{%
\hypersetup{pageanchor=false}
\begin{titlepage}
\newpage
\newgeometry{margin = 0in}
\parindent=0pt
\renewcommand\baselinestretch{2.5}
\includegraphics[width=\linewidth]{cover.jpg}
\setlength{\fboxsep}{0pt}
\colorbox{second}{\makebox[\linewidth][c]{\shortstack[c]{\vspace{0.5in}}}}
\vfill
\hfill
\hspace{2em}
\begin{minipage}[c]{0.68\linewidth}
{\bfseries\Huge \@title\\}
{\color{darkgray}\bfseries\Large \the\subtitle\\[2ex]}
\color{gray}\kaishu\normalsize
{\renewcommand{\arraystretch}{0.618}
\begin{tabular}{l}
\ifdefstring{\ELEGANT@lang}{en}{\textbf{Author: }}{\textbf{}}\@author \\
\ifdefstring{\ELEGANT@lang}{en}{\textbf{Institute: }}{\textbf{}}\the\institute\\
\ifdefstring{\ELEGANT@lang}{en}{\textbf{Update: }}{\textbf{}}\@date\\
\ifdefstring{\ELEGANT@lang}{en}{\textbf{Version: }}{\textbf{}}\the\version \\
\end{tabular}}
\end{minipage}
\begin{minipage}[c]{0.27\linewidth}
\begin{tikzpicture}[remember picture,overlay]
\begin{pgfonlayer}{background}
\node[opacity=0.8,anchor=south east,outer sep=0pt,inner sep=0pt] at ($(current page.south east) +(-0.8in,1.5in)$) {\includegraphics[width=0.7\textwidth]{logo.png}};
\end{pgfonlayer}
\end{tikzpicture}
\end{minipage}
\vfill
\centerline{\itshape \@equote}
\vfill
\restoregeometry
\end{titlepage}
\thispagestyle{empty}
}
\RequirePackage{listings}
\definecolor{lightgrey}{rgb}{0.9,0.9,0.9}
\definecolor{frenchplum}{RGB}{190,20,83}
\lstset{language=[LaTeX]TeX,
texcsstyle=*\bf\color{winered}\ttfamily,
basicstyle=\ttfamily,
numbers=none,
breaklines=true,
keywordstyle=\bf\color{winered}\ttfamily,
commentstyle=\color{gray},
emph={elegantpaper,fontenc,fontspec,xeCJK,FiraMono,xunicode,newtxmath,figure,fig,image,img,table,itemize,enumerate,newtxtext,newtxtt,ctex,microtype,description,times,newtx,booktabs,tabular,PDFLaTeX,XeLaTeX,type1cm,BibTeX,device,color,mode,lang,amsthm,tcolorbox,titlestyle},
emphstyle={\color{frenchplum}},
morekeywords={DeclareSymbolFont,SetSymbolFont,toprule,midrule,bottomrule,institute,version,includegraphics,setmainfont,setsansfont,setmonofont ,setCJKmainfont,setCJKsansfont,setCJKmonofont,RequirePackage,figref,tabref,email,maketitle,keywords,definecolor,equote,logo,cover,subtitle,appendix,chapter,hypersetup,mainmatter,tableofcontents},
frame=none,
tabsize=2,
rulecolor=\color{main},
}
\bibliographystyle{aer}
\RequirePackage{natbib}
\setlength{\bibsep}{0.0pt}
\def\bibfont{\footnotesize}

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@@ -1,228 +0,0 @@
\documentclass{elegantbook}
\author{ddswhu \& Liam Huang}
\email{ddswhu@outlook.com}
\zhtitle{优美的 \LaTeX{} 书籍}
\zhend{模板}
\entitle{Elegant\LaTeX{} Book}
\enend{Template}
\version{3.02}
\myquote{Victory won\rq t come to us unless we go to it.}
\logo{logo.png}
\cover{cover.pdf}
%green color
\definecolor{main1}{RGB}{0,120,2}
\definecolor{second1}{RGB}{230,90,7}
\definecolor{third1}{RGB}{0,160,152}
%cyan color
\definecolor{main2}{RGB}{0,175,152}
\definecolor{second2}{RGB}{239,126,30}
\definecolor{third2}{RGB}{120,8,13}
%blue color
\definecolor{main3}{RGB}{20,50,104}
\definecolor{second3}{RGB}{180,50,131}
\definecolor{third3}{RGB}{7,127,128}
\usepackage{makecell}
\usepackage{lipsum}
\usepackage{texnames}
\begin{document}
\maketitle
\tableofcontents
\mainmatter
\chapter{Elegant\LaTeX{} 系列模板介绍}
值此版本发行之际,我们 Elegant\LaTeX{} 项目组向大家重新介绍一下我们的工作我们致力于打造一系列美观、优雅、简便的模板方便用户使用。Elegant\LaTeX{} 系列模板目前由 ElegantNoteElegantBookElegantPaperElegantBeamer 组成,分别用于排版笔记,书籍,工作论文和幻灯片讲稿。这些子项目的名词是一体的,请在使用这些名词的时候不要将其断开(如 Elegant Note 是不正确的写法。并且Elegant\LaTeX{} Book 指的即是 ElegantBook。
请用户在作者的主页下载最新版本,下载地址:\href{https://ddswhu.me/resource/}{https://ddswhu.me/resource/}。本文将介绍本模板的一些设置内容以及基本使用方法。如果您在使用此模板,欢迎把您使用此模板制作的成品发一份给我们,谢谢!如果您有其他问题,建议或者意见,欢迎联系我:\mailto{ddswhu@outlook.com}
\section{ElegantBook 更新说明}
在这几年间,我们收到了很多用户的反馈,主要的问题涉及到字体安装,编码支持,定理浮动,定理跨页,交叉引用等等。我们思前想后,原先让用户安装字体以追求视觉上的美观并不完美,用户陷入了巨大的麻烦,这违背了我们的模板初衷。因此我们在新版中删除了这部分,用户无需安装任何字体。让我们来看下此次 ElegantBook 模板 3.0 更新的主要内容有:
\begin{enumerate}[noitemsep]
\item 删除了自定义字体设置,改用 \texttt{ctex} 宏包用以支持中文。
\item 使用 \texttt{tcolorbox} 宏包改写了原先的定理类环境,目前定理环境等均可以跨页。
\item 重新命名了定理类环境的名称theoremdefinitionproposition 等)。
\item 重新命名了颜色的名字firstsecondthird
\end{enumerate}
\section{未来更新计划}
\begin{enumerate}[noitemsep]
\item 设计一个适合的 LOGO
\item 重新设计 base 图标;
\item 重新设计一个好看的封面。
\item 将基础模板改为英文模板,添加选项使其支持中文。
\item 将最早的 ElegantNote 重新设计为简版发布。
\item 添加一个简化风格plain的颜色主题。
\end{enumerate}
\chapter{ElegantBook 设置说明}
\section{编译方式}
本模板基于基础的 book 文类,所以 book 的选项对于本模板也是有效的。默认编码为 UTF-8推荐使用 \TeX{} Live 编译。作者编写环境为 Win10(64bit) + \TeX{} Live 2018。由于使用的是 \texttt{ctex} 宏包,所以支持 \texttt{pdflatex} 以及 \texttt{xelatex} 编译。
\section{选项设置}
本文特殊选项设置共有 2 类,分为 {\color{main}主题颜色}设置 以及 {\color{main}章标题显示风格}设置。
第 1 类为{\color{main}主题颜色}设置,内置 3 组颜色主题,分别为 \verb|green|(默认)、\verb|cyan|、\verb|blue|,另外还有一个自定义的选项 \verb|nocolor|。调用颜色主题 \verb|green| 的方法为 \\
\verb|\documentclass[green]{elegantbook}| 或者 \verb|\documentclass[color=green]{elegantbook}|。需要改变颜色的话请选择 \verb|nocolor| 选项或者使用 \verb|color=none|,然后在导言区定义 main、second、third 颜色,具体的方法如下:
\begin{verbatim}
\definecolor{main}{RGB}{70,70,70} %定义 main 颜色值
\definecolor{second}{RGB}{115,45,2} %定义 second 颜色值
\definecolor{third}{RGB}{0,80,80} %定义 third 颜色值
\end{verbatim}
\begin{table}[htp]
\caption{ElegantBook 模板中的三套颜色主题\label{tab:color thm}}
\centering
\begin{tabular}{ccccc}
\toprule
& green & cyan & blue & 主要使用的环境\\
\midrule
main & \makecell{{\color{main1}\rule{1cm}{1cm}}}& \makecell{{\color{main2}\rule{1cm}{1cm}}}&\makecell{ {\color{main3}\rule{1cm}{1cm}}}& definition \\
second &\makecell{ {\color{second1}\rule{1cm}{1cm}}}& \makecell{{\color{second2}\rule{1cm}{1cm}}}&\makecell{ {\color{second3}\rule{1cm}{1cm}}}&theorem \ lemma \ corollary\\
third &\makecell{ {\color{third1}\rule{1cm}{1cm}}}& \makecell{{\color{third2}\rule{1cm}{1cm}}}&\makecell{ {\color{third3}\rule{1cm}{1cm}}}&proposition\\
\bottomrule
\end{tabular}
\end{table}
第 2 类为{\color{main} 章标题显示风格},包含 \verb|hang|(默认)与 \verb|display| 两种风格,区别在于章标题单行显示(\verb|hang|)与双行显示(\verb|display|),本说明使用了 \verb|hang|。调用方式为 \verb|\documentclass[hang]{elegantbook}| 或者 \verb|\documentclass[titlestyle=hang]{elegantbook}|。
综合起来,同时调用三个选项使用 \verb|\documentclass[color=X,titlestyle=Y]{elegantbook}|。其中 \verb|X| 可以选择 \verb|green|,\verb|cyan|,\verb|blue|,\verb|none|\verb|Z| 可以选择 \verb|hang| 或者 \verb|display|。
\section{数学环境简介}
在我们这个模板中,定义了三大类环境
\begin{enumerate}[noitemsep]
\item 定理类环境包含标题和内容两部分。根据格式的不同分为3种
\begin{itemize}[noitemsep]
\item {\color{main}\bfseries definition} 环境,含有一个可选项,编号以章节为单位,颜色为 {\color{main}main}
\item {\color{second}\bfseries theorem、lemma、corollary} 环境,颜色为主颜色 {\color{second}second},编号均以章节为单位;
\item {\color{third}\bfseries proposition} 环境,含有一个可选项,编号以章节为单位,颜色为 {\color{third}{third}}
\end{itemize}
\item 示例类环境,有 \textbf{example、exercise} 环境,自动编号,编号以章节为单位。
\item 证明类环境,有 \textbf{proof、note} 环境,特点是,有引导符或者结尾符,\textbf{note} 环境有引导符号,\textbf{proof} 环境有证明完毕标志。
\item 结论类环境,有\textbf{conclusion、assumption、propertyremark、solution} 环境,三者均以粗体的引导词为开头,和普通段落格式一致。
\end{enumerate}
\section{可编辑的字段}
在模板中,可以编辑的字段分别为作者 \verb|\author|、邮箱 \verb|\email|、中文标题 \verb|\zhtitle|、中文标题结尾 \verb|\zhend|、英文标题\verb| \entitle|、英文标题结尾 \verb|\enend|、名言 \verb|\myquote|、版本号 \verb|\version|。并且,可以根据自己的喜好把封面水印效果的 \verb|cover.pdf| 替换掉,以及封面中用到的 \verb|logo.png|。
\section{参考文献}
此模板使用了 Bib\TeX{} 来生成参考文献,默认使用的文献样式 aer 样式。参考文献示例:~\cite{Chen2018} 使用了中国一个大型的 P2P 平台人人贷的数据来检验男性投资者和女性投资者在投资表现上是否有显著差异。你可以在谷歌学术MendeleyEndnote 中获得文献条目bib item然后把它们添加到 \verb|reference.bib| 中。在文中引用的时候引用它们的键值bib key即可。注意需要在编译的过程中添加 Bib\TeX{} 编译。
\chapter{ElegantBook 写作示例}
\section{Lebesgue 积分}
在前面各章做了必要的准备后,本章开始介绍新的积分。在 Lebesgue 测度理论的基础上建立了 Lebesgue 积分,其被积函数和积分域更一般,可以对有界函数和无界函数统一处理。正是由于 Lebesgue 积分的这些特点,使得 Lebesgue 积分比 Riemann 积分具有在更一般条件下的极限定理和累次积分交换积分顺序的定理,这使得 Lebesgue 积分不仅在理论上更完善,而且在计算上更灵活有效。
Lebesgue 积分有几种不同的定义方式。我们将采用逐步定义非负简单函数,非负可测函数和一般可测函数积分的方式。
由于现代数学的许多分支如概率论、泛函分析、调和分析等常常用到一般空间上的测度与积分理论,在本章最后一节将介绍一般的测度空间上的积分。
\subsection{积分的定义}
我们将通过三个步骤定义可测函数的积分。首先定义非负简单函数的积分。以下设 $E$$\mathcal{R}^n$ 中的可测集。
\begin{definition}{可积性}{inter}
$ f(x)=\sum\limits_{i=1}^{k} a_i \chi_{A_i}(x)$$E$ 上的非负简单函数,其中 $\{A_1,A_2,\ldots,A_k\}$$E$ 上的一个可测分割,$a_1,a_2,\ldots,a_k$ 是非负实数。定义 $f$$E$ 上的积分为
\begin{equation}
\label{inter}
\int_{E} f dx = \sum_{i=1}^k a_i m(A_i).
\end{equation}
一般情况下 $0 \leq \int_{E} f dx \leq \infty$。若 $\int_{E} f dx < \infty$,则称 $f$$E$ 上可积。
\end{definition}
一个自然的问题是Lebesgue 积分与我们所熟悉的 Riemann 积分有什么联系和区别?在 4.4 在我们将详细讨论 Riemann 积分与 Lebesgue 积分的关系。这里只看一个简单的例子。设 $D(x)$ 是区间 $[0,1]$ 上的 Dirichlet 函数。即 $D(x)=\chi_{Q_0}(x)$,其中 $Q_0$ 表示 $[0,1]$ 中的有理数的全体。根据非负简单函数积分的定义,$D(x)$$[0,1]$ 上的 Lebesgue 积分为
\begin{equation}
\label{inter2}
\int_0^1 D(x)dx = \int_0^1 \chi_{Q_0} (x) dx = m(Q_0) = 0
\end{equation}
$D(x)$$[0,1]$ 上是 Lebesgue 可积的并且积分值为零。但 $D(x)$$[0,1]$ 上不是 Riemann 可积的。
有界变差函数是与单调函数有密切联系的一类函数。有界变差函数可以表示为两个单调递增函数之差。与单调函数一样,有界变差函数几乎处处可导。与单调函数不同,有界变差函数类对线性运算是封闭的,它们构成一线空间。
\begin{exercise}
$f\in L(\mathcal{R}^1)$$g$$\mathcal{R}^1$ 上的有界可测函数。证明函数
\begin{equation}
\label{ex:1}
I(t) = \int_{\mathcal{R}^1} f(x+t)g(x)dx \quad t \in \mathcal{R}^1
\end{equation}
$\mathcal{R}^1$ 上的连续函数。
\end{exercise}
\begin{theorem}{Fubini 定理}{31}
1$f(x,y)$$\mathcal{R}^p\times\mathcal{R}^q$ 上的非负可测函数,则对几乎处处的 $x\in \mathcal{R}^p$$f(x,y)$ 作为 $y$ 的函数是 $\mathcal{R}^q$ 上的非负可测函数,$g(x)=\int_{\mathcal{R}^q}f(x,y) dy$$\mathcal{R}^p$ 上的非负可测函数。并且
\begin{equation}
\label{eq:461}
\int_{\mathcal{R}^p\times\mathcal{R}^q} f(x,y) dxdy=\int_{\mathcal{R}^p}\left(\int_{\mathcal{R}^q}f(x,y)dy\right)dx.
\end{equation}
2$f(x,y)$$\mathcal{R}^p\times\mathcal{R}^q$ 上的可积函数,则对几乎处处的 $x\in\mathcal{R}^p$$f(x,y)$ 作为 $y$ 的函数是 $\mathcal{R}^q$ 上的可积函数,并且 $g(x)=\int_{\mathcal{R}^q}f(x,y) dy$$\mathcal{R}^p$ 上的可积函数。而且~\ref{eq:461} 成立。
\end{theorem}
\begin{note}
在本模板中引理lemma推论corollary )的样式和定理的样式一致,包括颜色,仅仅只有计数器的设置不一样。
\end{note}
我们说一个实变或者复变量的实值或者复值函数是在区间上平方可积的,如果其绝对值的平方在该区间上的积分是有限的。所有在勒贝格积分意义下平方可积的可测函数构成一个希尔伯特空间,也就是所谓的 $L^2$ 空间,几乎处处相等的函数归为同一等价类。形式上,$L^2$ 是平方可积函数的空间和几乎处处为 0 的函数空间的商空间。
\begin{proposition}{最优性原理}{max}
如果 $u^*$$[s,T]$ 上为最优解,则 $u^*$$[s,T]$ 任意子区间都是最优解,假设区间为 $[t_0,t_1]$ 的最优解为 $u^*$ ,则 $u(t_0)=u^{*}(t_0)$,即初始条件必须还是在 $u^*$ 上。
\end{proposition}
我们知道最小二乘法可以用来处理一组数据,可以从一组测定的数据中寻求变量之间的依赖关系,这种函数关系称为经验公式。本课题将介绍最小二乘法的精确定义及如何寻求点与点之间近似成线性关系时的经验公式。假定实验测得变量之间的 $n$ 个数据,则在平面上,可以得到 $n$ 个点,这种图形称为 “散点图”,从图中可以粗略看出这些点大致散落在某直线近旁, 我们认为其近似为一线性函数,下面介绍求解步骤。
考虑函数 $y=a+bx$, 其中 $a$$b$ 是待定常数。如果离散点完全的在一直线上,可以认为变量之间的关系为一元函数。但一般说来,这些点不可能在同一直线上。但是它只能用直线来描述时,计算值与实际值会产生偏差。当然要求偏差越小越好,但由于偏差可正可负,因此不能认为总偏差时,拟合函数很好地反映了变量之间的关系,但是因为此时每个偏差的绝对值可能很大。为了改进这一缺陷,就考虑用平均值来代替。但是由于绝对值不易作解析运算,因此,进一步用残差平方和函数来度量总偏差。偏差的平方和最小可以保证每个偏差都不会很大。于是问题归结为确定拟合函数中的常数和使残差平方和函数最小。
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.6\textwidth]{mpg.png}
\caption{MPG 和 Weight 的关系图\label{fig:mpg}}
\end{figure}
以最简单的一元线性模型来解释最小二乘法。什么是一元线性模型呢?监督学习中,如果预测的变量是离散的,我们称其为分类(如决策树,支持向量机等),如果预测的变量是连续的,我们称其为回归。回归分析中,如果只包括一个自变量和一个因变量,且二者的关系可用一条直线近似表示,这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量,且因变量和自变量之间是线性关系,则称为多元线性回归分析。对于二维空间线性是一条直线;对于三维空间线性是一个平面,对于多维空间线性是一个超平面。
\begin{property}
柯西列的性质
\begin{enumerate}[noitemsep]
\item $\{x_k\}$ 是柯西列,则其子列 $\{x_k^i\}$ 也是柯西列。
\item $x_k\in \mathcal{R}^n$$\rho(x,y)$ 是欧几里得空间,则柯西列是收敛的,$(\mathcal{R}^n,\rho)$ 空间是完备的。
\end{enumerate}
\end{property}
\begin{conclusion}
回归分析regression analysis) 是确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法。运用十分广泛,回归分析按照涉及的变量的多少,分为一元回归和多元回归分析;按照因变量的多少,可分为简单回归分析和多重回归分析;按照自变量和因变量之间的关系类型,可分为线性回归分析和非线性回归分析。如果在回归分析中,只包括一个自变量和一个因变量,且二者的关系可用一条直线近似表示,这种回归分析称为一元线性回归分析。如果回归分析中包括两个或两个以上的自变量,且自变量之间存在线性相关,则称为多重线性回归分析。
\end{conclusion}
\nocite{EINAV2010,Havrylchyk2018}
\bibliographystyle{aer}
\bibliography{reference}
\addcontentsline{toc}{chapter}{参考文献}
\end{document}

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# This file is the source file of the scatter.pdf
# source page: https://matplotlib.org/gallery/shapes_and_collections/scatter.html
import numpy as np
import matplotlib.pyplot as plt
# Fixing random state for reproducibility
np.random.seed(19680801)
N = 50
x = np.random.rand(N)
y = np.random.rand(N)
colors = np.random.rand(N)
area = (30 * np.random.rand(N))**2 # 0 to 15 point radii
ax = plt.subplot(111)
ax.scatter(x, y, s=area, c=colors, alpha=0.5)
# Hide the right and top spines
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
# Only show ticks on the left and bottom spines
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
plt.savefig('scatter.pdf', transparent=True)