<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[letterpaper,11pt]{article}
\usepackage{fixdif}
\date{2023/03/20\quad Version 2.1%
  \thanks{æºä»£ç&nbsp;è§~\hyperref{https://github.com/AlphaZTX/fixdif}{}{}{GitHub} 
  æˆ–~\hyperref{https://www.ctan.org/pkg/fixdif}{}{}{CTAN}ã€‚}
}
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\usepackage{manfnt,marginnote}
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\newcommand\attention[1][1]{\setcounter{fixdifattention}{1}%
  \ifnum#1=1 \def\attentiontext{\dbend}\else
  \def\attentiontext{\loop\dbend\kern1pt%
    \addtocounter{fixdifattention}{1}%
    \ifnum \value{fixdifattention}&lt;#1 \repeat\dbend}\fi%
  \marginnote{\hbox to 0pt{\hss\attentiontext}}}
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\begin{document}
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\thispagestyle{plain}

\begin{abstract}
\pkg{fixdif} å®åŒ…é‡å®šä¹‰äº† \LaTeX{} ä¸­çš„ \cs{d} å‘½ä»¤ï¼Œä½¿ä¹‹åœ¨æ•°å­¦æ¨¡å¼ä¸‹å¯ä»¥å¾—åˆ°
å¾®åˆ†ç®—ç¬¦ $\d{}$ï¼Œåœ¨æ­£æ–‡ä¸­ä»ç„¶æ˜¯åŽŸæ¥çš„é‡éŸ³ç¬¦å·ï¼ˆä¾‹å¦‚ |\d{o}| å¾—åˆ° \d oï¼‰ã€‚

æœ¬å®åŒ…æ”¯æŒä¸åŒçš„ç¼–è¯‘æ–¹å¼ï¼Œåœ¨ \pdflatexã€\xelatex{} å’Œ \lualatex{} å‡å¯ä½¿ç”¨ã€‚
æœ¬å®åŒ…åœ¨ \xelatex{} å’Œ \lualatex{} ä¸‹å…¼å®¹ \pkg{unicode-math} å®åŒ…ã€‚
\end{abstract}

\section*{\contentsname}
\begin{multicols}{2}
\parskip0pt
\csname @starttoc\endcsname{toc}
\end{multicols}

\section{èƒŒæ™¯}
æˆ‘ä»¬ä¸€èˆ¬æ›´æŽ¨èåœ¨å¾®åˆ†ç®—ç¬¦ä¸Žå‰é¢çš„å†…å®¹ä¹‹é—´ç•™å‡ºä¸€ä¸ªæ¯”è¾ƒå°çš„é—´è·\footnote{%
è§ \hyperref{https://tex.stackexchange.com/questions/14821/whats-the-%
proper-way-to-typeset-a-differential-operator}{}{}{\TeX.SX}ã€‚}ï¼Œæ¯”å¦‚åœ¨ä¸‹é¢å±•ç¤ºçš„
ä¸¤ç§æƒ…å†µä¸­ï¼Œå³è¾¹çš„æ¯”å·¦è¾¹çš„æ›´å¥½ï¼š
\[f(x)\mathrm{d}x \qquad\hbox{\&amp;}\qquad f(x)\d x.\]
å¾®åˆ†ç®—ç¬¦ $\d{}$ ä¸Žå…¶å‰é¢çš„è¡¨è¾¾å¼ä¹‹é—´çš„é—´è·å¯è®¤ä¸ºæ˜¯ä¹˜ç§¯çš„ä¸€ç§è¡¨ç¤ºã€‚

æœ‰äº›ç”¨æˆ·ä¹&nbsp;æƒ¯ä½¿ç”¨ä¸‹é¢çš„æ–¹æ³•å®šä¹‰ä¸€ä¸ªå®ï¼š
\begin{Verbatim}
\renewcommand\d{\mathop{\mathrm{d}}\!}
\end{Verbatim}
è¿™ä¸ªå‘½ä»¤åœ¨å¾ˆå¤šæƒ…å†µä¸‹ä¸ä¼šäº§ç”Ÿä»€ä¹ˆå¤§é—®é¢˜ï¼Œä½†æ˜¯åœ¨ä¸‹é¢ç»™å‡ºçš„ 3 ä¸ªä½¿ç”¨åœºæ™¯ä¸‹å°±ä¼šå‡ºçŽ°
ä¸å®¹å¿½ç•¥çš„é—®é¢˜ï¼š
\begin{enumerate}
\item å½“ $\d{}$ å‡ºçŽ°åœ¨ç”¨æ–œæ&nbsp;è¡¨ç¤ºçš„åˆ†å¼çš„åˆ†æ¯ä¸­æ—¶ï¼Œ$\d{}$ å‰é¢ä¼šç•™å‡ºå¤šä½™çš„é—´è·ã€‚
ä¾‹å¦‚ |$\d y/\d x$| å¾—åˆ° $\mathrm{d}y/\,\mathrm{d}x$ï¼›

\item ä¸Šé¢å®šä¹‰çš„ \cs{d} ä¼šè¦†ç›–åŽŸæ¥çš„ \cs{d} å‘½ä»¤ã€‚åœ¨ \LaTeX{} çš„åŽŸå§‹å®šä¹‰ä¸‹ï¼Œ\cs{d} 
æ˜¯ä¸€ä¸ªé‡éŸ³ç¬¦å·å‘½ä»¤ï¼Œç”¨æ¥äº§ç”Ÿå­—æ¯ä¸‹æ–¹çš„ç‚¹ã€‚å¦‚æžœä½¿ç”¨äº†ä¸Šé¢çš„å®šä¹‰ï¼Œåˆ™åœ¨æ­£æ–‡ä¸­ |\d{o}| 
å°†ä¸ä¼šå¾—åˆ°â€œ\d{o}â€è€Œæ˜¯å¾—åˆ°ä¸€æ¡æŠ¥é”™ã€‚

\item å‰é¢è¯´åˆ°ï¼Œ$\d{}$ å‰é¢çš„é—´è·å¯ä»¥è®¤ä¸ºæ˜¯ä¹˜ç§¯çš„ä¸€ç§è¡¨ç¤ºï¼Œå›&nbsp;æ­¤è¿™ä¸ªé—´è·å¯è¢«è§†ä¸º
ä¸€ä¸ªäºŒå…ƒè¿ç®—ç¬¦ã€‚åœ¨ä¸Šä¸‹æ&nbsp;‡ä¸­æ—¶ï¼ŒäºŒå…ƒè¿ç®—ç¬¦åœ¨ä¸¤ä¾§çš„é—´è·åº”å½“æ¶ˆå¤±ï¼Œä¾‹å¦‚ $a+b$ æ”¾åˆ°ä¸Šæ&nbsp;‡
ä¸­å°±ä¼šå˜æˆ $^{a+b}$ã€‚ä½†æ˜¯é€šè¿‡ä¸Šé¢çš„æ–¹æ³•å®šä¹‰çš„ \cs{d} åœ¨ä¸Šä¸‹æ&nbsp;‡ä¸­ï¼Œå…¶å‰é¢çš„é—´è·ä¸ä¼š
æ¶ˆå¤±ï¼Œä¾‹å¦‚ |$a^{f(x)\d x}$| ä¼šå¾—åˆ° $a^{f(x)\,\mathrm{d}x}$ è€Œä¸æ˜¯ $a^{f(x)\d x}$ã€‚
\end{enumerate}
é¢å¯¹ä»¥ä¸Šé—®é¢˜ï¼Œè§£å†³æ–¹æ¡ˆæ˜¯ä½¿ç”¨æœ¬å®åŒ…ã€‚

\section{æ‰‹åŠ¨å®‰è£…}
\pkg{fixdif} å®åŒ…æœ€æ—©äºŽ 2022 å¹´ä¸Šä¼&nbsp;è‡³ CTANï¼Œä»Ž 2023 å¹´èµ·è¢« \TeX\ Live é»˜è®¤æ”¶å½•ã€‚
å¯¹äºŽ \TeX\ Live 2018\textasciitilde2022ï¼Œ å¦‚æžœä¸èƒ½é€šè¿‡ \texttt{tlmgr} èŽ·å– 
\pkg{fixdif}ï¼Œåˆ™éœ€æ‰‹åŠ¨å®‰è£…ã€‚å¦‚æžœä½&nbsp;çš„ \TeX\ Live ç‰ˆæœ¬ä½ŽäºŽ 2018ï¼Œåˆ™å¯èƒ½æ—&nbsp;æ³•æ­£å¸¸
ä½¿ç”¨ \pkg{fixdif}ï¼Œå¦‚éœ€ä½¿ç”¨æœ¬å®åŒ…ï¼Œå»ºè®®å°† \TeX\ Live æ›´æ–°è‡³æœ€æ–°ç‰ˆã€‚

æ‰‹åŠ¨å®‰è£…åˆ†ä¸ºä»¥ä¸‹å‡&nbsp;æ­¥ï¼š

\textcolor{titlecolor}{ç¬¬ä¸€æ­¥ï¼Œ}ç‚¹å‡»ä¸‹é¢çš„é“¾æŽ¥ä¸‹è½½ \pkg{fixdif} å®åŒ…çš„åŽ‹ç¼©åŒ…ï¼š
\begin{center}
\hyperref{https://mirrors.ctan.org/macros/latex/contrib/fixdif.zip}{}{}%
  {\bfseries Get \pkg{fixdif}.zip on CTAN}
\end{center}
ä¸‹è½½å®ŒæˆåŽï¼Œè§£åŽ‹ç¼©ï¼Œå³å¯å¾—åˆ°ï¼š
\begin{itemize}[itemsep=0pt,parsep=0pt]
\item \pkg{fixdif}.dtxï¼›
\item \pkg{fixdif}.insï¼›
\item \pkg{fixdif}-zh-cn.texï¼›
\item \pkg{fixdif}.pdfï¼›
\item \pkg{fixdif}-zh-cn.pdfï¼›
\item README.mdã€‚
\end{itemize}
çŽ°åœ¨ä½&nbsp;éœ€è¦èŽ·å¾— \pkg{fixdif}.sty å¹¶å°†å…¶å®‰è£…åˆ°æ­£ç¡®çš„è·¯å¾„ä¸­ã€‚

\textcolor{titlecolor}{ç¬¬äºŒæ­¥ï¼Œ}åœ¨è§£åŽ‹ç¼© \pkg{fixdif}.zip å¾—åˆ°çš„ 
\pkg{fixdif}.dtx æ‰€åœ¨çš„è·¯å¾„ä¸‹æ‰“å¼€å‘½ä»¤è¡Œ
ï¼ˆcmd/Powershell/Windows Terminal/Bash/Terminalï¼‰ï¼Œæ‰§è¡Œä¸‹é¢çš„å‘½ä»¤ï¼š
\begin{Verbatim}[formatcom=\bfseries]
latex fixdif.ins
\end{Verbatim}
å³å¯åœ¨å½“å‰è·¯å¾„ä¸‹å¾—åˆ° \pkg{fixdif}.styã€‚è¿™ä¸€æ­¥å¾—åˆ°çš„ \pkg{fixdif}.log å¯ä»¥åˆ&nbsp;é™¤ã€‚

\textcolor{titlecolor}{ç¬¬ä¸‰æ­¥ï¼Œ}å°†å¯¹åº”çš„æ–‡ä»¶ç§»åŠ¨è‡³å¯¹åº”çš„è·¯å¾„ä¸‹ã€‚å‡è®¾ \TeX{} å‘è¡Œç‰ˆ
çš„ TDS æ&nbsp;¹ç›®å½•ä¸º \texttt{TEXMF}ï¼ˆä¾‹å¦‚ Windows ç³»ç»Ÿåœ¨ \texttt{C:/} ä¸‹å®‰è£…çš„ 
\TeX\ Live 2021 çš„ \texttt{TEXMF} ä¸º \texttt{C:/texlive/2021/texmf-dist}ï¼‰ï¼Œ
æŒ‰ä¸‹é¢çš„ç›®å½•ç»“æž„å¤åˆ¶å®åŒ…ä¸­çš„æ–‡ä»¶ï¼š
\begin{Verbatim}
TEXMF/tex/latex/fixdif/fixdif.sty
TEXMF/doc/latex/fixdif/fixdif.pdf
TEXMF/doc/latex/fixdif/fixdif-zh-cn.pdf
TEXMF/doc/latex/fixdif/fixdif-zh-cn.tex
TEXMF/doc/latex/fixdif/README.md
TEXMF/source/latex/fixdif/fixdif.dtx
TEXMF/source/latex/fixdif/fixdif.ins
\end{Verbatim}
ä¸å­˜åœ¨çš„æ–‡ä»¶å¤¹éœ€è¦è‡ªè¡Œåˆ›å»ºã€‚

\textcolor{titlecolor}{ç¬¬å››æ­¥ï¼Œ}åœ¨å‘½ä»¤è¡Œæ‰§è¡Œä¸‹é¢çš„å‘½ä»¤ï¼š
\begin{Verbatim}[formatcom=\bfseries]
texhash
\end{Verbatim}
åˆ·æ–°æ–‡ä»¶åæ•°æ®åº“ã€‚è¿™ä¸€æ­¥çš„å‘½ä»¤å¯åœ¨ä»»æ„è·¯å¾„ä¸‹æ‰§è¡Œï¼Œä½†å¯èƒ½éœ€è¦ç®¡ç†å‘˜æƒé™ï¼ˆWindows ç”¨æˆ·
å¯ä»¥ä»¥ç®¡ç†å‘˜èº«ä»½è¿è¡Œ cmd/Powershell/Windows Terminalï¼Œç±» Unix ç”¨æˆ·å¯ä»¥ä½¿ç”¨ 
\texttt{sudo}ï¼‰ã€‚

å®Œæˆä¸Šé¢å››ä¸ªæ­¥éª¤åŽï¼Œå³å¯åœ¨éžæœ€æ–°ç‰ˆçš„ \TeX\ Live ä¸­ä½¿ç”¨ \pkg{fixdif} å®åŒ…äº†ã€‚
\begin{center}
\color{titlecolor}\itshape Happy \TeX ing!
\end{center}

\section{å®åŒ…ç®€ä»‹}
åœ¨å¯¼è¨€åŒºæ·»åŠ&nbsp;
\begin{Verbatim}
\usepackage{fixdif}
\end{Verbatim}
ä»¥ä½¿ç”¨æœ¬å®åŒ…ã€‚ä½¿ç”¨äº†æœ¬å®åŒ…åŽï¼Œåœ¨æ­£æ–‡ä¸­è¾“å…¥
\begin{Verbatim}
\[ f(x)\d x,          \quad    \frac{\d y}{\d x}, 
   \quad\d y/\d x,    \quad    a^{y\d x}.         \]
\end{Verbatim}
ä¼šå¾—åˆ°
\[f(x)\d x,\quad \frac{\d y}{\d x},\quad \d y/\d x,\quad a^{y\d x}.\]

\subsection{åŸºæœ¬çš„ \cs{d} å‘½ä»¤}
\DescribeMacro{\d}%
\pkg{fixdif} å®åŒ…æä¾›äº† \cs{d} å‘½ä»¤ç”¨äºŽåœ¨æ•°å­¦æ¨¡å¼ä¸­å¾—åˆ°å¾®åˆ†ç®—ç¬¦â€œ$\d$â€ã€‚
åœ¨æ­£æ–‡ä¸­ï¼Œ\cs{d} ä¼šä¿ç•™å…¶åŽŸæœ‰çš„é‡éŸ³ç¬¦å·çš„åŠŸèƒ½ã€‚ä¾‹å¦‚ï¼š
\begin{Verbatim}
$\d x$ å’Œ \d x
\end{Verbatim}
ä»¥ä¸Šä»£ç&nbsp;ä¼šå¾—åˆ°â€œ$\d x$ å’Œ \d xâ€ã€‚

\subsection{è®¾ç½® \cs{d} çš„å­—ä½“}
æœ¬å®åŒ…æä¾›äº†ä¸¤ä¸ªé€‰é¡¹æ¥æŽ§åˆ¶ \cs{d} çš„å­—ä½“ï¼Œåˆ†åˆ«ä¸º \opt{rm} å’Œ \opt{normal}ã€‚
å…¶ä¸­ï¼Œ\opt{rm} ä¸ºé»˜è®¤å€¼ï¼Œè¡¨ç¤º \cs{d} çš„å­—ä½“ä¸ºç½—é©¬ä½“ï¼ˆ\cs{mathrm}ï¼‰ï¼›
\opt{normal} è¡¨ç¤º \cs{d} çš„å­—ä½“ä¸ºæ•°å­¦æ¨¡å¼ä¸‹çš„å¸¸è§„ä½“ï¼ˆ\cs{mathnormal}ï¼‰ï¼Œ
æ•ˆæžœç±»ä¼¼äºŽæ„å¤§åˆ©ä½“ã€‚ä¾‹å¦‚åœ¨è½½å…¥å®åŒ…æ—¶å¼€å¯ \opt{normal} é€‰é¡¹ï¼š
\begin{Verbatim}
\usepackage[normal]{fixdif} % å¯¼è¨€åŒº
\end{Verbatim}
æ­£æ–‡ä¸­çš„ |$f(x)\d x$| ä¼šå¾—åˆ° $f(x)\,dx$ã€‚

\DescribeMacro{\resetdfont}
é™¤äº†ä¸Šé¢çš„ä¸¤ç§å­—ä½“ï¼Œ\pkg{fixdif} ä¹Ÿæ”¯æŒé€šè¿‡åœ¨å¯¼è¨€åŒºä½¿ç”¨ \cs{resetdfont} å‘½ä»¤
è‡ªå®šä¹‰ \cs{d} çš„å­—ä½“ã€‚ä¾‹å¦‚ï¼š
\begin{Verbatim}
\resetdfont{\mathsf}        % å¯¼è¨€åŒº
\end{Verbatim}
åœ¨æ­¤è®¾ç½®ä¸‹ï¼Œæ­£æ–‡ä¸­çš„ |\d x| ä¼šå¾—åˆ° $\mathsf{d}x$ã€‚

\subsection{\cs{partial} çš„è¡Œä¸º}
\DescribeMacro{\partial}%
\pkg{fixdif} å®åŒ…å°† \cs{partial} å½’ä¸ºå¾®åˆ†ç®—ç¬¦ï¼Œæ­£æ–‡ä¸­çš„ \cs{partial} å‰é¢ä¹Ÿä¼šæœ‰
è‡ªåŠ¨çš„é—´è·ã€‚ä¾‹å¦‚ |$\partial x\partial y$| ä¼šå¾—åˆ° $\partial x\partial y$ã€‚
è‹¥ä¸éœ€è¦å°† \cs{partial} è§†ä¸ºå¾®åˆ†ç®—ç¬¦ï¼Œå¯ä»¥å¼€å¯ \opt{nopartial} é€‰é¡¹ï¼š
\begin{Verbatim}
\usepackage[nopartial]{fixdif}
\end{Verbatim}
åœ¨é»˜è®¤çš„è®¾ç½®ä¸‹ï¼Œä½œä¸ºæ™®é€šæ•°å­¦ç¬¦å·çš„ $\partialnondif$ å¯ä»¥ä½¿ç”¨ 
\hypertarget{cs:partialnondif}{\cs{partialnondif}} è¾“å…¥ã€‚

\section{å®šä¹‰å¾®åˆ†ç®—ç¬¦å‘½ä»¤}
{\attention[6]}æ³¨æ„ï¼æœ¬èŠ‚ä¸­çš„å‘½ä»¤åªèƒ½åœ¨\zhemph{å¯¼è¨€åŒº}ä¸­ä½¿ç”¨ï¼

\subsection{é€šè¿‡å‘½ä»¤åç§°å®šä¹‰å¾®åˆ†ç®—ç¬¦å‘½ä»¤}
\noindent\textcolor{titlecolor}{\cs{letdif}\marg{cmd}\marg{csname}}%
\DescribeMacro{\letdif}\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼‰

\cs{letdif} å‘½ä»¤æœ‰ä¸¤ä¸ªå‚æ•°ï¼šç¬¬ä¸€ä¸ªå‚æ•° \meta{cmd} æ˜¯æ–°å®šä¹‰çš„å¾®åˆ†ç®—ç¬¦å‘½ä»¤ï¼Œ
ä»¥åæ–œæ&nbsp;å¼€å¤´ï¼›ç¬¬äºŒä¸ªå‚æ•° \meta{csname} æ˜¯éœ€è¦è®¾ç½®ä¸ºå¾®åˆ†ç®—ç¬¦çš„æ•°å­¦ç¬¦å·çš„å‘½ä»¤åç§°ï¼Œ
ä¹Ÿå°±æ˜¯ä¸€ä¸ªå®Œæ•´çš„å‘½ä»¤åŽ»æŽ‰æœ€å‰é¢çš„åæ–œæ&nbsp;ã€‚ä¸¾ä¸ªä¾‹å­ï¼š
\begin{Verbatim}
\letdif{\vr}{delta}
\end{Verbatim}
è¿™æ&nbsp;·å®šä¹‰çš„ |\vr| åœ¨æ•°å­¦æ¨¡å¼ä¸­å°±ç›¸å½“äºŽä¸€ä¸ª |\delta|ï¼Œä½†æ˜¯å®ƒçš„å‰é¢ä¼šåŠ&nbsp;ä¸Šè‡ªåŠ¨çš„é—´è·ã€‚

é€šè¿‡ \cs{letdif} å‘½ä»¤ï¼Œæˆ‘ä»¬å¯ä»¥åŽŸå°ä¸åŠ¨åœ°æŠŠä¸€ä¸ªæ•°å­¦ç¬¦å·å˜æˆå¾®åˆ†ç®—ç¬¦ã€‚ä¾‹å¦‚ï¼š
\begin{Verbatim}
\letdif{\delta}{delta}
\end{Verbatim}
è¿™æ&nbsp;· |\delta| æœ¬èº«å°±ä¼šå…·å¤‡å¾®åˆ†ç®—ç¬¦çš„å±žæ€§ã€‚

\cs{letdif} çš„ç¬¬äºŒä¸ªå‚æ•° \meta{csname} å¯ä»¥é‡å¤ä½¿ç”¨ï¼Œä¹Ÿå°±æ˜¯è¯´ï¼Œä½&nbsp;å¯ä»¥æŠŠåŒä¸€ä¸ªç¬¦å·
å®šä¹‰ä¸ºä¸¤ä¸ªä¸åŒçš„å¾®åˆ†ç®—ç¬¦å‘½ä»¤ã€‚ä¾‹å¦‚ï¼š
\begin{Verbatim}
\letdif{\nabla}{nabla}
\letdif{\grad}{nabla}
\end{Verbatim}
è¿™æ&nbsp;· |\nabla| å’Œ |\grad| éƒ½ä¼šå¾—åˆ°å¾®åˆ†ç®—ç¬¦ $\nabla$ã€‚

{\attention[2]}å¦‚éœ€å¾—åˆ°åŽŸæ¥çš„æ™®é€šæ•°å­¦ç¬¦å· \texttt{\textbackslash}\meta{csname}ï¼Œ
åªéœ€åœ¨æ•°å­¦æ¨¡å¼ä¸­è¾“å…¥ \texttt{\textbackslash}\meta{csname}\texttt{nondif}ã€‚
ä¾‹å¦‚\hyperlink{cs:partialnondif}{\textcolor{titlecolor!75!black}{å‰é¢ä»‹ç»çš„ \cs{partialnondif}}}ã€‚

\noindent\textcolor{titlecolor}{\cs{letdif*}\marg{cmd}\marg{csname}}%
\DescribeMacro{\letdif*}\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼‰

\cs{letdif*} ä¸Ž \cs{letdif} åŸºæœ¬ç›¸åŒï¼Œå”¯ä¸€çš„åŒºåˆ«åœ¨äºŽ \cs{letdif*} ä¼šåœ¨å¾®åˆ†ç®—ç¬¦
åŽé¢æ·»åŠ&nbsp;é¢å¤–çš„çŸ«æ­£ã€‚å»ºè®®åœ¨ä½¿ç”¨äº† \pkg{unicode-math} çš„æ–‡æ¡£ä¸­ä½¿ç”¨ \cs{letdif*}ã€‚
ä¾‹å¦‚ï¼š
\begin{Verbatim}
\usepackage{unicode-math}
\setmathfont{TeX Gyre Termes Math}
\usepackage{fixdif}
\letdif{\vr}{updelta}
\end{Verbatim}
è¿™æ&nbsp;·å®šä¹‰çš„ |\vr| åŽé¢å°±ä¼šæœ‰è´Ÿçš„é—´è·ï¼Œå¦‚æžœä¸å¸Œæœ›å¾—åˆ°è¿™ä¸€è´Ÿé—´è·ï¼Œå¯ä»¥æŠŠä¸Šé¢çš„æœ€åŽä¸€è¡Œ
æ”¹ä¸ºï¼š
\begin{Verbatim}
\letdif*{\vr}{updelta}
\end{Verbatim}

\subsection{å®šä¹‰åŒ…å«å¤šä¸ªå‘½ä»¤æˆ–å­—ç¬¦çš„å¾®åˆ†ç®—ç¬¦å‘½ä»¤}

\noindent\textcolor{titlecolor}{\cs{newdif}\marg{cmd}\marg{multi-cmd}}%
\DescribeMacro{\newdif}\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼ŒåŽæ—&nbsp;çŸ«æ­£ï¼‰\\
\noindent\textcolor{titlecolor}{\cs{newdif*}\marg{cmd}\marg{multi-cmd}}%
\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼ŒåŽæœ‰çŸ«æ­£ï¼‰

ä¸Šé¢ä¸¤ä¸ªå‘½ä»¤çš„ç¬¬ä¸€ä¸ªå‚æ•° \meta{cmd} æ˜¯æ–°å®šä¹‰çš„å¾®åˆ†ç®—ç¬¦å‘½ä»¤ï¼Œç¬¬äºŒä¸ªå‚æ•° 
\meta{multi-cmd} æ˜¯è¶…è¿‡ä¸€ä¸ªå­—ï¼ˆtokenï¼‰çš„å‘½ä»¤ç»„åˆæˆ–å­—ç¬¦ä¸²ã€‚ä¸¾ä¸ªä¾‹å­ï¼Œåœ¨ 
\pkg{xcolor} å®åŒ…ä¸‹å¯ä»¥è¿™æ&nbsp;·ä½¿ç”¨ï¼š
\begin{Verbatim}
\newdif{\redsfd}{\textsf{\color{red}d}}
\end{Verbatim}
è¿™æ&nbsp;·å°±å®šä¹‰äº†ä¸€ä¸ª |\redsfd| å‘½ä»¤ã€‚å†ä¸¾ä¸€ä¸ªä¾‹å­ï¼š
\begin{Verbatim}
\newdif{\D}{\mathrm{D}}
\end{Verbatim}
è¿™æ&nbsp;·ï¼Œåœ¨æ­£æ–‡ä¸­è¾“å…¥ |$y\D x$| å°±ä¼šå¾—åˆ° $y\,\mathrm{D}x$ã€‚

{\attention[2]}å¦‚æžœ \cs{newdif}(\texttt{*}) åŽé¢çš„ç¬¬äºŒä¸ªå‚æ•° \meta{multi-cmd} 
ä»…åŒ…å«ä¸€ä¸ªå­—ï¼ˆtokenï¼‰ï¼Œä¹Ÿå°±æ˜¯ä¸€ä¸ªå‘½ä»¤æˆ–å­—ç¬¦ï¼Œè¯·ä½¿ç”¨ \cs{letdif}(\texttt{*}) å‘½ä»¤
è€Œä¸æ˜¯ \cs{newdif}(\texttt{*})ã€‚

\cs{newdif}(\texttt{*}) ä¼šæ£€æŸ¥ç¬¬ä¸€ä¸ªå‚æ•° \meta{cmd} æ˜¯å¦å·²ç»è¢«å®šä¹‰ï¼Œè‹¥ \meta{cmd} 
å·²è¢«å®šä¹‰ï¼Œåˆ™ä¼šæŠ¥é”™ã€‚

\noindent\textcolor{titlecolor}{\cs{renewdif}\marg{cmd}\marg{multi-cmd}}%
\DescribeMacro{\renewdif}\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼ŒåŽæ—&nbsp;çŸ«æ­£ï¼‰\\
\noindent\textcolor{titlecolor}{\cs{renewdif*}\marg{cmd}\marg{multi-cmd}}%
\hfillï¼ˆä»…é™åœ¨å¯¼è¨€åŒºä½¿ç”¨ï¼ŒåŽæœ‰çŸ«æ­£ï¼‰

è¿™ä¸¤ä¸ªå‘½ä»¤ç”¨äºŽå°† \meta{cmd} é‡å®šä¹‰ä¸ºå¾®åˆ†ç®—ç¬¦å‘½ä»¤ã€‚
è‹¥ \meta{cmd} è¿˜æœªè¢«å®šä¹‰ï¼Œåˆ™ä¼šæŠ¥é”™ã€‚

\section{æ­£æ–‡ä¸­ä¸´æ—¶çš„å¾®åˆ†ç®—ç¬¦å‘½ä»¤}
\noindent\textcolor{titlecolor}{\cs{mathdif}\marg{symbol}}%
\DescribeMacro{\mathdif}\hfillï¼ˆä»…é™åœ¨æ•°å­¦æ¨¡å¼ä½¿ç”¨ï¼ŒåŽæ—&nbsp;çŸ«æ­£ï¼‰\\ 
\noindent\textcolor{titlecolor}{\cs{mathdif*}\marg{symbol}}%
\hfillï¼ˆä»…é™åœ¨æ•°å­¦æ¨¡å¼ä½¿ç”¨ï¼ŒåŽæœ‰çŸ«æ­£ï¼‰

å¦‚éœ€åœ¨æ­£æ–‡ä¸­å°‘é‡ä½¿ç”¨æŸä¸€æ•°å­¦ç¬¦å·ä½œä¸ºå¾®åˆ†ç®—ç¬¦ï¼Œå¯ä»¥ä½¿ç”¨ä¸Šé¢çš„ä¸¤ä¸ªå‘½ä»¤ã€‚
ä¾‹å¦‚ï¼Œ\verb|$x\mathdif{\Delta}\psi$| ä¼šå¾—åˆ° $x\mathdif{\Delta}\psi$ã€‚

\section{ä¸¾ä¾‹}

æœ¬èŠ‚å°†å‘Šè¯‰ä½&nbsp;å¦‚ä½•åœ¨æ–‡æ¡£ä¸­æ­£ç¡®ä½¿ç”¨ \pkg{fixdif} å®åŒ…ã€‚

çœ‹ä»¥ä¸‹ä¸¤è¡Œä»£ç&nbsp;ï¼š
\begin{Verbatim}
\letdif{\Delta}{Delta}
\letdif{\nabla}{nabla}
\end{Verbatim}
å“ªä¸€è¡Œæ›´åˆç†ä¸€äº›ï¼Ÿç­”æ¡ˆæ˜¯ç¬¬äºŒè¡Œã€‚

æœ‰æ—¶ï¼Œå¤§å†™çš„â€œ$\Delta$â€ä¼šè¢«ç”¨ä½œæ‹‰æ™®æ‹‰æ–¯ç®—ç¬¦ï¼ˆä¸Ž $\nabla^2$ æ„ä¹‰ç›¸åŒï¼‰ï¼›
å¦ä¸€äº›æ—¶å€™ï¼Œå¤§å†™çš„â€œ$\Delta$â€ä¼šè¢«å½“ä½œå˜é‡æˆ–å‡½æ•°ã€‚æ‰€ä»¥å¯¹ $\Delta$ ä½œä¸º
æ‹‰æ™®æ‹‰æ–¯ç®—ç¬¦å’Œå˜é‡æˆ–å‡½æ•°çš„æƒ…å†µåˆ†åˆ«è¿›è¡Œå®šä¹‰æ˜¯æ›´å¥½çš„åšæ³•ã€‚æˆ‘ä»¬å»ºè®®å°† |$\Delta$| 
ä½œä¸º $\Delta$ çš„åŽŸå§‹å®šä¹‰è¿›è¡Œä¿ç•™ï¼Œå¯¹è¡¨ç¤ºæ‹‰æ™®æ‹‰æ–¯ç®—ç¬¦çš„ $\Delta$ å¦åŠ&nbsp;å®šä¹‰ã€‚
ä»Žè€Œæˆ‘ä»¬è¿™æ&nbsp;·ä¿®æ”¹ä¸Šé¢çš„ç¬¬ä¸€è¡Œï¼š
\begin{Verbatim}
\letdif{\laplacian}{Delta}
\end{Verbatim}

\paragraph{å¤„ç†æ­£è´Ÿå·ä¸Žå¾®åˆ†ç®—ç¬¦ä¹‹é—´çš„é—´è·}
è¾“å…¥ |$-\d x$| ä¼šå¾—åˆ° $-\d x$ã€‚å¦‚æžœä½&nbsp;ä¸å¸Œæœ›åœ¨æ­£è´Ÿå·ä¸Žå¾®åˆ†ç®—ç¬¦ä¹‹é—´ä¿ç•™
ä¸€å®šçš„é—´è·ï¼Œå¯ä»¥è¾“å…¥ |$-{\d x}$|ï¼Œè¿™æ&nbsp;·å°±ä¼šå¾—åˆ° $-{\d x}$ã€‚
ä¸è¿‡è¯è¯´å›žæ¥ï¼Œ$-\d x$ çš„æ•ˆæžœä¹Ÿå¹¶éžä¸å¯æŽ¥å—ã€‚

\end{document}</pre></body></html>