<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% -*- coding: utf-8 -*-
% This is part of the book TeX for the Impatient.
% Copyright (C) 2003 Paul W. Abrahams, Kathryn A. Hargreaves, Karl Berry.
% See file fdl.tex for copying conditions.

\input macros
%\chapter {Commands \linebreak for composing \linebreak math formulas}
\chapter {ć•°ĺ­¦ĺ…¬ĺĽŹĺ‘˝ä»¤}

%\bix^^{math}
%\chapterdef{math}
\bix^^{ć•°ĺ­¦}
\chapterdef{math}

%This section covers commands for constructing math formulas.
%For an explanation of the conventions used in this section,
%see \headcit{Descriptions of the commands}{cmddesc}.
čż™ä¸€ç«&nbsp;ĺŚ…ć‹¬äş†ćŽ’ĺŤ°ć•°ĺ­¦ĺ…¬ĺĽŹć‰€éś€č¦çš„ĺ‘˝ä»¤ă€‚
ĺś¨\headcit{ĺ‘˝ä»¤ćŹŹčż°}{cmddesc}čż™ä¸€čŠ‚ä¸­ç»™ĺ‡şäş†čż™ç«&nbsp;çš„ćŻäľ‹ă€‚

\begindescriptions
%==========================================================================
%\section {Simple parts of formulas}
\section {ç®€ĺŤ•ĺ…¬ĺĽŹćŽ’ç‰}

%==========================================================================
%\subsection {Greek letters}
\subsection {ĺ¸Śč…Šĺ­—ćŻŤ}

%\begindesc
%\bix^^{Greek letters}
%\dothreecolumns 40
%\easy\ctsdisplay alpha {}
%\ctsdisplay beta {}
%\ctsdisplay chi {}
%\ctsdisplay delta {}
%\ctsdisplay Delta {}
%\ctsdisplay epsilon {}
%\ctsdisplay varepsilon {}
%\ctsdisplay eta {}
%\ctsdisplay gamma {}
%\ctsdisplay Gamma {}
%\ctsdisplay iota {}
%\ctsdisplay kappa {}
%\ctsdisplay lambda {}
%\ctsdisplay Lambda {}
%\ctsdisplay mu {}
%\ctsdisplay nu {}
%\ctsdisplay omega {}
%\ctsdisplay Omega {}
%\ctsdisplay phi {}
%\ctsdisplay varphi {}
%\ctsdisplay Phi {}
%\ctsdisplay pi {}
%\ctsdisplay varpi {}
%\ctsdisplay Pi {}
%\ctsdisplay psi {}
%\ctsdisplay Psi {}
%\ctsdisplay rho {}
%\ctsdisplay varrho {}
%\ctsdisplay sigma {}
%\ctsdisplay varsigma {}
%\ctsdisplay Sigma {}
%\ctsdisplay tau {}
%\ctsdisplay theta {}
%\ctsdisplay vartheta {}
%\ctsdisplay Theta {}
%\ctsdisplay upsilon {}
%\ctsdisplay Upsilon {}
%\ctsdisplay xi {}
%\ctsdisplay Xi {}
%\ctsdisplay zeta {}
%\egroup
\begindesc
\bix^^{ĺ¸Śč…Šĺ­—ćŻŤ}
\dothreecolumns 40
\easy\ctsdisplay alpha {}
\ctsdisplay beta {}
\ctsdisplay chi {}
\ctsdisplay delta {}
\ctsdisplay Delta {}
\ctsdisplay epsilon {}
\ctsdisplay varepsilon {}
\ctsdisplay eta {}
\ctsdisplay gamma {}
\ctsdisplay Gamma {}
\ctsdisplay iota {}
\ctsdisplay kappa {}
\ctsdisplay lambda {}
\ctsdisplay Lambda {}
\ctsdisplay mu {}
\ctsdisplay nu {}
\ctsdisplay omega {}
\ctsdisplay Omega {}
\ctsdisplay phi {}
\ctsdisplay varphi {}
\ctsdisplay Phi {}
\ctsdisplay pi {}
\ctsdisplay varpi {}
\ctsdisplay Pi {}
\ctsdisplay psi {}
\ctsdisplay Psi {}
\ctsdisplay rho {}
\ctsdisplay varrho {}
\ctsdisplay sigma {}
\ctsdisplay varsigma {}
\ctsdisplay Sigma {}
\ctsdisplay tau {}
\ctsdisplay theta {}
\ctsdisplay vartheta {}
\ctsdisplay Theta {}
\ctsdisplay upsilon {}
\ctsdisplay Upsilon {}
\ctsdisplay xi {}
\ctsdisplay Xi {}
\ctsdisplay zeta {}
\egroup
%\explain
%These commands produce Greek letters suitable for mathematics.
%You can only use them
%within a math formula, so if you need a Greek letter within ordinary
%text you must enclose it in dollar signs (|$|).  \TeX\ does not have
%commands for Greek letters that look like their roman
%counterparts, since you can get them by using those roman
%counterparts.  For example, you can get a lowercase
%^{omicron} in a formula by writing the letter `o', i.e.,
%`|{\rm o}|' or an uppercase ^{beta} (`B') by writing
%`|{\rm B}|'.
\explain
čľ“ĺ…Ąčż™äş›ĺ‘˝ä»¤ĺŹŻä»ĄćŽ’ĺŤ°ĺ‡şć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„ç›¸ĺş”çš„ĺ¸Śč…Šĺ­—ćŻŤç¬¦ĺŹ·.
ä˝&nbsp;ĺŹŞč˝ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹä¸­ä˝żç”¨ĺ®ä»¬, ć‰€ä»Ąĺ¦‚ĺś¨ć™®é€šçš„ć–‡ćś¬ä¸­ä˝żç”¨ĺ®ä»¬ć—¶,
ä˝&nbsp;ĺż…éˇ»ćŠŠĺ®ä»¬ć‹¬ĺś¨çľŽĺ…ç¬¦ĺŹ· (|$|) ĺ†….
\TeX\ ĺą¶ä¸ŤĺŚ…ĺ«čż™äş›ć•°ĺ­¦ä¸­ä˝żç”¨çš„ĺ¸Śč…Šĺ­—ćŻŤć‰€ĺŻąĺş”çš„ć­Łä˝“ĺ­—ç¬¦çš„ĺ‘˝ä»¤,
ä¸Ťčż‡ä˝&nbsp;ĺŹŻä»Ąĺľć–ąäľżĺś°ĺľ—ĺ°čż™äş›ĺ­—ç¬¦.
ćŻ”ĺ¦‚čŻ´, ä˝&nbsp;ĺŹŻä»Ąĺś¨ĺ…¬ĺĽŹä¸­ä˝żç”¨ `|{\rm o}|' ćťĄĺľ—ĺ°ä¸€ä¸Şĺ°Źĺ†™çš„ ^{omicron} `o',
ĺŹćŻ”ĺ¦‚, ä˝&nbsp;ĺŹŻä»Ąä˝żç”¨ `|{\rm B}|' ĺľ—ĺ°ĺ¤§ĺ†™çš„ ^{beta} (`B').

%Don't confuse the following letters:
%\ulist \compact
%\li |\upsilon| (`$\upsilon$'), |{\rm v}| (`v'), and |\nu| (`$\nu$').
%\li |\varsigma| (`$\varsigma$') and |\zeta| (`$\zeta$').
%\endulist
ćł¨ć„Źä¸Ťč¦ć··ć·†ä¸‹éť˘çš„ç¬¦ĺŹ·:
\ulist \compact
\li |\upsilon| (`$\upsilon$'), |{\rm v}| (`v'), ĺ’Ś |\nu| (`$\nu$').
\li |\varsigma| (`$\varsigma$') ĺ’Ś |\zeta| (`$\zeta$').
\endulist

%You can get slanted capital Greek letters by using the math italic
%(|\mit|) \minref{font}.
ä˝żç”¨ć•°ĺ­¦çš„ć„Źĺ¤§ĺ©\minref{ĺ­—ä˝“} (|\mit|) ĺŹŻä»Ąĺľ—ĺ°ć–śä˝“çš„ĺ¤§ĺ†™ĺ¸Śč…Šĺ­—ćŻŤ.

%\TeX\ treats Greek letters as ordinary symbols when it's figuring how
%much space to put around them.
ĺś¨č®ˇç®—ĺś¨ĺ¸Śč…Šĺ­—ćŻŤĺ‘¨ĺ›´ćŹ’ĺ…Ąĺ¤šĺ°‘çš„ç©şç™˝ć—¶ďĽŚ\TeX\ ćŠŠĺ®ä»¬ĺ˝“ä˝ść­Łĺ¸¸çš„ç¬¦ĺŹ·ă€‚

%\example
%If $\rho$ and $\theta$ are both positive, then $f(\theta)
%-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
%|
%\produces
%If $\rho$ and $\theta$ are both positive, then
%$f(\theta)-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
%\endexample
%\eix^^{Greek letters}
%\enddesc
\example
ĺ¦‚ćžś $\rho$ ĺ’Ś $\theta$ é˝ćŻć­Łć•°, é‚Łäą $f(\theta)
-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
|
\produces
ĺ¦‚ćžś $\rho$ ĺ’Ś $\theta$ é˝ćŻć­Łć•°, é‚Łäą
$f(\theta)-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
\endexample
\eix^^{ĺ¸Śč…Šĺ­—ćŻŤ}
\enddesc

%==========================================================================
%\subsection {Miscellaneous ordinary math symbols}
\subsection {ĺ„ç§Ťć™®é€šć•°ĺ­¦ç¬¦ĺŹ·}

\begindesc
\xrdef{specsyms}
\dothreecolumns 34
\easy\ctsdisplay infty {}
\ctsdisplay Re {}
\ctsdisplay Im {}
\ctsdisplay angle {}
\ctsdisplay triangle {}
\ctsdisplay backslash {}
\ctsdisplay vert {}
\writeidxfalse\ctsydisplay | @bar {}\writeidxtrue
\ctsdisplay Vert {}
\ctsdisplay emptyset {}
\ctsdisplay bot {}
\ctsdisplay top {}
\ctsdisplay exists {}
\ctsdisplay forall {}
\ctsdisplay hbar {}
\ctsdisplay ell {}
\ctsdisplay aleph {}
\ctsdisplay imath {}
\ctsdisplay jmath {}
\ctsdisplay nabla {}
\ctsdisplay neg {}
\ctsdisplay lnot {}
\actdisplay ' @prime \ (ä¸Šć&nbsp;‡ç‚ą)
\ctsdisplay prime {}
\ctsdisplay partial {}
\ctsdisplay surd {}
\ctsdisplay wp {}
\ctsdisplay flat {}
\ctsdisplay sharp {}
\ctsdisplay natural {}
\ctsdisplay clubsuit {}
\ctsdisplay diamondsuit {}
\ctsdisplay heartsuit {}
\ctsdisplay spadesuit {}
\egroup
\explain
^^{éźłç¬¦} ^^{čŠ±č‰˛}
čż™äş›ĺ‘˝ä»¤ĺŹŻä»ĄćŽ’ĺŤ°ĺ„ç§Ťç¬¦ĺŹ·.
ä¸şäş†ćŠŠĺ®ä»¬ĺ’Śĺ…¶ĺ®çš„ç¬¦ĺŹ·, ćŻ”ĺ¦‚ĺ…łçł»ç¬¦ĺŹ·ç­‰, ĺŚşĺ†ĺĽ€ćťĄ, ĺ®ä»¬č˘«ç§°ä¸şć™®é€šć•°ĺ­¦ç¬¦ĺŹ·.
ä˝&nbsp;ĺŹŞč˝ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹä¸­ä˝żç”¨čż™äş›ç¬¦ĺŹ·, ć‰€ä»Ąĺ¦‚ćžśĺś¨ć™®é€šçš„ć–‡ćś¬ä¸­ä˝żç”¨, ä˝&nbsp;ĺż…éˇ»ä˝żç”¨çľŽĺ…ç¬¦ĺŹ· (|$|) ćŠŠĺ®ä»¬ć‹¬čµ·ćťĄ.

ĺ˝“ä˝&nbsp;ćłĺś¨ `$i$' ć– `$j$' ä¸ŠĺŠ&nbsp;ä¸Šé‡Ťéźłç¬¦ĺŹ·, ĺ™éś€č¦ä˝żç”¨ |\imath| ĺ’Ś |\jmath| ĺ‘˝ä»¤ćťĄčˇ¨ç¤şĺ®ä»¬ćś¬čş«.

ä¸Šć&nbsp;‡ç‚ąç¬¦ĺŹ· (|'|) ćŻä¸€ä¸Ş |\prime| çš„ä¸Šć&nbsp;‡çš„ç®€ĺ†™.
(|\prime| ćś¬čş«ĺŹŻä»ĄćŽ’ĺŤ°ä¸€ä¸Şĺľĺ¤§çš„ä¸‘é™‹çš„ć’‡ĺŹ·.)

|\!|| ĺ’Ś ^|\Vert| ĺ‘˝ä»¤ćŻç­‰ä»·çš„, ĺ°±ĺŹ ^|\neg| ĺ’Ś ^|\lnot| ĺ‘˝ä»¤ä¸€ć&nbsp;·.
\margin{ĺ˘žĺŠ&nbsp;äş† {\tt\\vert} çš„č§Łé‡Š}
|\vert| ç¬¦ĺŹ·ĺŹŻä»ĄćŽ’ĺŤ°ĺ‡şĺ’Ś `|!||' ç›¸ĺŚçš„ć•ćžś.
\indexchar |

ç”± |\backslash|, |\vert|, ĺ’Ś |\Vert| ćŽ’ĺŤ°çš„ĺ‘˝ä»¤ĺŹ«ĺš \minref{ĺ†ç•Śç¬¦}.
ä˝żç”¨ ^|\bigm| ç­‰ (\xref \bigm) ĺ‘˝ä»¤ĺŹŻä»ĄćŽ’ĺŤ°ĺ¤§ĺŹ·çš„čż™äş›ĺ­—ç¬¦.

\example
The Knave of $\heartsuit$s, he stole some tarts.
|
\produces
The Knave of $\heartsuit$s, he stole some tarts.
\nextexample
ĺ¦‚ $\hat\imath &lt; \hat\jmath$ ĺ™ $i' \leq j^\prime$.
|
\produces
ĺ¦‚ $\hat\imath &lt; \hat\jmath$ ĺ™ $i' \leq j^\prime$.
\nextexample
$${{x-a}\over{x+a}}\biggm\backslash{{y-b}\over{y+b}}$$
|
\dproduces
$${{x-a}\over{x+a}}\biggm\backslash{{y-b}\over{y+b}}$$
\endexample
\enddesc

%==========================================================================
\subsection {äşŚĺ…čżç®—ç¬¦}

\begindesc
\bix^^{čżç®—ç¬¦}
\xrdef{binops}
\dothreecolumns 34
\easy\ctsdisplay vee {}
\ctsdisplay wedge {}
\ctsdisplay amalg {}
\ctsdisplay cap {}
\ctsdisplay cup {}
\ctsdisplay uplus {}
\ctsdisplay sqcap {}
\ctsdisplay sqcup {}
\ctsdisplay dagger {}
\ctsdisplay ddagger {}
\ctsdisplay land {}
\ctsdisplay lor {}
\ctsdisplay cdot {}
\ctsdisplay diamond {}
\ctsdisplay bullet {}
\ctsdisplay circ {}
\ctsdisplay bigcirc {}
\ctsdisplay odot {}
\ctsdisplay ominus {}
\ctsdisplay oplus {}
\ctsdisplay oslash {}
\ctsdisplay otimes {}
\ctsdisplay pm {}
\ctsdisplay mp {}
\ctsdisplay triangleleft {}
\ctsdisplay triangleright {}
\ctsdisplay bigtriangledown {}
\ctsdisplay bigtriangleup {}
\ctsdisplay ast {}
\ctsdisplay star {}
\ctsdisplay times {}
\ctsdisplay div {}
\ctsdisplay setminus {}
\ctsdisplay wr {}
\egroup
\explain
čż™äş›ĺ‘˝ä»¤ĺŹŻä»ĄćŽ’ĺŤ°ĺ„ç§ŤäşŚĺ…čżç®—ç¬¦.
äşŚĺ…čżç®—ç¬¦ćŻ \TeX\ çš„ä¸€ç§Ťç¬¦ĺŹ·\minref{é›†}.
\TeX\ ĺś¨ä¸ŤĺŚçš„ç¬¦ĺŹ·é›†ĺ‘¨ĺ›´äĽšćŹ’ĺ…Ąä¸ŤĺŚçš„ç©şç™˝.
ĺ˝“ \TeX\ éś€č¦ĺś¨ä¸€ä¸Şć•°ĺ­¦ĺ…¬ĺĽŹä¸­é—´ć–­čˇŚć—¶,
ĺ®äĽšč€č™‘ĺś¨äşŚĺ…čżç®—ç¬¦ĺŽéť˘čż›čˇŚć–­čˇŚ---ä¸Ťčż‡ä»…ĺś¨ĺ®ĺ‡şçŽ°ĺś¨ĺ…¬ĺĽŹçš„ćś€ĺ¤–ĺ±‚ć—¶, č€Śä¸ŤćŻĺś¨ä¸€ä¸Şç»„ä¸­.

é™¤äş†čż™äş›ĺ‘˝ä»¤ä»Ąĺ¤–, \TeX\ äąźćŠŠ `|+|' and `|-|' ä˝śä¸şäşŚĺ…čżç®—ç¬¦.
ĺ®ćŠŠ `|/|' ĺ˝“ä˝śä¸€ä¸Şć™®é€šç¬¦ĺŹ·,
ĺ›&nbsp;ä¸şč™˝ç„¶äş‹ĺ®žä¸Šĺś¨ć•°ĺ­¦ä¸­ĺ®ćŻä¸€ä¸ŞäşŚĺ…čżç®—,
ä˝†ćŻĺ®ĺś¨ĺ‘¨ĺ›´ĺŠ&nbsp;ĺ…Ąçš„ç©şç™˝ć›´ĺ°‘ć—¶çś‹ä¸ŠĺŽ»ć›´ćĽ‚äş®.

\example
$$z = x \div y \quad \hbox{ĺ˝“ä¸”ä»…ĺ˝“} \quad
z \times y = x \;\hbox{ä¸”}\; y \neq 0$$
|
\dproduces
$$z = x \div y \quad \hbox{ĺ˝“ä¸”ä»…ĺ˝“} \quad
z \times y = x \;\hbox{ä¸”}\; y \neq 0$$
\endexample
\enddesc

\begindesc
\ctspecial * \ctsxrdef{@star}
\explain
ĺ‘˝ä»¤ |\*| čˇ¨ç¤şäąćł•ç¬¦ĺŹ· ($\times$), äąźćŻä¸€ä¸ŞäşŚĺ…ç¬¦ĺŹ·.
äąćł•ç¬¦ĺŹ·ĺś¨ć–‡ćś¬ä¸­çš„ć•°ĺ­¦ĺ…¬ĺĽŹä¸­ĺ‡şçŽ°ć—¶čˇ¨çŽ°ĺľ—ĺ’Śä¸€ä¸Şĺ†čŻŤç¬¦ç±»äĽĽ.
čż™ĺ°±ćŻčŻ´, \TeX\ \emph{ä»…}äĽšĺś¨ĺ…¬ĺĽŹčŻĄç‚ąéś€č¦ć–­čˇŚć—¶ćŽ’ç‰ |\times| ç¬¦ĺŹ·.
ĺ›&nbsp;ä¸ş \TeX\ ć°¸čżśä¸ŤäĽšĺś¨é™ĺ—ĺ…¬ĺĽŹä¸­ć–­čˇŚ, ć‰€ä»Ą |\*| ĺś¨é™ĺ—ĺ…¬ĺĽŹ \minrefs{é™ĺ—ĺ…¬ĺĽŹ} ä¸­ćŻć˛ˇćś‰ä»»ä˝•ä˝śç”¨çš„.

\example
Let $c = a\*b$. In the case that $c=0$ or $c=1$, let
$\Delta$ be $(\hbox{the smallest $q$})\*(\hbox{the
largest $q$})$ in the set of approximate $\tau$-values.
|
\produces
Let $c = a\*b$. In the case that $c=0$ or $c=1$, let
$\Delta$ be $(\hbox{the smallest $q$})\*(\hbox{the
largest $q$})$ in the set of approximate $\tau$-values.

\eix^^{čżç®—ç¬¦}
\endexample
\enddesc

%==========================================================================
\subsection {ĺ…łçł»ç¬¦ĺŹ·}

\begindesc
\xrdef {relations}
\bix^^{ĺ…łçł»ç¬¦}
\dothreecolumns 39
\easy\ctsdisplay asymp {}
\ctsdisplay cong {}
\ctsdisplay dashv {}
\ctsdisplay vdash {}
\ctsdisplay perp {}
\ctsdisplay mid {}
\ctsdisplay parallel {}
\ctsdisplay doteq {}
\ctsdisplay equiv {}
\ctsdisplay ge {}
\ctsdisplay geq {}
\ctsdisplay le {}
\ctsdisplay leq {}
\ctsdisplay gg {}
\ctsdisplay ll {}
\ctsdisplay models {}
\ctsdisplay ne {}
\ctsdisplay neq {}
\ctsdisplay notin {}
\ctsdisplay in {}
\ctsdisplay ni {}
\ctsdisplay owns {}
\ctsdisplay prec {}
\ctsdisplay preceq {}
\ctsdisplay succ {}
\ctsdisplay succeq {}
\ctsdisplay bowtie {}
\ctsdisplay propto {}
\ctsdisplay approx {}
\ctsdisplay sim {}
\ctsdisplay simeq {}
\ctsdisplay frown {}
\ctsdisplay smile {}
\ctsdisplay subset {}
\ctsdisplay subseteq {}
\ctsdisplay supset {}
\ctsdisplay supseteq {}
\ctsdisplay sqsubseteq {}
\ctsdisplay sqsupseteq {}
\egroup
\explain
čż™äş›ĺ‘˝ä»¤ĺŹŻä»ĄćŽ’ĺŤ°ĺ„ç§Ťĺ…łçł»ç¬¦ĺŹ·.
ĺ…łçł»ç¬¦ĺŹ·ćŻ \TeX\ çš„ć•°ĺ­¦ç¬¦ĺŹ·ä¸­çš„\minref{ç±»}äą‹ä¸€.
\TeX\ ĺś¨ä¸ŤĺŚçš„\minref{ç±»}äą‹é—´ćŹ’ĺ…Ąä¸ŤĺŚçš„ç©şç™˝é•żĺş¦.
ĺ˝“ \TeX\ éś€č¦ĺś¨ä¸€ä¸Şć•°ĺ­¦ĺ…¬ĺĽŹĺ¤„ć–­čˇŚ, \minrefs{ć–­čˇŚ}
ĺ®äĽšč€č™‘ĺś¨ä¸€ä¸Şĺ…łçł»ç¬¦ĺŽčż›čˇŚć–­čˇŚ---ä¸Ťčż‡ä»…ĺś¨ĺ®ĺ‡şçŽ°ĺś¨ĺ…¬ĺĽŹçš„ćś€ĺ¤–ĺ±‚ć—¶, č€Śä¸ŤćŻĺś¨ä¸€ä¸Şç»„ä¸­.

é™¤äş†čż™é‡Śĺ—ĺ‡şçš„ĺ‘˝ä»¤ä»Ąĺ¤–, \TeX\ äąźćŠŠ `^|=|' ĺ’Ś``arrow'' ĺ‘˝ä»¤ (\xref{arrows}) ä˝śä¸şĺ…łçł»čżç®—ç¬¦.

ä¸€äş›ĺ…łçł»ç¬¦ćś‰ĺ¤šç§Ťĺ‘˝ä»¤čˇ¨čľľć–ąĺĽŹ, ä˝&nbsp;ĺŹŻä»Ąä˝żç”¨ä»»ä˝•ä¸€ä¸ŞćťĄćŽ’ĺŤ°ĺ®ä»¬:
\ulist \compact
\li `$\ge$' (|\ge| ĺ’Ś |\geq|).
\li `$\le$' (|\le| ĺ’Ś |\leq|).
\li `$\ne$' (|\ne|, |\neq|, ĺ’Ś |\not=|).
\li `$\ni$' (|\ni| ĺ’Ś |\owns|).
\endulist

\xrdef{\not}
ĺś¨čż™äş›ç¬¦ĺŹ·ĺ‰ŤĺŠ&nbsp;ä¸Š |\not|, ĺŹŻä»ĄćŽ’ĺŤ°ĺ®ä»¬çš„éťžčżç®—:

\nobreak
\threecolumns 21
\basicdisplay {$\not\asymp$}{\\not\\asymp}\ctsidxref{asymp}
\basicdisplay {$\not\cong$}{\\not\\cong}\ctsidxref{cong}
\basicdisplay {$\not\equiv$}{\\not\\equiv}\ctsidxref{equiv}
\basicdisplay {$\not=$}{\\not=}\ttidxref{=}
\basicdisplay {$\not\ge$}{\\not\\ge}\ctsidxref{ge}
\basicdisplay {$\not\geq$}{\\not\\geq}\ctsidxref{geq}
\basicdisplay {$\not\le$}{\\not\\le}\ctsidxref{le}
\basicdisplay {$\not\leq$}{\\not\\leq}\ctsidxref{leq}
\basicdisplay {$\not\prec$}{\\not\\prec}\ctsidxref{prec}
\basicdisplay {$\not\preceq$}{\\not\\preceq}\ctsidxref{preceq}
\basicdisplay {$\not\succ$}{\\not\\succ}\ctsidxref{succ}
\basicdisplay {$\not\succeq$}{\\not\\succeq}\ctsidxref{succeq}
\basicdisplay {$\not\approx$}{\\not\\approx}\ctsidxref{approx}
\basicdisplay {$\not\sim$}{\\not\\sim}\ctsidxref{sim}
\basicdisplay {$\not\simeq$}{\\not\\simeq}\ctsidxref{simeq}
\basicdisplay {$\not\subset$}{\\not\\subset}\ctsidxref{subset}
\basicdisplay {$\not\subseteq$}{\\not\\subseteq}\ctsidxref{subseteq}
\basicdisplay {$\not\supset$}{\\not\\supset}\ctsidxref{supset}
\basicdisplay {$\not\supseteq$}{\\not\\supseteq}\ctsidxref{supseteq}
\basicdisplay {$\not\sqsubseteq$}{\\not\\sqsubseteq}%
   \ctsidxref{sqsubseteq}
\basicdisplay {$\not\sqsupseteq$}{\\not\\sqsupseteq}%
   \ctsidxref{sqsupseteq}
\egroup

\example
ć‘ä»¬ĺŹŻä»Ąĺľ—ĺ° $AB \perp AC$,ä¸”
$\triangle ABF \not\sim \triangle ACF$.
|
\produces
ć‘ä»¬ĺŹŻä»Ąĺľ—ĺ° $AB \perp AC$,ä¸”
$\triangle ABF \not\sim \triangle ACF$.

\eix^^{ĺ…łçł»ç¬¦}
\endexample
\enddesc

%==========================================================================
%\subsection {Left and right delimiters}
\subsection {ĺ·¦ĺŹłĺ®šç•Śç¬¦}

%\begindesc
%\bix^^{delimiters}
%%
%\dothreecolumns 12
%\easy\ctsdisplay lbrace {}
%\ctsydisplay { @lbrace {}
%\ctsdisplay rbrace {}
%\ctsydisplay } @rbrace {}
%\ctsdisplay lbrack {}
%\ctsdisplay rbrack {}
%\ctsdisplay langle {}
%\ctsdisplay rangle {}
%\ctsdisplay lceil {}
%\ctsdisplay rceil {}
%\ctsdisplay lfloor {}
%\ctsdisplay rfloor {}
%\egroup
%\explain
%These commands produce left and right \minref{delimiter}s.
%Mathematicians use delimiters to indicate the boundaries between parts
%of a formula.  Left delimiters are also called ``^{opening}s'', and
%right delimiters are also called ``^{closing}s''.  Openings and closings
%are two of \TeX's \minref{class}es of math symbols.  \TeX\ puts
%different amounts of space around different \minref{class}es of math
%symbols. You might expect the space that \TeX\ puts around openings and
%closings to be symmetrical, but in fact it isn't.
\begindesc
\bix^^{ĺ®šç•Śç¬¦}
%
\dothreecolumns 12
\easy\ctsdisplay lbrace {}
\writeidxfalse\ctsydisplay { @lbrace {}\writeidxtrue
\ctsdisplay rbrace {}
\writeidxfalse\ctsydisplay } @rbrace {}\writeidxtrue
\ctsdisplay lbrack {}
\ctsdisplay rbrack {}
\ctsdisplay langle {}
\ctsdisplay rangle {}
\ctsdisplay lceil {}
\ctsdisplay rceil {}
\ctsdisplay lfloor {}
\ctsdisplay rfloor {}
\egroup
\explain
čż™äş›ĺ‘˝ä»¤ćŽ’ĺŤ°ĺ„ç§Ťĺ·¦ĺŹł\minref{ĺ®šç•Śç¬¦}ă€‚
ć•°ĺ­¦ĺ®¶ç”¨ĺ®šç•Śç¬¦ćŚ‡ćŽĺ…¬ĺĽŹĺ„é¨ĺ†çš„čľąç•Śă€‚
ĺ·¦ĺ®šç•Śç¬¦ĺŹç§°ä¸ş``^{ĺĽ€ç¬¦ĺŹ·}''ďĽŚĺŹłĺ®šç•Śç¬¦ĺŹç§°ä¸ş``^{é—­ç¬¦ĺŹ·}''ă€‚
ĺĽ€ç¬¦ĺŹ·ĺ’Śé—­ç¬¦ĺŹ·ćŻ \TeX\ ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„ä¸¤ç§Ťĺ­—ç¬¦ç±»ă€‚
\TeX\ ĺś¨ä¸ŤĺŚ\minref{ç±»}çš„ć•°ĺ­¦ç¬¦ĺŹ·äą‹é—´ç•™ä¸‹ä¸ŤĺŚĺ¤§ĺ°Źçš„é—´éš”ă€‚
ä˝&nbsp;äąźč®¸č®¤ä¸şĺś¨ĺĽ€ç¬¦ĺŹ·ĺ’Śé—­ç¬¦ĺŹ·ć—čľąçš„é—´éš”ćŻĺŻąç§°çš„ďĽŚä˝†ĺ®žé™…ä¸Šĺą¶éťžĺ¦‚ć­¤ă€‚

%Some left and right delimiters have more than one command that you can
%use to produce them:
ćś‰äş›ĺ·¦ĺ®šç•Śç¬¦ĺ’ŚĺŹłĺ®šç•Śç¬¦ĺŹŻä»Ąç”¨ä¸Ťć­˘ä¸€ä¸Şĺ‘˝ä»¤ćŽ’ĺŤ°ďĽš

%\ulist\compact
%\li `$\{$' (|\lbrace| and |\{|)
%\li `$\}$' (|\rbrace| and |\}|)
%\li `$[$' (|\lbrack| and `|[|')
%\li `$]$' (|\rbrack| and `|]|')
%\endulist
%\noindent You can also use the left and right bracket characters
%(in either form) outside of math mode.
\ulist\compact
\li `$\{$' (|\lbrace| ĺ’Ś |\{|)
\li `$\}$' (|\rbrace| ĺ’Ś |\}|)
\li `$[$' (|\lbrack| ĺ’Ś `|[|')
\li `$]$' (|\rbrack| ĺ’Ś `|]|')
\endulist
\noindent ĺ·¦ĺŹłć–ąć‹¬ĺŹ·ďĽä¸¤ç§Ťĺ˝˘ĺĽŹçš†ĺŹŻďĽ‰ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹäą‹ĺ¤–äąźĺŹŻä»Ąä˝żç”¨ă€‚

%In addition to these commands, \TeX\ treats `|(|' as a left
%delimiter and `|)|' as a right delimiter.
é™¤čż™äş›ĺ‘˝ä»¤äą‹ĺ¤–ďĽŚ\TeX\ čżĺ°† `|(|' č§†ä¸şĺ·¦ĺ®šç•Śç¬¦ďĽŚĺ°† `|)|' č§†ä¸şĺŹłĺ®šç•Śç¬¦ă€‚

%You can have \TeX\
%choose the size for a delimiter by using |\left| and |\right| (\xref\left).
%Alternatively,
%you can get a delimiter of a specific size by using one of the |\big|$x$
%commands (see |\big| et al., \xref{\big}).
ĺ©ç”¨ |\left| ĺ’Ś |\right|ďĽ\xref\left ďĽ‰ĺ‘˝ä»¤ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąč®© \TeX\ é€‰ć‹©ĺ®šç•Śç¬¦çš„ĺ°şĺŻ¸ă€‚
ć–č€…ĺ©ç”¨ćźä¸Ş |\big|$x$ ĺ‘˝ä»¤ďĽč§ |\big| ç­‰ďĽŚ\xref{\big}ďĽ‰ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąé€‰ć‹©ç‰ąĺ®šĺ°şĺŻ¸çš„ĺ®šç•Śç¬¦ă€‚

%\example
%The set $\{\,x \mid x&gt;0\,\}$ is empty.
%|
%\produces
%The set $\{\,x \mid x&gt;0\,\}$ is empty.
\example
é›†ĺ $\{\,x \mid x&gt;0\,\}$ ćŻç©şé›†.
|
\produces
é›†ĺ $\{\,x \mid x&gt;0\,\}$ ćŻç©şé›†.

%\eix^^{delimiters}
%\endexample
%\enddesc
\eix^^{ĺ®šç•Śç¬¦}
\endexample
\enddesc

%==========================================================================
%\subsection {Arrows}
\subsection {ç®­ĺ¤´}

%\begindesc
%\bix^^{arrows}
%\xrdef{arrows}
%%
%{\symbolspace=24pt \makecolumns 34/2:
%\easy%
%\ctsdisplay leftarrow {}
%\ctsdisplay gets {}
%\ctsdisplay Leftarrow {}
%\ctsdisplay rightarrow {}
%\ctsdisplay to {}
%\ctsdisplay Rightarrow {}
%\ctsdisplay leftrightarrow {}
%\ctsdisplay Leftrightarrow {}
%\ctsdisplay longleftarrow {}
%\ctsdisplay Longleftarrow {}
%\ctsdisplay longrightarrow {}
%\ctsdisplay Longrightarrow {}
%\ctsdisplay longleftrightarrow {}
%\ctsdisplay Longleftrightarrow {}
%\basicdisplay {$\Longleftrightarrow$}{\\iff}\pix\ctsidxref{iff}\xrdef{\iff}
%\ctsdisplay hookleftarrow {}
%\ctsdisplay hookrightarrow {}
%\ctsdisplay leftharpoondown {}
%\ctsdisplay rightharpoondown {}
%\ctsdisplay leftharpoonup {}
%\ctsdisplay rightharpoonup {}
%\ctsdisplay rightleftharpoons {}
%\ctsdisplay mapsto {}
%\ctsdisplay longmapsto {}
%\ctsdisplay downarrow {}
%\ctsdisplay Downarrow {}
%\ctsdisplay uparrow {}
%\ctsdisplay Uparrow {}
%\ctsdisplay updownarrow {}
%\ctsdisplay Updownarrow {}
%\ctsdisplay nearrow {}
%\ctsdisplay searrow {}
%\ctsdisplay nwarrow {}
%\ctsdisplay swarrow {}
%}
%\explain
%These commands provide arrows of different kinds.  They
%are classified as relations (\xref{relations}).
%The vertical arrows in the list are also \minref{delimiter}s, so you can make
%them larger by using |\big| et al.\ (\xref \big).
\begindesc
\bix^^{ç®­ĺ¤´}
\xrdef{arrows}
%
{\symbolspace=24pt \makecolumns 34/2:
\easy%
\ctsdisplay leftarrow {}
\ctsdisplay gets {}
\ctsdisplay Leftarrow {}
\ctsdisplay rightarrow {}
\ctsdisplay to {}
\ctsdisplay Rightarrow {}
\ctsdisplay leftrightarrow {}
\ctsdisplay Leftrightarrow {}
\ctsdisplay longleftarrow {}
\ctsdisplay Longleftarrow {}
\ctsdisplay longrightarrow {}
\ctsdisplay Longrightarrow {}
\ctsdisplay longleftrightarrow {}
\ctsdisplay Longleftrightarrow {}
\basicdisplay {$\Longleftrightarrow$}{\\iff}\pix\ctsidxref{iff}\xrdef{\iff}
\ctsdisplay hookleftarrow {}
\ctsdisplay hookrightarrow {}
\ctsdisplay leftharpoondown {}
\ctsdisplay rightharpoondown {}
\ctsdisplay leftharpoonup {}
\ctsdisplay rightharpoonup {}
\ctsdisplay rightleftharpoons {}
\ctsdisplay mapsto {}
\ctsdisplay longmapsto {}
\ctsdisplay downarrow {}
\ctsdisplay Downarrow {}
\ctsdisplay uparrow {}
\ctsdisplay Uparrow {}
\ctsdisplay updownarrow {}
\ctsdisplay Updownarrow {}
\ctsdisplay nearrow {}
\ctsdisplay searrow {}
\ctsdisplay nwarrow {}
\ctsdisplay swarrow {}
}
\explain
čż™äş›ĺ‘˝ä»¤ćŹäľ›ĺ„ç§Ťç®­ĺ¤´ă€‚ĺ®ä»¬č˘«ĺ’ĺ†ä¸şĺ…łçł»ç¬¦ĺŹ·ďĽ\xref{relations}ďĽ‰ă€‚
ä¸Šéť˘çš„ç«–ç›´ç®­ĺ¤´ĺŚć—¶äąźćŻ\minref{ĺ®šç•Śç¬¦}ďĽŚ
ĺ›&nbsp;ć­¤ä˝&nbsp;ĺŹŻä»Ąç”¨ |\big| ç­‰ĺ‘˝ä»¤č®©ĺ®ä»¬ĺŹĺ¤§ďĽ\xref \big ďĽ‰ă€‚

%The command |\iff| differs from |\Longleftrightarrow| in that
%it produces extra space to the left and right of the arrow.
ĺ‘˝ä»¤ |\iff| ĺ’Ś |\Longleftrightarrow| çš„ĺ·®ĺ«äą‹ĺ¤„ĺś¨äşŽďĽŚ
ĺ®ĺś¨ç®­ĺ¤´ä¸¤čľąç”źćé˘ťĺ¤–é—´éš”ă€‚

%You can place symbols or other legends on top of a left or right arrow
%with |\buildrel| (\xref \buildrel).
ä˝&nbsp;ĺŹŻä»Ąç”¨ |\buildrel|ďĽ\xref \buildrel ďĽ‰ĺ‘˝ä»¤ĺ°†ç¬¦ĺŹ·ć–č€…ĺ…¶ä»–ć–‡ĺ­—ć”ľĺś¨ç®­ĺ¤´ä¸Ščľąă€‚

%\example
%$$f(x)\mapsto f(y) \iff x \mapsto y$$
%|
%\dproduces
%$$f(x)\mapsto f(y) \iff x \mapsto y$$
\example
$$f(x)\mapsto f(y) \iff x \mapsto y$$
|
\dproduces
$$f(x)\mapsto f(y) \iff x \mapsto y$$

%\eix^^{arrows}
%\endexample
%\enddesc
\eix^^{ç®­ĺ¤´}
\endexample
\enddesc

%==========================================================================
%\subsection {Named mathematical functions}
\subsection {ĺ·˛ĺ‘˝ĺŤçš„ć•°ĺ­¦ĺ‡˝ć•°}

%\begindesc
%\xrdef{namedfns}
%\bix^^{functions, names of}
%{\symbolspace = 36pt
%\threecolumns 32
%\easy\ctsdisplay cos {}
%\ctsdisplay sin {}
%\ctsdisplay tan {}
%\ctsdisplay cot {}
%\ctsdisplay csc {}
%\ctsdisplay sec {}
%\ctsdisplay arccos {}
%\ctsdisplay arcsin {}
%\ctsdisplay arctan {}
%\ctsdisplay cosh {}
%\ctsdisplay coth {}
%\ctsdisplay sinh {}
%\ctsdisplay tanh {}
%\ctsdisplay det {}
%\ctsdisplay dim {}
%\ctsdisplay exp {}
%\ctsdisplay ln {}
%\ctsdisplay log {}
%\ctsdisplay lg {}
%\ctsdisplay arg {}
%\ctsdisplay deg {}
%\ctsdisplay gcd {}
%\ctsdisplay hom {}
%\ctsdisplay ker {}
%\ctsdisplay inf {}
%\ctsdisplay sup {}
%\ctsdisplay lim {}
%\ctsdisplay liminf {}
%\ctsdisplay limsup {}
%\ctsdisplay max {}
%\ctsdisplay min {}
%\ctsdisplay Pr {}
%\egroup}
%\explain
%These commands set the names of various mathematical functions
%in roman type, as is customary.
%If you apply a superscript or subscript to one of these commands,
%\TeX\ will in most cases typeset it in the usual place.
%In display style, \TeX\ typesets superscripts and subscripts
%on |\det|, |\gcd|, |\inf|, |\lim|, |\liminf|,
%|\limsup|, |\max|, |\min|, |\Pr|, and |\sup|
%as though they were limits,
%i.e., directly above or directly below the function name.
\begindesc
\xrdef{namedfns}
\bix^^{ĺ‡˝ć•°ĺŤç§°}
{\symbolspace = 36pt
\threecolumns 32
\easy\ctsdisplay cos {}
\ctsdisplay sin {}
\ctsdisplay tan {}
\ctsdisplay cot {}
\ctsdisplay csc {}
\ctsdisplay sec {}
\ctsdisplay arccos {}
\ctsdisplay arcsin {}
\ctsdisplay arctan {}
\ctsdisplay cosh {}
\ctsdisplay coth {}
\ctsdisplay sinh {}
\ctsdisplay tanh {}
\ctsdisplay det {}
\ctsdisplay dim {}
\ctsdisplay exp {}
\ctsdisplay ln {}
\ctsdisplay log {}
\ctsdisplay lg {}
\ctsdisplay arg {}
\ctsdisplay deg {}
\ctsdisplay gcd {}
\ctsdisplay hom {}
\ctsdisplay ker {}
\ctsdisplay inf {}
\ctsdisplay sup {}
\ctsdisplay lim {}
\ctsdisplay liminf {}
\ctsdisplay limsup {}
\ctsdisplay max {}
\ctsdisplay min {}
\ctsdisplay Pr {}
\egroup}
\explain
čż™äş›ĺ‘˝ä»¤ä»ĄćŻç”¨çš„ç˝—é©¬ĺ­—ä˝“ćŽ’ĺŤ°ĺ„ç§Ťć•°ĺ­¦ĺ‡˝ć•°çš„ĺŤç§°ă€‚
ĺ¦‚ćžśä˝&nbsp;ç»™čż™äş›ĺ‘˝ä»¤ä¸­çš„ä»»ä˝•ä¸€ä¸ŞĺŠ&nbsp;ä¸Šä¸Šć&nbsp;‡ć–ä¸‹ć&nbsp;‡ďĽŚ
\TeX\ ĺ°†ĺś¨é€šĺ¸¸çš„ä˝Ťç˝®ćŽ’ç‰ĺ®ă€‚
ĺś¨é™ĺ—ć&nbsp;·ĺĽŹä¸­ďĽŚĺŻąäşŽ |\det|ă€|\gcd|ă€|\inf|ă€|\lim|ă€|\liminf|ă€
|\limsup|ă€|\max|ă€|\min|ă€|\Pr| ĺ’Ś |\sup|ďĽŚ
\TeX\ ĺ°†ä¸Šć&nbsp;‡ĺ’Śä¸‹ć&nbsp;‡ĺ˝“ććžé™é‚Łć&nbsp;·ćŽ’ç‰ďĽŚ
ĺŤłĺ°†ĺ®ä»¬ç›´ćŽĄć”ľĺś¨ĺ‡˝ć•°ĺŤçš„ä¸Ščľąć–ä¸‹čľąă€‚

%\example
%$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
%|
%\produces
%$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
%\endexample\enddesc
\example
$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
|
\produces
$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
\endexample\enddesc

%\begindesc
%\cts bmod {}
%\explain
%This command produces a binary operation for indicating a ^{modulus}
%within a formula.
%\example
%$$x = (y+1) \bmod 2$$
%|
%\dproduces
%$$x = (y+1) \bmod 2$$
%\endexample
%\enddesc
\begindesc
\cts bmod {}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸€ä¸Şć&nbsp;‡ćŽĺ…¬ĺĽŹĺ†…çš„^{ć¨ˇčżç®—}çš„äşŚĺ…čżç®—ç¬¦ă€‚
\example
$$x = (y+1) \bmod 2$$
|
\dproduces
$$x = (y+1) \bmod 2$$
\endexample
\enddesc

%\begindesc
%\cts pmod {}
%\explain
%This command provides a notation for indicating a ^{modulus} in parentheses
%at the end of a formula.
%\example
%$$x \equiv y+1 \pmod 2$$
%|
%\dproduces
%$$x \equiv y+1 \pmod 2$$
\begindesc
\cts pmod {}
\explain
ć­¤ĺ‘˝ä»¤ĺś¨ĺ…¬ĺĽŹćś«ĺ°ľćŽ’ĺŤ°ć”ľĺś¨ĺś†ć‹¬ĺŹ·ä¸­çš„^{ć¨ˇčżç®—}ă€‚
\example
$$x \equiv y+1 \pmod 2$$
|
\dproduces
$$x \equiv y+1 \pmod 2$$

%\eix^^{functions, names of}
%\endexample
%\enddesc
\eix^^{ĺ‡˝ć•°ĺŤç§°}
\endexample
\enddesc


%==========================================================================
%\subsection {Large operators}
\subsection {ĺ·¨ç®—ç¬¦}

%\begindesc
%\bix^^{operators//large}
%\threecolumns 15
%\easy\ctsdoubledisplay bigcap {}
%\ctsdoubledisplay bigcup {}
%\ctsdoubledisplay bigodot {}
%\ctsdoubledisplay bigoplus {}
%\ctsdoubledisplay bigotimes {}
%\ctsdoubledisplay bigsqcup {}
%\ctsdoubledisplay biguplus {}
%\ctsdoubledisplay bigvee {}
%\ctsdoubledisplay bigwedge {}
%\ctsdoubledisplay coprod {}
%{\symbolspace = 42pt\basicdisplay {\hskip 26pt$\smallint$}%
%   {\\smallint}\ddstrut}%
%   \xrdef{\smallint} \pix\ctsidxref{smallint}
%\ctsdoubledisplay int {}
%\ctsdoubledisplay oint {}
%\ctsdoubledisplay prod {}
%\ctsdoubledisplay sum {}
%}
%\explain
%These commands produce various large operator symbols.
%\TeX\ produces the smaller size when it's in ^{text style}
%\minrefs{math mode} and the larger size when it's in ^{display style}.
%Operators are one of \TeX's \minref{class}es of math symbols.
%\TeX\ puts different amounts of space
%around different classes of math symbols.
\begindesc
\bix^^{čżç®—ç¬¦//ĺ·¨ç®—ç¬¦}
\threecolumns 15
\easy\ctsdoubledisplay bigcap {}
\ctsdoubledisplay bigcup {}
\ctsdoubledisplay bigodot {}
\ctsdoubledisplay bigoplus {}
\ctsdoubledisplay bigotimes {}
\ctsdoubledisplay bigsqcup {}
\ctsdoubledisplay biguplus {}
\ctsdoubledisplay bigvee {}
\ctsdoubledisplay bigwedge {}
\ctsdoubledisplay coprod {}
{\symbolspace = 42pt\basicdisplay {\hskip 26pt$\smallint$}%
   {\\smallint}\ddstrut}%
   \xrdef{\smallint} \pix\ctsidxref{smallint}
\ctsdoubledisplay int {}
\ctsdoubledisplay oint {}
\ctsdoubledisplay prod {}
\ctsdoubledisplay sum {}
}
\explain
čż™äş›ĺ‘˝ä»¤ćŽ’ĺŤ°ĺ„ç§Ťĺ·¨ç®—ç¬¦ă€‚
\TeX\ ĺś¨^{ć–‡ĺ†…ć&nbsp;·ĺĽŹ}ä¸­ćŽ’ĺŤ°ĺ°ŹĺŹ·ĺ­—ç¬¦ďĽŚ
\minrefs{math mode}č€Śĺś¨^{é™ĺ—ć&nbsp;·ĺĽŹ}ä¸­ćŽ’ĺŤ°ĺ¤§ĺŹ·ĺ­—ç¬¦.
ĺ·¨ç®—ç¬¦ćŻ \TeX\ ć•°ĺ­¦ç¬¦ĺŹ·çš„ĺ…¶ä¸­ä¸€\minref{ç±»}ă€‚
\TeX\ ĺś¨ä¸ŤĺŚç±»ć•°ĺ­¦ç¬¦ĺŹ·é—´ç•™ä¸‹ä¸ŤĺŚĺ¤§ĺ°Źçš„é—´éš”ă€‚

%The large operator symbols with `|big|' in their names are different
%from the corresponding binary operations (see \xref{binops}) such as
%|\cap| ($\cap$) since they usually appear at the beginning
%of a formula.  \TeX\ uses different spacing for a large operator
%than it does for a binary operation.
ĺŤç§°ä¸­ĺ¸¦ćś‰ `|big|' çš„ĺ·¨ç®—ç¬¦ĺ’ŚĺŻąĺş”çš„äşŚĺ…čżç®—ç¬¦%
ďĽćŻ”ĺ¦‚ |\cap| ($\cap$)ďĽŚč§\xref{binops}ďĽ‰ä¸ŤĺŚďĽŚ
ĺ›&nbsp;ä¸şĺ®ä»¬é€šĺ¸¸ĺ‡şçŽ°ĺ…¬ĺĽŹçš„ĺĽ€ĺ¤´ă€‚
\TeX\ ç»™ĺ·¨ç®—ç¬¦ç•™ä¸‹çš„é—´éš”ä¸ŽäşŚĺ…čżç®—ç¬¦çš„ä¸ŤĺŚă€‚

%Don't confuse `$\sum$' (|\sum|) with `$\Sigma$'^^|\Sigma| (|\Sigma|)
%or confuse `$\prod$' (|\prod|) with `$\Pi$' ^^|\Pi| (|\Pi|).
%|\Sigma| and |\Pi| produce capital Greek letters, which are smaller and
%have a different appearance.
ä¸Ťč¦ć··ć·† `$\sum$' (|\sum|) ĺ’Ś `$\Sigma$'^^|\Sigma| (|\Sigma|)ďĽŚ
ć–č€… `$\prod$' (|\prod|) ĺ’Ś `$\Pi$' ^^|\Pi| (|\Pi|)ă€‚
|\Sigma| ĺ’Ś |\Pi| ćŽ’ĺŤ°ĺ¤§ĺ†™ĺ¸Śč…Šĺ­—ćŻŤďĽŚĺ®ä»¬ĺ°şĺŻ¸ć›´ĺ°ŹďĽŚĺ¤–č§‚äąźä¸ŤĺŚă€‚

%A large operator can have ^{limits}.  The lower limit is specified as a
%subscript and the upper limit as a superscript.
ĺ·¨ç®—ç¬¦ĺŹŻä»Ąĺ¸¦ćś‰^{ćžé™}ă€‚ä¸‹ćžé™ç”¨ä¸‹ć&nbsp;‡ćŚ‡ĺ®šďĽŚč€Śä¸Šćžé™ç”¨ä¸Šć&nbsp;‡ćŚ‡ĺ®šă€‚

%\example
%$$\bigcap_{k=1}^r (a_k \cup b_k)$$
%|
%\dproduces
%$$\bigcap_{k=1}^r (a_k \cup b_k)$$
%\endexample
%\interexampleskip
%\example
%$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
%|
%\dproduces
%$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
%\endexample
%\enddesc
\example
$$\bigcap_{k=1}^r (a_k \cup b_k)$$
|
\dproduces
$$\bigcap_{k=1}^r (a_k \cup b_k)$$
\endexample
\interexampleskip
\example
$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
|
\dproduces
$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
\endexample
\enddesc

%\begindesc
%\cts limits {}
%\explain
%When it's in text style, \TeX\ normally places limits after a large operator.
%This command tells \TeX\ to place
%limits above and below a large operator rather than after it.
\begindesc
\cts limits {}
\explain
ĺś¨ć–‡ĺ†…ć&nbsp;·ĺĽŹä¸­ďĽŚ\TeX\ é€šĺ¸¸ĺ°†ćžé™ć”ľĺś¨ĺ·¨ç®—ç¬¦ĺŽčľąă€‚
ć­¤ĺ‘˝ä»¤č®© \TeX\ ĺ°†ćžé™ć”ľĺś¨ĺ·¨ç®—ç¬¦çš„ä¸Ščľąĺ’Śä¸‹čľąďĽŚč€Śä¸ŤćŻĺś¨ĺŽčľąă€‚

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
ĺ¦‚ćžśä˝&nbsp;ĺ¤šć¬ˇä˝żç”¨ |\limits|ă€|\nolimits| ć– |\display!-limits|ďĽŚ
ä»…ćś€ĺŽä¸€ä¸Şĺ‘˝ä»¤ç”źć•ă€‚

%\example
%Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
%two elements.
%|
%\produces
%Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
%two elements.
%\endexample
%\enddesc
\example
Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
two elements.
|
\produces
Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
two elements.
\endexample
\enddesc

%\begindesc
%\cts nolimits {}
%\explain
%When it's in display
%style, \TeX\ normally places limits above and below a large operator.
%(The |\int| operator is an exception---\TeX\
%places limits for |\int| after the operator in all cases.)
%^^|\int//limits after|
%This command tells \TeX\ to place
%limits after a large operator rather than above and below it.
\begindesc
\cts nolimits {}
\explain
ĺś¨é™ĺ—ć&nbsp;·ĺĽŹä¸­ďĽŚ\TeX\ é€šĺ¸¸ĺ°†ćžé™ć”ľĺś¨ĺ·¨ç®—ç¬¦çš„ä¸Ščľąĺ’Śä¸‹čľąă€‚%
ďĽ|\int| ç®—ç¬¦ćŻä¸€ä¸Şäľ‹ĺ¤–â€”â€” \TeX\ ć€»ćŻĺ°†ćžé™ć”ľĺś¨ç®—ç¬¦çš„ĺŽčľąă€‚ďĽ‰%
^^|\int//ćžé™ć”ľĺś¨ĺŽéť˘|
ć­¤ĺ‘˝ä»¤č®© \TeX\ ĺ°†ćžé™ć”ľĺś¨ĺ·¨ç®—ç¬¦ĺŽčľąďĽŚč€Śä¸ŤćŻä¸Ščľąĺ’Śä¸‹čľąă€‚

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
ĺ¦‚ćžśä˝&nbsp;ĺ¤šć¬ˇä˝żç”¨ |\limits|ă€|\nolimits| ć– |\display!-limits|ďĽŚ
ä»…ćś€ĺŽä¸€ä¸Şĺ‘˝ä»¤ç”źć•ă€‚

%\example
%$$\bigcap\nolimits_{i=1}^Nq_i$$
%|
%\dproduces
%$$\bigcap\nolimits_{i=1}^Nq_i$$
%\endexample
%\enddesc
\example
$$\bigcap\nolimits_{i=1}^Nq_i$$
|
\dproduces
$$\bigcap\nolimits_{i=1}^Nq_i$$
\endexample
\enddesc

%\begindesc
%\cts displaylimits {}
%\explain
%This command tells \TeX\ to
%follow its normal rules for placement of limits:
%\olist\compact
%\li Limits on ^|\int| are placed after the operator.
%\li Limits on other large operators are placed after the
%operator in text style.
%\li Limits on other large operators are placed above and below the operator
%in display style.
%\endolist
%It's usually simpler to use |\limits| or |\nolimits|
%to produce a specific effect, but |\display!-limits| is sometimes
%useful in \minref{macro} definitions.
\begindesc
\cts displaylimits {}
\explain
ć­¤ĺ‘˝ä»¤č®© \TeX\ ćŚ‰ç…§é€šĺ¸¸ć–ąĺĽŹć”ľç˝®ćžé™ďĽš
\olist\compact
\li ^|\int| ç®—ç¬¦çš„ćžé™ć€»ć”ľĺś¨ç®—ç¬¦ĺŽčľąă€‚%
\footnote{čŻ‘ćł¨ďĽšć­¤ĺ¤„äĽĽäąŽćś‰čŻŻďĽŚĺś¨ |\displaylimits| ä¸‹ ^|\int| ĺ’Śĺ…¶ä»–ç®—ç¬¦ĺş”čŻĄćś‰ç›¸ĺŚçš„čˇ¨çŽ°ă€‚}
\li ĺś¨ć–‡ĺ†…ć&nbsp;·ĺĽŹä¸­ďĽŚĺ…¶ä»–ĺ·¨ç®—ç¬¦çš„ćžé™ć”ľĺś¨ç®—ç¬¦çš„ĺŽčľąă€‚
\li ĺś¨é™ĺ—ć&nbsp;·ĺĽŹä¸­ďĽŚĺ…¶ä»–ĺ·¨ç®—ç¬¦çš„ćžé™ć”ľĺś¨ç®—ç¬¦çš„ä¸Ščľąĺ’Śä¸‹čľąă€‚
\endolist
ç”¨ |\limits| ć– |\nolimits| ćťĄćŽ’ĺŤ°ç‰ąĺ®šć•ćžść›´ä¸şç®€ĺŤ•ďĽŚ
ä˝† |\display!-limits| ĺś¨\minref{ĺ®Ź}ĺ®šäą‰ä¸­ćś‰ć—¶äĽšç”¨ĺ°ă€‚

%Note that \plainTeX\ defines ^|\int| as a macro that sets |\nolimits|,
%so |\int\displaylimits| in text style restores the |\limits|
%convention.
ćł¨ć„Ź \plainTeX\ ĺś¨ĺ®šäą‰ ^|\int| ć—¶ĺ°±ĺ¸¦ćś‰ |\nolimits|ďĽŚ
ĺ›&nbsp;ć­¤ć–‡ĺ†…ć&nbsp;·ĺĽŹçš„ |\int\displaylimits| ĺ°†ć˘ĺ¤Ť |\limits| çş¦ĺ®šă€‚%
\footnote{čŻ‘ćł¨ďĽšć­¤ĺ¤„äĽĽäąŽćś‰čŻŻďĽŚĺś¨ć–‡ĺ†…ć&nbsp;·ĺĽŹä¸­ďĽŚ|\int\displaylimits| çš„ćžé™ĺş”čŻĄčżćŻĺś¨ĺŽčľąă€‚}

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
ĺ¦‚ćžśä˝&nbsp;ĺ¤šć¬ˇä˝żç”¨ |\limits|ă€|\nolimits| ć– |\display!-limits|ďĽŚ
ä»…ćś€ĺŽä¸€ä¸Şĺ‘˝ä»¤ç”źć•ă€‚

%\example
%$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
%_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
%|
%\dproduces
%$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
%_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
\example
$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
|
\dproduces
$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$

%\eix^^{operators//large}
%\endexample
%\enddesc
\eix^^{čżç®—ç¬¦//ĺ·¨ç®—ç¬¦}
\endexample
\enddesc


%==========================================================================
%\subsection {Punctuation}
\subsection {ć&nbsp;‡ç‚ą}

%\begindesc
%\bix^^{punctuation in math formulas}
%\cts cdotp {}
%\cts ldotp {}
%\explain
%These two commands respectively produce a centered dot and a dot
%positioned on the \minref{baseline}.  They are valid only in math
%\minref{mode}.  \TeX\ treats them as punctuation, putting no extra space in
%front of them but a little extra space after them.
%In contrast, \TeX\ puts an equal amount of space on both sides
%of a centered dot generated by the ^|\cdot| command (\xref \cdot).
%\example
%$x \cdotp y \quad x \ldotp y \quad x \cdot y$
%|
%\produces
%$x \cdotp y \quad x \ldotp y \quad x \cdot y$
%\endexample
%\enddesc
\begindesc
\bix^^{ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„ć&nbsp;‡ç‚ą}
\cts cdotp {}
\cts ldotp {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺ†ĺ«ćŽ’ĺŤ°ĺ±…ä¸­çš„ĺś†ç‚ąĺ’Śĺś¨\minref{ĺźşçşż}ä¸Šçš„ĺś†ç‚ąă€‚
ĺ®ä»¬ä»…ĺŹŻç”¨äşŽć•°ĺ­¦\minref{ć¨ˇĺĽŹ}ä¸­ă€‚
\TeX\ ĺ°†ĺ®ä»¬č§†ä¸şć&nbsp;‡ç‚ąďĽŚĺś¨ĺ‰Ťéť˘ä¸Ťç•™é—´éš”č€Śĺś¨ĺŽéť˘ç•™ä¸‹ä¸€ç‚ąé—´éš”ă€‚
ä¸Žć­¤ç›¸ĺŹŤďĽŚĺŻąäşŽç”¨ ^|\cdot| ĺ‘˝ä»¤ďĽ\xref\cdot ďĽ‰ç”źćçš„ĺ±…ä¸­ĺś†ç‚ąďĽŚ
\TeX\ ĺś¨ĺ…¶ä¸¤äľ§ç•™ä¸‹ç›¸ĺŚĺ¤§ĺ°Źçš„é—´éš”ă€‚
\example
$x \cdotp y \quad x \ldotp y \quad x \cdot y$
|
\produces
$x \cdotp y \quad x \ldotp y \quad x \cdot y$
\endexample
\enddesc

%\begindesc
%\cts colon {}
%\explain
%This command produces a colon punctation symbol.
%It is valid only in math mode.
%The difference between |\colon| and the colon character (|:|) is that
%`|:|' is an operator, so \TeX\ puts extra space to the left of it whereas
%it doesn't put extra space to the left of |\colon|.
%\example
%$f \colon t \quad f : t$
%|
%\produces
%$f \colon t \quad f : t$
\begindesc
\cts colon {}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸€ä¸Şĺ†’ĺŹ·ć&nbsp;‡ç‚ąďĽŚĺ®ĺŹŞč˝ç”¨ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹä¸­ă€‚
ĺ†’ĺŹ·ć&nbsp;‡ç‚ą |\colon| ĺ’Śĺ†’ĺŹ·ĺ­—ç¬¦(|:|)çš„ĺŚşĺ«ĺś¨äşŽďĽŚ
`|:|' ćŻä¸€ä¸Şčżç®—ç¬¦ďĽŚĺ›&nbsp;ć­¤ \TeX\ ĺś¨ĺ…¶ĺ·¦äľ§ç•™ä¸‹é˘ťĺ¤–é—´éš”ďĽŚ
ç„¶č€Śĺś¨ |\colon| ĺ·¦äľ§ĺŤ´ä¸Ťç•™é˘ťĺ¤–é—´éš”ă€‚
\example
$f \colon t \quad f : t$
|
\produces
$f \colon t \quad f : t$

%\eix^^{punctuation in math formulas}
%\endexample
%\enddesc
\eix^^{ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„ć&nbsp;‡ç‚ą}
\endexample
\enddesc


%==========================================================================
%\secondprinting{\vfill\eject\null\vglue-30pt\vskip0pt}
%\section {Superscripts and subscripts}
\section {ä¸Šć&nbsp;‡ĺ’Śä¸‹ć&nbsp;‡}

%\begindesc
%\margin{Two groups of commands have been combined here.}
%\bix^^{superscripts}
%\bix^^{subscripts}
%\secondprinting{\vglue-12pt}
%\makecolumns 4/2:
%\easy\ctsact _ \xrdef{@underscore} {\&lt;argument&gt;}
%\cts sb {\&lt;argument&gt;}
%\ctsact ^ \xrdef{@hat} {\&lt;argument&gt;}
%\cts sp {\&lt;argument&gt;}
%\secondprinting{\vglue-4pt}
%\explain
%The commands in each column are equivalent.  The commands in the first
%column typeset \&lt;argument&gt; as a subscript, and those in the second
%column typeset \&lt;argument&gt; as a superscript.  The |\sb| and |\sp|
%commands are mainly useful if you're working on a terminal that lacks an
%underscore or caret, or if you've redefined `|_|' or `|^|' and need
%access to the original definition.  These commands are also used for
%setting lower and upper limits on summations and integrals.  ^^{lower
%limits} ^^{upper limits}
\begindesc
\margin{Two groups of commands have been combined here.}
\bix^^{ä¸Šć&nbsp;‡}
\bix^^{ä¸‹ć&nbsp;‡}
\secondprinting{\vglue-12pt}
\makecolumns 4/2:
\easy\ctsact _ \xrdef{@underscore} {\&lt;argument&gt;}
\cts sb {\&lt;argument&gt;}
\ctsact ^ \xrdef{@hat} {\&lt;argument&gt;}
\cts sp {\&lt;argument&gt;}
\secondprinting{\vglue-4pt}
\explain
ĺ„ć&nbsp;Źçš„ä¸¤ä¸Şĺ‘˝ä»¤é˝ćŻç­‰ä»·çš„ă€‚ç¬¬ä¸€ć&nbsp;Źçš„ĺ‘˝ä»¤ĺ°† \&lt;argument&gt; ćŽ’ç‰ä¸şä¸‹ć&nbsp;‡ďĽŚ
č€Śç¬¬äşŚć&nbsp;Źçš„ĺ‘˝ä»¤ĺ°† \&lt;argument&gt; ćŽ’ç‰ä¸şä¸Šć&nbsp;‡ă€‚
|\sb| ĺ’Ś |\sp| ĺ‘˝ä»¤ä¸»č¦ç”¨äşŽć—&nbsp;ćł•ä˝żç”¨ä¸‹ĺ’çşżĺ’ŚćŹ’ĺ…Ąç¬¦çš„ç»ç«Żä¸­ďĽŚ
ć–č€…ç”¨ĺś¨é‡Ťć–°ĺ®šäą‰äş† `|_|' or `|^|' ä˝†éś€č¦ĺ…¶ĺŽźĺ§‹ĺ®šäą‰çš„ć…ĺ†µä¸‹ă€‚
čż™äş›ĺ‘˝ä»¤äąźç”¨äşŽč®ľĺ®šć±‚ĺ’ŚĺŹ·ĺ’Śç§Żĺ†ĺŹ·çš„ä¸‹ćžé™ĺ’Śä¸Šćžé™ă€‚
^^{ä¸‹ćžé™} ^^{ä¸Šćžé™}

%If a subscript or superscript is not a single \minref{token}, you need
%to enclose it in a \minref{group}.  \TeX\ does not prioritize subscripts
%or superscripts, so it will reject formulas such as |a_i_j|, |a^i^j|, or
%|a^i_j|.
ĺ¦‚ćžśä¸‹ć&nbsp;‡ć–ä¸Šć&nbsp;‡ä¸ŤćŻĺŤ•ä¸Ş\minref{č®°ĺŹ·}ďĽŚä˝&nbsp;éś€č¦ĺ°†ĺ®ć”ľĺś¨\minref{çĽ–ç»„}ä¸­ă€‚
\TeX\ ĺą¶ä¸Ťĺ¤„ç†ä¸‹ć&nbsp;‡ĺ’Śä¸Šć&nbsp;‡çš„äĽĺ…çş§ďĽŚ
ĺ›&nbsp;ć­¤ĺ®ĺ°†ć‹’ç»ťç±»äĽĽ |a_i_j|ă€|a^i^j| ć– |a^i_j| çš„ĺ…¬ĺĽŹă€‚

%Subscripts and superscripts are normally typeset in ^{script style}, or
%in ^{scriptscript style} if they are second-order, e.g., a subscript on
%a subscript or a superscript on a a subscript.  You can set \emph{any}
%text in a math formula in a script or scriptscript \minref{style} with
%the ^|\scriptstyle| and ^|\scriptscriptstyle| commands (\xref
%\scriptscriptstyle).
ä¸‹ć&nbsp;‡ĺ’Śä¸Šć&nbsp;‡ćŽ’ç‰ć—¶é€šĺ¸¸ç”¨^{ć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ}ďĽŚć–č€…^{ĺ°Źć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ}ďĽŚ
ĺ¦‚ćžśĺ®ä»¬ćŻäşŚé¶ć&nbsp;‡ĺŹ·ďĽŚćŻ”ĺ¦‚ä¸‹ć&nbsp;‡ä¸­çš„ä¸‹ć&nbsp;‡ć–ä¸‹ć&nbsp;‡ä¸­çš„ä¸Šć&nbsp;‡ă€‚
ĺ©ç”¨ ^|\scriptstyle| ĺ’Ś ^|\scriptscriptstyle| ĺ‘˝ä»¤ďĽ\xref\scriptscriptstyle ďĽ‰ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąĺ°†ć•°ĺ­¦ĺ…¬ĺĽŹçš„\emph{ä»»ä˝•}ć–‡ćś¬č®ľä¸şć&nbsp;‡ĺŹ·ć–ĺ°Źć&nbsp;‡ĺŹ·\minref{ć&nbsp;·ĺĽŹ}ă€‚

%You can apply a subscript or superscript to any of the commands that
%produce named mathematical functions in roman type (see
%\xref{namedfns}).  In certain cases (again, see \xref{namedfns}) the
%subscript or superscript appears directly above or under the function
%name as shown in the examples of ^|\lim| and ^|\det| below.
ĺŻąä»»ä˝•ä»Ąç˝—é©¬ĺ­—ä˝“ćŽ’ĺŤ°ĺ‘˝ĺŤć•°ĺ­¦ĺ‡˝ć•°ďĽč§\xref{namedfns}ďĽ‰çš„ĺ‘˝ä»¤ďĽŚ
ä˝&nbsp;é˝ĺŹŻä»Ąç»™ĺ®ć·»ĺŠ&nbsp;ä¸‹ć&nbsp;‡ĺ’Śä¸Šć&nbsp;‡ă€‚
ĺś¨ćźäş›ć…ĺ˝˘ä¸­ďĽĺŚć&nbsp;·č§\xref{namedfns}ďĽ‰ďĽŚ
ä¸‹ć&nbsp;‡ĺ’Śä¸Šć&nbsp;‡ĺ†ĺ«ĺ‡şçŽ°ĺś¨ĺ‡˝ć•°ĺŤçš„ä¸‹čľąĺ’Śä¸ŠčľąďĽŚ
ĺ¦‚ä¸‹éť˘äľ‹ĺ­ä¸­çš„ ^|\lim| ĺ’Ś ^|\det| ć‰€ç¤şă€‚

%\example
%$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
%   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
%   \int_0^\infty{f(x)\,dx}$
%$$\lim_{x\leftarrow0}f(x)\qquad\det^{z\in A}\qquad\sin^2t$$
%|
%\produces
%\secondprinting{\divide\abovedisplayskip by 2}
%$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
%   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
%   \int_0^\infty{f(x)\,dx}$
%$$\lim_{x \leftarrow 0} f(x)\qquad
%   \det^{z \in A}\qquad \sin^2 t$$
\example
$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
   \int_0^\infty{f(x)\,dx}$
$$\lim_{x\leftarrow0}f(x)\qquad\det^{z\in A}\qquad\sin^2t$$
|
\produces
%\secondprinting{\divide\abovedisplayskip by 2}
$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
   \int_0^\infty{f(x)\,dx}$
$$\lim_{x \leftarrow 0} f(x)\qquad
   \det^{z \in A}\qquad \sin^2 t$$

%\eix^^{superscripts}
%\eix^^{subscripts}
%\endexample
%\enddesc
\eix^^{ä¸Šć&nbsp;‡}
\eix^^{ä¸‹ć&nbsp;‡}
\endexample
\enddesc

%\secondprinting{\vfill\eject}

%==========================================================================
%\subsection {Selecting and using styles}
\subsection {é€‰ç”¨ć&nbsp;·ĺĽŹ}

%\begindesc
%\bix^^{styles}
%\cts textstyle {}
%\cts scriptstyle {}
%\cts scriptscriptstyle {}
%\cts displaystyle {}
%\explain
%^^{text style} ^^{script style} ^^{scriptscript style} ^^{display style}
%These commands override the normal \minref{style} and hence the
%font that \TeX\ uses in setting a formula.  Like
%font-setting commands such as |\it|, they are in
%effect until the end of the group containing them.
%They are useful when \TeX's choice of style is inappropriate for the formula
%you happen to be setting.
%\example
%$t+{\scriptstyle t + {\scriptscriptstyle t}}$
%|
%\produces
%$t+{\scriptstyle t + {\scriptscriptstyle t}}$
%\endexample
%\enddesc
\begindesc
\bix^^{ć&nbsp;·ĺĽŹ}
\cts textstyle {}
\cts scriptstyle {}
\cts scriptscriptstyle {}
\cts displaystyle {}
\explain
^^{ć–‡ćś¬ć&nbsp;·ĺĽŹ} ^^{ć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ} ^^{ĺ°Źć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ} ^^{é™ĺ—ć&nbsp;·ĺĽŹ}
čż™äş›ĺ‘˝ä»¤č¦†ç›– \TeX\ ćŽ’ç‰ĺ…¬ĺĽŹć—¶é€šĺ¸¸ä˝żç”¨çš„\minref{ć&nbsp;·ĺĽŹ}ĺŹŠĺ…¶ĺ­—ä˝“ă€‚
ĺ¦‚ĺŚç±»äĽĽ |\it| çš„ĺ­—ä˝“č®ľç˝®ĺ‘˝ä»¤ďĽŚĺ®ä»¬ĺś¨ĺ…¶ć‰€ĺś¨çĽ–ç»„ç»“ćťźĺ‰Ťä¸€ç›´ćś‰ć•ă€‚
ĺ˝“ \TeX\ ç»™ä˝&nbsp;č¦ćŽ’ç‰çš„ĺ…¬ĺĽŹé€‰ç”¨äş†ä¸Ťĺé€‚çš„ć&nbsp;·ĺĽŹć—¶ďĽŚä˝&nbsp;ĺŹŻä»Ąä˝żç”¨čż™äş›ĺ‘˝ä»¤ă€‚
\example
$t+{\scriptstyle t + {\scriptscriptstyle t}}$
|
\produces
$t+{\scriptstyle t + {\scriptscriptstyle t}}$
\endexample
\enddesc

%\begindesc
%\cts mathchoice {%
%   \rqbraces{\&lt;math$_1$&gt;}
%   \rqbraces{\&lt;math$_2$&gt;}
%   \rqbraces{\&lt;math$_3$&gt;}
%   \rqbraces{\&lt;math$_4$&gt;}}
%\explain
%This command tells \TeX\ to typeset one of the subformulas
%\&lt;math$_1$&gt;, \&lt;math$_2$&gt;, \&lt;math$_3$&gt;, or \&lt;math$_4$&gt;, making its choice
%according to the current \minref{style}.
%That is, if \TeX\ is in
%display style it sets the |\mathchoice| as \&lt;math$_1$&gt;; in text style it sets
%it as \&lt;math$_2$&gt;; in script style it sets it as \&lt;math$_3$&gt;;
%and in scriptscript style it sets it as \&lt;math$_4$&gt;.
%\example
%\def\mc{{\mathchoice{D}{T}{S}{SS}}}
%The strange formula $\mc_{\mc_\mc}$ illustrates a
%mathchoice.
%|
%\produces
%\def\mc{{\mathchoice{D}{T}{S}{SS}}}
%The strange formula $\mc_{\mc_\mc}$ illustrates a
%mathchoice.
%\endexample
%\enddesc
\begindesc
\cts mathchoice {%
   \rqbraces{\&lt;math$_1$&gt;}
   \rqbraces{\&lt;math$_2$&gt;}
   \rqbraces{\&lt;math$_3$&gt;}
   \rqbraces{\&lt;math$_4$&gt;}}
\explain
ć­¤ĺ‘˝ä»¤č®© \TeX\ ć&nbsp;ąćŤ®ĺ˝“ĺ‰Ť\minref{ć&nbsp;·ĺĽŹ}é€‰ć‹©ĺą¶ćŽ’ç‰ĺ…¶ä¸­ä¸€ä¸Şĺ­ĺ…¬ĺĽŹ
\&lt;math$_1$&gt;ă€\&lt;math$_2$&gt;ă€\&lt;math$_3$&gt; ć– \&lt;math$_4$&gt;ă€‚
äąźĺ°±ćŻčŻ´ďĽŚĺ¦‚ćžśĺś¨é™ĺ—ć&nbsp;·ĺĽŹä¸­ďĽŚ\TeX\ ĺ°† |\mathchoice| ćŽ’ç‰ä¸ş \&lt;math$_1$&gt;ďĽ›
ĺś¨ć–‡ćś¬ć&nbsp;·ĺĽŹä¸­ćŽ’ç‰ä¸ş \&lt;math$_2$&gt;ďĽŚĺś¨ć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹä¸­ćŽ’ç‰ä¸ş \&lt;math$_3$&gt;ďĽ›
č€Śĺś¨ĺ°Źć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹä¸­ćŽ’ç‰ä¸ş \&lt;math$_4$&gt;ă€‚
\example
\def\mc{{\mathchoice{D}{T}{S}{SS}}}
The strange formula $\mc_{\mc_\mc}$ illustrates a
mathchoice.
|
\produces
\def\mc{{\mathchoice{D}{T}{S}{SS}}}
The strange formula $\mc_{\mc_\mc}$ illustrates a
mathchoice.
\endexample
\enddesc

%\begindesc
%\cts mathpalette {\&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
%\explain
%^^{math symbols}
%This command provides a convenient way of
%producing a math construct that works in all four \minref{style}s.
%To use it, you'll normally need to define an additional macro,
%which we'll call |\build|.
%The call on |\math!-palette| should then have the form
%|\mathpalette|\allowbreak|\build|\&lt;argument&gt;.
\begindesc
\cts mathpalette {\&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
\explain
^^{ć•°ĺ­¦ç¬¦ĺŹ·}
ć­¤ĺ‘˝ä»¤ćŹäľ›ä¸€ç§Ťç”źćé€‚ç”¨äşŽĺ››ç§Ť\minref{ć&nbsp;·ĺĽŹ}çš„ć•°ĺ­¦ç»“ćž„çš„ç®€äľżć–ąćł•ă€‚%
\footnote{čŻ‘ćł¨ďĽščŻĄĺ®Źĺ®šäą‰ä¸ş
|\def\mathpalette#1#2{\mathchoice{#1\displaystyle{#2}}|\break
|{#1\textstyle{#2}}{#1\scriptstyle{#2}}{#1\scriptscriptstyle{#2}}}|ă€‚}
č¦ä˝żç”¨ĺ®ďĽŚé€šĺ¸¸ä˝&nbsp;éś€č¦ĺ®šäą‰ä¸€ä¸Şé˘ťĺ¤–çš„ĺ®ŹďĽŚĺ‡č®ľć‘ä»¬ç§°ĺ®ä¸ş |\build|ă€‚
č°ç”¨ |\math!-palette| ĺ°±ĺş”čŻĄç”¨
|\mathpalette|\allowbreak|\build|\&lt;argument&gt; čż™ç§Ťĺ˝˘ĺĽŹă€‚


%|\build| tests what style \TeX\ is in and typesets \&lt;argu\-ment&gt; accordingly.
%It should be defined to have two parameters.
%When you call |\math!-palette|, it will in turn call |\build|,
%with |#1| being a
%command that selects the current style and |#2| being \&lt;argument&gt;.
%Thus, within the definition of |\build| you can typeset something
%in the current style by preceding it with `|#1|'.
%See \knuth{page~360} for examples of using |\mathpalette|
%and \knuth{page~151} for a further explanation of how it works.
|\build| ćµ‹čŻ• \TeX\ ä˝ŤäşŽä˝•ç§Ťć&nbsp;·ĺĽŹďĽŚĺą¶ç›¸ĺş”ĺś°ćŽ’ç‰ \&lt;argu\-ment&gt;ă€‚
ĺ®ĺş”čŻĄĺ®šäą‰ä¸şćś‰ä¸¤ä¸ŞĺŹ‚ć•°ă€‚
ĺ˝“ä˝&nbsp;č°ç”¨ |\math!-palette| ć—¶ďĽŚĺ®ä»Ą |#1| ä¸şé€‰ć‹©ć&nbsp;·ĺĽŹçš„ĺ‘˝ä»¤ďĽŚ
|#2| ä¸ş \&lt;argument&gt; č˝¬č€Śč°ç”¨ |\build|ă€‚
ĺ›&nbsp;ć­¤ďĽŚĺś¨ |\build| çš„ĺ®šäą‰ä¸­ďĽŚ
é€ščż‡ĺ°†ćźäş›ä¸śčĄżć”ľĺś¨ `|#1|' ĺ‰Ťéť˘ďĽŚĺ°±ĺŹŻä»Ąç”¨ĺ˝“ĺ‰Ťć&nbsp;·ĺĽŹćŽ’ç‰ĺ®ă€‚
ĺś¨\knuth{ç¬¬~360~éˇµ}ä¸­ćś‰ĺ¦‚ä˝•ä˝żç”¨ |\mathpalette| çš„äľ‹ĺ­ďĽŚ
č€Śĺś¨\knuth{ç¬¬~151~éˇµ}ä¸­ćś‰ĺ®ĺ¦‚ä˝•čżä˝śçš„čż›ä¸€ć­Ąč§Łé‡Šă€‚

%\eix^^{styles}
%\enddesc
\eix^^{ć&nbsp;·ĺĽŹ}
\enddesc

%==========================================================================
%\section {Compound symbols}
\section {ĺ¤Ťĺç¬¦ĺŹ·}

%==========================================================================
%\subsection {Math accents}
\subsection {ć•°ĺ­¦é‡Ťéźł}

%\begindesc
%\xrdef{mathaccent}
%^^{accents}
%^^{math//accents}
%%
%\easy\ctsx acute {^{acute accent} as in $\acute x$}
%\ctsx b {^{bar-under accent} as in $\b x$}
%\ctsx bar {^{bar accent} as in $\bar x$}
%\ctsx breve {^{breve accent} as in $\breve x$}
%\ctsx check {^{check accent} as in $\check x$}
%\ctsx ddot {^{double dot accent} as in $\ddot x$}
%\ctsx dot {^{dot accent} as in $\dot x$}
%\ctsx grave {^{grave accent} as in $\grave x$}
%\ctsx hat {^{hat accent} as in $\hat x$}
%\ctsx widehat {^{wide hat accent} as in $\widehat {x+y}$}
%\ctsx tilde {^{tilde accent} as in $\tilde x$}
%\ctsx widetilde {^{wide tilde accent} as in $\widetilde {z+a}$}
%\ctsx vec {^{vector accent} as in $\vec x$}
%\explain
%These commands produce accent marks in math formulas.  You'll ordinarily
%need to leave a space after any one of them.
%A wide accent can be applied to a multicharacter subformula;
%\TeX\ will center the accent over the subformula.
%The other accents are usefully applied only to a single character.
\begindesc
\xrdef{mathaccent}
^^{é‡Ťéźł}
^^{ć•°ĺ­¦//ć•°ĺ­¦é‡Ťéźł}
%
\easy\ctsx acute {^{é”éźłç¬¦}ďĽŚĺ¦‚ĺŚ $\acute x$}
\ctsx b {^{ä¸‹çşżç¬¦}ďĽŚĺ¦‚ĺŚ $\b x$}
\ctsx bar {^{ä¸Šçşżç¬¦}ďĽŚĺ¦‚ĺŚ $\bar x$}
\ctsx breve {^{çź­éźłç¬¦}ďĽŚĺ¦‚ĺŚ $\breve x$}
\ctsx check {^{ćŠ‘ć‰¬ç¬¦}ďĽŚĺ¦‚ĺŚ $\check x$}
\ctsx ddot {^{ĺŹŚç‚ąç¬¦}ďĽŚĺ¦‚ĺŚ $\ddot x$}
\ctsx dot {^{ä¸Šç‚ąç¬¦}ďĽŚĺ¦‚ĺŚ $\dot x$}
\ctsx grave {^{é’ťéźłç¬¦}ďĽŚĺ¦‚ĺŚ $\grave x$}
\ctsx hat {^{ĺ°–č§’ç¬¦}ďĽŚĺ¦‚ĺŚ $\hat x$}
\ctsx widehat {^{ĺ®˝ĺ°–č§’ç¬¦}ďĽŚĺ¦‚ĺŚ $\widehat {x+y}$}
\ctsx tilde {^{ćł˘ćµŞç¬¦}ďĽŚĺ¦‚ĺŚ $\tilde x$}
\ctsx widetilde {^{ĺ®˝ćł˘ćµŞç¬¦}ďĽŚĺ¦‚ĺŚ $\widetilde {z+a}$}
\ctsx vec {^{ĺ‘é‡Źç¬¦}ďĽŚĺ¦‚ĺŚ $\vec x$}
\explain
čż™äş›ĺ‘˝ä»¤ĺś¨ć•°ĺ­¦ĺ…¬ĺĽŹä¸ŠćŽ’ĺŤ°é‡Ťéźłć&nbsp;‡č®°ă€‚ä˝&nbsp;é€šĺ¸¸éś€č¦ĺś¨ĺ®ä»¬ĺŽéť˘ç•™ä¸‹ç©şć&nbsp;Ľă€‚
ĺ®˝é‡ŤéźłĺŹŻä»Ąĺş”ç”¨ĺ°ĺ¤šĺ­—ç¬¦ĺ­ĺ…¬ĺĽŹä¸­ďĽ›\TeX\ ĺ°†ćŠŠé‡Ťéźłć”ľĺś¨ĺ­ĺ…¬ĺĽŹçš„ä¸­é—´ă€‚
ĺ…¶ä»–é‡Ťéźłä»…ĺś¨ĺş”ç”¨ĺ°ĺŤ•ä¸Şĺ­—ç¬¦ć—¶ć‰Ťćś‰ç”¨ă€‚

%\example
%$\dot t^n \qquad \widetilde{v_1 + v_2}$
%|
%\produces
%$\dot t^n \qquad \widetilde{v_1 + v_2}$
%\endexample
\example
$\dot t^n \qquad \widetilde{v_1 + v_2}$
|
\produces
$\dot t^n \qquad \widetilde{v_1 + v_2}$
\endexample

%\begindesc
%\cts mathaccent {\&lt;mathcode&gt;}
%\explain
%This command tells \TeX\ to typeset a math accent
%whose family and character code are given by \&lt;mathcode&gt;.  (\TeX\ ignores
%the class of the \minref{mathcode}.)
%See \knuth{Appendix~G} for the details of how \TeX\ positions such an accent.
%The usual way to use |\mathaccent| is to put it in a macro definition
%that gives a name to a math accent.
%\example
%\def\acute{\mathaccent "7013}
%|
%\endexample
%\enddesc
\begindesc
\cts mathaccent {\&lt;mathcode&gt;}
\explain
ć­¤ĺ‘˝ä»¤č®© \TeX\ ćŽ’ç‰ĺ­—ä˝“ć—Źĺ’Śĺ­—ç¬¦çĽ–ç&nbsp;ç”± \&lt;mathcode&gt; ç»™ĺ‡şçš„ć•°ĺ­¦é‡Ťéźłă€‚%
ďĽ\TeX\ ĺż˝ç•Ą\minref{ć•°ĺ­¦ç&nbsp;}ä¸­çš„ç±»ă€‚ďĽ‰
čŻ·ĺŹ‚é…\knuth{é™„ĺ˝•~G}ĺŻą \TeX\ ĺ¦‚ä˝•ć”ľç˝®čŻĄé‡Ťéźłçš„čŻ¦ç»†ä»‹ç»Ťă€‚
ç»Źĺ¸¸ĺ°† |\mathaccent| ć”ľĺś¨ĺ®Źĺ®šäą‰ä¸­ďĽŚä»Ąç»™ć•°ĺ­¦é‡Ťéźłä¸€ä¸ŞĺŤç§°ă€‚
\example
\def\acute{\mathaccent "7013}
|
\endexample
\enddesc

%\see ``Accents'' (\xref {accents}).
%\enddesc
\see ``Accents''ďĽ\xref {accents}ďĽ‰ă€‚
\enddesc

%==========================================================================
%\subsection {Fractions and other stacking operations}
\subsection {ĺ†ĺĽŹĺ’Śĺ…¶ä»–ĺ&nbsp;†ĺŹ&nbsp;čżç®—}

%\begindesc
%\bix^^{fractions}
%\bix^^{stacking subformulas}
%\easy\cts over {}
%\cts atop {}
%\cts above {\&lt;dimen&gt;}
%\cts choose {}
%\cts brace {}
%\cts brack {}
%\explain
%{\def\fri{\&lt;formula$_1$&gt;}%
%\def\frii{\&lt;formula$_2$&gt;}%
%These commands stack one subformula on top of another one.  We will explain how
%|\over| works, and then relate the other commands to it.
\begindesc
\bix^^{ĺ†ĺĽŹ}
\bix^^{ĺ&nbsp;†ĺŹ&nbsp;ĺ­ĺ…¬ĺĽŹ}
\easy\cts over {}
\cts atop {}
\cts above {\&lt;dimen&gt;}
\cts choose {}
\cts brace {}
\cts brack {}
\explain
{\def\fri{\&lt;formula$_1$&gt;}%
\def\frii{\&lt;formula$_2$&gt;}%
čż™äş›ĺ‘˝ä»¤ĺ°†ä¸€ä¸Şĺ­ĺ…¬ĺĽŹĺ&nbsp;†ć”ľĺś¨ĺŹ¦ä¸€ä¸Şĺ­ĺ…¬ĺĽŹäą‹ä¸Šă€‚
ć‘ä»¬ĺ°†č§Łé‡Š |\over| ĺ¦‚ä˝•ä˝śç”¨ďĽŚç„¶ĺŽčŻ´ćŽĺ…¶ä»–ĺ‘˝ä»¤ä¸Žĺ®çš„ĺ…łçł»ă€‚

%|\over| is the command that you'd normally use to produce a fraction.
%^^{fractions//produced by \b\tt\\over\e}
%If you write something in one of the following forms:
%\csdisplay
%$$!fri\over!frii$$
%$!fri\over!frii$
%\left!&lt;delim&gt;!fri\over!frii\right!&lt;delim&gt;
%{!fri\over!frii}
%|
%you'll get a fraction with numerator \fri\  and denominator \&lt;for\-mu\-la$_2$&gt;,
%i.e., \fri\ over \frii.
%In the first three of
%these forms the |\over| is not implicitly contained in a group;
%it absorbs
%everything to its left and to its right until it comes to a boundary,
%namely, the beginning or end of a group.
|\over| ĺ‘˝ä»¤é€šĺ¸¸ç”¨äşŽćŽ’ĺŤ°ĺ†ĺĽŹă€‚
^^{ĺ†ĺĽŹ//ç”¨ \b\tt\\over\e ç”źć}
ĺ¦‚ćžśä˝&nbsp;ćŚ‰ä¸‹éť˘ĺ‡&nbsp;ç§Ťĺ˝˘ĺĽŹäą‹ä¸€ć’°ĺ†™ďĽš
\csdisplay
$$!fri\over!frii$$
$!fri\over!frii$
\left!&lt;delim&gt;!fri\over!frii\right!&lt;delim&gt;
{!fri\over!frii}
|
ä˝&nbsp;ĺ°†ĺľ—ĺ°ĺ†ĺ­ä¸ş \fri\ ĺ†ćŻŤä¸ş \&lt;for\-mu\-la$_2$&gt; çš„ĺ†ĺĽŹďĽŚ
ĺŤł \fri\ é™¤ä»Ą \frii ă€‚
ĺś¨ĺ‰Ťéť˘ä¸‰ç§Ťĺ˝˘ĺĽŹä¸­ďĽŚ|\over| éťžćľĺĽŹĺś°ĺŚ…ĺ«ĺś¨ä¸€ä¸ŞçĽ–ç»„ä¸­ďĽ›
ĺ®ĺ¸ć”¶ĺ·¦čľąĺ’ŚĺŹłčľąçš„ĺ†…ĺ®ąç›´ĺ°é‡ĺ°čľąç•ŚďĽŚĺŤłçĽ–ç»„çš„ĺĽ€ĺ¤´ĺ’Śç»“ĺ°ľă€‚

%You can't use |\over| or any of the other commands in this group
%more than once in a formula.
%Thus a formula such as:
%\csdisplay
%$$a \over n \choose k$$
%|
%isn't legal.
%This is not a severe restriction because
%you can always enclose one of the commands in braces.
%The reason for the restriction is that if you had two of these commands
%in a single formula, \TeX\ wouldn't know how to group them.
ä˝&nbsp;ä¸ŤĺŹŻä»Ąĺś¨ä¸€ä¸Şĺ…¬ĺĽŹä¸­ĺ¤šć¬ˇä˝żç”¨ |\over| ć–čż™ć‰ąĺ‘˝ä»¤çš„ĺ…¶ä»–ĺ‘˝ä»¤ă€‚
ĺ›&nbsp;ć­¤ä¸‹éť˘çš„ĺ…¬ĺĽŹďĽš
\csdisplay
$$a \over n \choose k$$
|
ćŻä¸Ťĺćł•çš„ă€‚čż™ä¸ŤćŻä»€äąä¸Ąé‡Ťçš„é™ĺ¶ďĽŚĺ›&nbsp;ä¸şä˝&nbsp;ć€»ĺŹŻä»Ąĺ°†ĺ…¶ä¸­ä¸€ä¸Şĺ‘˝ä»¤ć”ľĺś¨čŠ±ć‹¬ĺŹ·ä¸­ă€‚
ä˝ść­¤é™ĺ¶çš„ĺŽźĺ›&nbsp;ćŻďĽŚĺ¦‚ćžśä˝&nbsp;ćŠŠčż™äş›ĺ‘˝ä»¤çš„ĺ…¶ä¸­ä¸¤ä¸Şć”ľĺś¨ĺŚä¸€ä¸Şĺ…¬ĺĽŹä¸­ďĽŚ
\TeX\ ĺ°†ä¸ŤçźĄé“ĺ¦‚ä˝•ĺ’ĺ†ĺ®ä»¬ă€‚

%The other commands are similar to |\over|, with the following exceptions:
%\ulist\compact
%\li |\atop| leaves out the fraction bar.
%\li |\above| provides a fraction bar of thickness \&lt;dimen&gt;.
%\li |\choose|
%leaves out the fraction bar and encloses the construct in parentheses.
%(It's called ``choose'' because $n \choose k$ is the notation for the
%number of ways of choosing $k$ things out of $n$ things.)
%\li |\brace| leaves out the fraction bar and encloses the construct in braces.
%\li |\brack|
%leaves out the fraction bar and encloses the construct in brackets.
%\endulist
%}%
%\example
%$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
%  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
%  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
%|
%\dproduces
%$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
%  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
%  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
%\endexample
%\enddesc
ĺ…¶ä»–ĺ‘˝ä»¤ä¸Ž |\over| ç±»äĽĽďĽŚä˝†ćś‰ć‰€ä¸ŤĺŚďĽš
\ulist\compact
\li |\atop| ĺŽ»ćŽ‰ĺ†ĺĽŹçš„ć¨Şçşżă€‚
\li |\above| ç»™ĺ‡şĺŽšĺş¦ä¸ş \&lt;dimen&gt; çš„ĺ†ĺĽŹć¨Şçşżă€‚
\li |\choose| ĺŽ»ćŽ‰ĺ†ĺĽŹć¨ŞçşżďĽŚĺą¶ĺ°†ç»“ćž„ć”ľĺś¨ĺś†ć‹¬ĺŹ·ä¸­ă€‚%
ďĽç§°ĺ®ä¸ş``é€‰ć‹©''ďĽŚ
ćŻĺ›&nbsp;ä¸ş $n \choose k$ čˇ¨ç¤şä»Ž $n$ ä¸Şä¸śčĄżä¸­ä»»ĺŹ– $k$ ä¸Şçš„ć‰€ćś‰é€‰ĺŹ–ć–ąĺĽŹçš„ć•°ç›®ă€‚ďĽ‰%
\li |\brace| ĺŽ»ćŽ‰ĺ†ĺĽŹć¨ŞçşżďĽŚĺą¶ĺ°†ç»“ćž„ć”ľĺś¨čŠ±ć‹¬ĺŹ·ä¸­ă€‚
\li |\brack| ĺŽ»ćŽ‰ĺ†ĺĽŹć¨ŞçşżďĽŚĺą¶ĺ°†ç»“ćž„ć”ľĺś¨ć–ąć‹¬ĺŹ·ä¸­ă€‚
\endulist
}%
\example
$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
|
\dproduces
$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
\endexample
\enddesc

%\begindesc
%\cts overwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
%\cts atopwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
%\cts abovewithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt; \&lt;dimen&gt;}
%\explain
%Each of these commands stacks one subformula on top of another one and
%surrounds the entire construct with \&lt;delim$_1$&gt; on the left and
%\&lt;delim$_2$&gt; on the right.  These commands follow the same rules as
%|\over|, |\atop|, and |\above|. The \&lt;dimen&gt; in |\abovewithdelims|
%specifies the thickness of the fraction bar.
%\example
%$${m \overwithdelims () n}\qquad
%  {m \atopwithdelims !|!| n}\qquad
%  {m \abovewithdelims \{\} 2pt n}$$
%|
%\dproduces
%$${m \overwithdelims () n}\qquad
%  {m \atopwithdelims || n}\qquad
%  {m \abovewithdelims \{\} 2pt n}$$
%\endexample
%\enddesc
\begindesc
\cts overwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
\cts atopwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
\cts abovewithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt; \&lt;dimen&gt;}
\explain
čż™é‡Śçš„ćŻŹä¸Şĺ‘˝ä»¤é˝ĺ°†ä¸€ä¸Şĺ­ĺ…¬ĺĽŹĺ&nbsp;†ć”ľĺś¨ĺŹ¦ä¸€ä¸Şĺ­ĺ…¬ĺĽŹäą‹ä¸ŠďĽŚ
ĺą¶ĺ°†ć•´ä¸Şç»“ćž„çš„ĺ·¦čľąç”¨ \&lt;delim$_1$&gt;ďĽŚĺŹłčľąç”¨ \&lt;delim$_2$&gt; ĺŚ…ĺ›´ă€‚
čż™äş›ĺ‘˝ä»¤éµĺľŞä¸Ž |\over|ă€|\atop| ĺ’Ś |\above| ç›¸ĺŚçš„č§„ĺ™ă€‚
|\abovewithdelims| ĺŽéť˘çš„ \&lt;dimen&gt; ćŚ‡ĺ®šĺ†ĺĽŹć¨Şçşżçš„ĺŽšĺş¦ă€‚
\example
$${m \overwithdelims () n}\qquad
  {m \atopwithdelims !|!| n}\qquad
  {m \abovewithdelims \{\} 2pt n}$$
|
\dproduces
$${m \overwithdelims () n}\qquad
  {m \atopwithdelims || n}\qquad
  {m \abovewithdelims \{\} 2pt n}$$
\endexample
\enddesc

%\begindesc
%\cts cases {}
%\explain
%^^{combinations, notation for}
%This command produces the mathematical form that denotes a choice among
%several cases.
%Each case has two parts, separated by `|&amp;|'.
%\TeX\ treats the first part as a math formula
%and the second part as ordinary text.  Each
%case must be followed by |\cr|.
\begindesc
\cts cases {}
\explain
^^{ç»„ĺć•°č®°ćł•}
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸€ä¸Şčˇ¨ç¤şä»Žĺ¤šä¸Şć…ĺ˝˘ä¸­é€‰ć‹©çš„ć•°ĺ­¦ĺ˝˘ĺĽŹă€‚
ćŻŹç§Ťć…ĺ˝˘ç”±ä¸¤é¨ĺ†ç»„ćďĽŚä¸¤č€…ä»Ą `|&amp;|' ĺ†éš”ă€‚
\TeX\ ĺ°†ç¬¬ä¸€é¨ĺ†č§†ä¸şć•°ĺ­¦ĺ…¬ĺĽŹďĽŚç¬¬äşŚé¨ĺ†č§†ä¸şć™®é€šć–‡ćś¬ă€‚
ćŻŹä¸Şć…ĺ˝˘äą‹ĺŽĺż…éˇ»ĺŠ&nbsp;ä¸Š |\cr|ă€‚

%\example
%$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
%                  f(y,x),&amp;if $x&gt;y$\cr
%                  0,&amp;otherwise.\cr}$$
%|
%\dproduces
%$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
%                  f(y,x),&amp;if $x&gt;y$\cr
%                  0,&amp;otherwise.\cr}$$
%\endexample
%\enddesc
\example
$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
                  f(y,x),&amp;if $x&gt;y$\cr
                  0,&amp;otherwise.\cr}$$
|
\dproduces
$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
                  f(y,x),&amp;if $x&gt;y$\cr
                  0,&amp;otherwise.\cr}$$
\endexample
\enddesc

%\begindesc
%\cts underbrace {\&lt;argument&gt;}
%\cts overbrace {\&lt;argument&gt;}
%\cts underline {\&lt;argument&gt;}
%\cts overline {\&lt;argument&gt;}
%\cts overleftarrow {\&lt;argument&gt;}
%\cts overrightarrow {\&lt;argument&gt;}
%\explain
%These commands place extensible ^{braces}, lines, or ^{arrows}
%over or under the subformula given by \&lt;argument&gt;.
%\TeX\ will make these constructs as wide as they need to be for
%the context.
%When \TeX\ produces the extended braces, lines, or arrows, it considers
%only the dimensions of the \minref{box} containing \&lt;argument&gt;.
%If you use more than one of these commands in a single formula, the
%braces, lines, or arrows they produce
%may not line up properly with each other.
%You can use the |\mathstrut| command (\xref \mathstrut)
%to overcome this difficulty.
%\example
%$$\displaylines{
%\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
%\underline{x \circ y}\qquad \overline{x \circ y}\qquad
%\overleftarrow{x \circ y}\qquad
%\overrightarrow{x \circ y}\cr
%{\overline r + \overline t}\qquad
%{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
%}$$
%|
%\dproduces
%$$\displaylines{
%\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
%\underline{x \circ y}\qquad \overline{x \circ y}\qquad
%\overleftarrow{x \circ y}\qquad
%\overrightarrow{x \circ y}\cr
%{\overline r + \overline t}\qquad
%{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
%}$$
%\endexample
%\enddesc
\begindesc
\cts underbrace {\&lt;argument&gt;}
\cts overbrace {\&lt;argument&gt;}
\cts underline {\&lt;argument&gt;}
\cts overline {\&lt;argument&gt;}
\cts overleftarrow {\&lt;argument&gt;}
\cts overrightarrow {\&lt;argument&gt;}
\explain
čż™äş›ĺ‘˝ä»¤ĺ°†ĺŹŻäĽ¸é•żçš„^{čŠ±ć‹¬ĺŹ·}ă€ć¨Şçşżć–^{ç®­ĺ¤´}%
ć”ľĺś¨ç”± \&lt;argument&gt; ç»™ĺ‡şçš„ĺ­ĺ…¬ĺĽŹçš„ä¸Ščľąć–ä¸‹čľąă€‚
\TeX\ ĺ°†č®©čż™äş›ç»“ćž„č¶łĺ¤źĺ®˝ä»Ąé€‚ĺş”ĺ†…ĺ®ąă€‚
ĺ˝“ \TeX\ ćŽ’ĺŤ°ĺŹŻäĽ¸é•żçš„čŠ±ć‹¬ĺŹ·ă€ć¨Şçşżć–ç®­ĺ¤´ć—¶ďĽŚ
ĺ®ĺŹŞč€č™‘ĺŚ…ĺ« \&lt;argument&gt; çš„ \minref{ç›’ĺ­}çš„ĺ°şĺŻ¸ă€‚
ĺ¦‚ćžśä˝&nbsp;ĺś¨ä¸€ä¸Şĺ…¬ĺĽŹä¸­ä˝żç”¨čż™äş›ĺ‘˝ä»¤ä¸­çš„ä¸¤ä¸Şä»Ąä¸ŠďĽŚ
ĺ…¶ä¸­ćŽ’ĺŤ°çš„čŠ±ć‹¬ĺŹ·ă€ć¨Şçşżć–ç®­ĺ¤´äą‹é—´ĺŹŻč˝ć—&nbsp;ćł•ć°ĺ˝“ĺś°ĺŻąé˝ă€‚
ä˝&nbsp;ĺŹŻä»Ąä˝żç”¨ |\mathstrut| ĺ‘˝ä»¤ďĽ\xref\mathstrut ďĽ‰ĺ…‹ćśŤć­¤ĺ›°éšľă€‚
\example
$$\displaylines{
\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
\underline{x \circ y}\qquad \overline{x \circ y}\qquad
\overleftarrow{x \circ y}\qquad
\overrightarrow{x \circ y}\cr
{\overline r + \overline t}\qquad
{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
}$$
|
\dproduces
$$\displaylines{
\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
\underline{x \circ y}\qquad \overline{x \circ y}\qquad
\overleftarrow{x \circ y}\qquad
\overrightarrow{x \circ y}\cr
{\overline r + \overline t}\qquad
{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
}$$
\endexample
\enddesc

%\begindesc\secondprinting{\vglue-.5\baselineskip\vskip0pt}
%\cts buildrel {\&lt;formula&gt; {\bt \\over} \&lt;relation&gt;}
%\explain
%^^{relations//putting formulas above}
%This command produces a \minref{box} in which \&lt;formula&gt;
%is placed on top of \&lt;relation&gt;. \TeX\ treats the result as a relation
%for spacing purposes \seeconcept{class}.
%\example
%$\buildrel \rm def \over \equiv$
%|
%\produces
%$\buildrel \rm def \over \equiv$
\begindesc%\secondprinting{\vglue-.5\baselineskip\vskip0pt}
\cts buildrel {\&lt;formula&gt; {\bt \\over} \&lt;relation&gt;}
\explain
^^{ĺ…łçł»ç¬¦//ĺ°†ĺ…¬ĺĽŹć”ľĺś¨ĺ…¶ä¸Š}
ć­¤ĺ‘˝ä»¤ĺ°† \&lt;formula&gt; ć‰€ĺś¨çš„\minref{ç›’ĺ­}ć”ľĺś¨ \&lt;relation&gt; ä¸Ščľąă€‚
\TeX\ ĺ¤„ç†é—´éš”ć—¶ĺ°†ç»“ćžśč§†ä¸şä¸€ä¸Şĺ…łçł»ç¬¦\seeconcept{ç±»}ă€‚
\example
$\buildrel \rm def \over \equiv$
|
\produces
$\buildrel \rm def \over \equiv$

%\eix^^{fractions}
%\eix^^{stacking subformulas}
%\endexample
%\enddesc
\eix^^{ĺ†ĺĽŹ}
\eix^^{ĺ&nbsp;†ĺŹ&nbsp;ĺ­ĺ…¬ĺĽŹ}
\endexample
\enddesc

%\secondprinting{\vfill\eject}


%==========================================================================
%\subsection {Dots}
\subsection {ĺś†ç‚ą}

%\begindesc
%\bix^^{dots}
%\easy\cts ldots {}
%\cts cdots {}
%\explain
%These commands produce three ^{dots} in a row.  For |\ldots|, the dots
%are on the baseline; for |\cdots|, the dots are centered with respect to
%the axis (see the explanation of |\vcenter|, \xref\vcenter).
\begindesc
\bix^^{ĺś†ç‚ą}
\easy\cts ldots {}
\cts cdots {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤é˝ćŽ’ĺŤ°ä¸‰ä¸Şä¸€ćŽ’çš„^{ĺś†ç‚ą}ă€‚ĺŻąäşŽ |\ldots|ďĽŚ
ĺś†ç‚ąć”ľĺś¨ĺźşçşżä¸ŠďĽ›ĺŻąäşŽ |\cdots|ďĽŚĺś†ç‚ąć”ľĺś¨ä¸­č˝´çşżä¸Š%
ďĽč§ \xref\vcenter ĺŻą |\vcenter| çš„č§Łé‡ŠďĽ‰ă€‚

%\example
%$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
%|
%\produces
%$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
%\endexample
%\enddesc
\example
$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
|
\produces
$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
\endexample
\enddesc

%\begindesc
%\easy\cts vdots {}
%\explain
%This command produces three vertical dots.
%\example
%$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
%   \noalign{\kern -4pt}%
%   &amp;\phantom{a}\vdots\cr % moves the dots right a bit
%   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
%|
%\dproduces
%$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
%   \noalign{\kern -4pt}%
%   &amp;\phantom{a}\vdots\cr
%   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
%\endexample
%\enddesc
\begindesc
\easy\cts vdots {}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸‰ä¸Şç«–ç›´çš„ĺś†ç‚ąă€‚
\example
$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
   \noalign{\kern -4pt}%
   &amp;\phantom{a}\vdots\cr % moves the dots right a bit
   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
|
\dproduces
$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
   \noalign{\kern -4pt}%
   &amp;\phantom{a}\vdots\cr
   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
\endexample
\enddesc

%\begindesc
%\cts ddots {}
%\explain
%This command produces three dots on a diagonal.
%Its most common use is to indicate repetition along the diagonal of a matrix.
%\example
%$$\pmatrix{0&amp;\ldots&amp;0\cr
%           \vdots&amp;\ddots&amp;\vdots\cr
%           0&amp;\ldots&amp;0\cr}$$
%|
%\dproduces
%$$\pmatrix{0&amp;\ldots&amp;0\cr
%           \vdots&amp;\ddots&amp;\vdots\cr
%           0&amp;\ldots&amp;0\cr}$$
\begindesc
\cts ddots {}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ć–śçşżä¸Šçš„ä¸‰ä¸Şĺś†ç‚ąă€‚ĺ®ĺ¸¸ç”¨äşŽčˇ¨ç¤şć˛żçź©éµĺŻąč§’çşżçš„é‡Ťĺ¤Ťă€‚
\example
$$\pmatrix{0&amp;\ldots&amp;0\cr
           \vdots&amp;\ddots&amp;\vdots\cr
           0&amp;\ldots&amp;0\cr}$$
|
\dproduces
$$\pmatrix{0&amp;\ldots&amp;0\cr
           \vdots&amp;\ddots&amp;\vdots\cr
           0&amp;\ldots&amp;0\cr}$$

%\eix^^{dots}
%\endexample
%\enddesc
\eix^^{ĺś†ç‚ą}
\endexample
\enddesc

%\see |\dots| \ctsref\dots.
\see |\dots|\ctsref\dots ă€‚

%==========================================================================
%\subsection {Delimiters}
\subsection {ĺ®šç•Śç¬¦}

%\begindesc
%\bix^^{delimiters}
%%
%\cts lgroup {}
%\cts rgroup {}
%\explain
%These commands produce large left and right ^{parentheses}
%that are defined as opening and closing \minref{delimiter}s.
%The smallest available size for these delimiters is |\Big|.
%If you use smaller sizes, you'll get weird characters.
%\example
%$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
%|
%\dproduces
%$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
%\endexample
%\enddesc
\begindesc
\bix^^{ĺ®šç•Śç¬¦}
%
\cts lgroup {}
\cts rgroup {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤ćŽ’ĺŤ°ĺ¤§ĺŹ·çš„ĺ·¦ĺ’ŚĺŹł^{ĺś†ć‹¬ĺŹ·}ďĽŚ
ĺ®ä»¬ĺ†ĺ«ä˝śä¸şĺĽ€ĺ®šç•Śç¬¦ĺ’Śé—­\minref{ĺ®šç•Śç¬¦}ă€‚
čż™ä¸¤ä¸Şĺ®šç•Śç¬¦çš„ćś€ĺ°ŹĺŹŻç”¨ĺ°şĺŻ¸ä¸ş |\Big|ă€‚
ĺ¦‚ćžśä˝żç”¨ć›´ĺ°Źçš„ĺ°şĺŻ¸ďĽŚä˝&nbsp;ĺ°†ĺľ—ĺ°ĺĄ‡ć€Şçš„ĺ­—ç¬¦ă€‚
\example
$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
|
\dproduces
$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
\endexample
\enddesc

%\begindesc
%\margin{{\tt\\vert} and {\tt\\Vert} were explained elsewhere.}
%\easy\cts left {}
%\cts right {}
%\explain
%These commands must be used together in the pattern:
%\display
%{{\bt \\left} \&lt;delim$_1$&gt; \&lt;subformula&gt; {\bt \\right} \&lt;delim$_2$&gt;}
%This construct causes \TeX\ to produce \&lt;subformula&gt;,
%enclosed in the \minref{delimiter}s \&lt;delim$_1$&gt; and \&lt;delim$_2$&gt;.
%The vertical size of the delimiter is adjusted to fit the
%vertical size (height plus depth) of \&lt;subformula&gt;.  \&lt;delim$_1$&gt; and
%\&lt;delim$_2$&gt; need not correspond.
%For instance, you could use `|]|' as a left delimiter
%and `|(|' as a right delimiter in a single use of |\left|
%and |\right|.
\begindesc
\margin{{\tt\\vert} and {\tt\\Vert} were explained elsewhere.}
\easy\cts left {}
\cts right {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺż…éˇ»ćŚ‰ç…§ä¸‹éť˘ć¨ˇĺĽŹä¸€čµ·ä˝żç”¨ďĽš
\display
{{\bt \\left} \&lt;delim$_1$&gt; \&lt;subformula&gt; {\bt \\right} \&lt;delim$_2$&gt;}
čż™ä¸Şćž„é€&nbsp;ĺ°†č®© \TeX\ ćŽ’ĺŤ° \&lt;subformula&gt;ďĽŚ
ĺą¶ç”¨\minref{ĺ®šç•Śç¬¦} \&lt;delim$_1$&gt; ĺ’Ś \&lt;delim$_2$&gt; ĺŚ…ĺ›´ĺ®ă€‚
\TeX\ č°ć•´ĺ®šç•Śç¬¦çš„ç«–ç›´ĺ°şĺŻ¸ä»Ąé€‚ĺş” \&lt;subformula&gt; çš„ç«–ç›´ĺ°şĺŻ¸ďĽé«ĺş¦ĺŠ&nbsp;ć·±ĺş¦ďĽ‰ă€‚
\&lt;delim$_1$&gt; ĺ’Ś \&lt;delim$_2$&gt; ä¸Ťéś€č¦ç›¸ĺŻąĺş”ă€‚
ä¸ľä¸Şäľ‹ĺ­ďĽŚĺś¨ä˝żç”¨ |\left| ĺ’Ś |\right| ć—¶ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąĺ°† `|]|' ä˝śä¸şĺ·¦ĺ®šç•Śç¬¦ďĽŚč€Śĺ°† `|(|' ä˝śä¸şĺŹłĺ®šç•Śç¬¦ă€‚

%|\left| and |\right| have the important property that they define a
%group, i.e., they act like left and right braces.  This grouping
%property is particularly useful when you put ^|\over| (\xref{\over}) or
%a related command between |\left| and |\right|, since you don't need to
%put braces around the fraction constructed by |\over|.
|\left| ĺ’Ś |\right| ćś‰ä¸Şé‡Ťč¦ć€§č´¨ćŻĺ®ä»¬ĺ®šäą‰äş†ä¸€ä¸ŞçĽ–ç»„ďĽŚ
ĺŤłĺ®ä»¬č˝ĺ¤źĺ……ĺ˝“ĺ·¦ĺ’ŚĺŹłčŠ±ć‹¬ĺŹ·ă€‚
ĺ˝“ä˝&nbsp;ĺś¨|\left| ĺ’Ś |\right| äą‹é—´ć”ľä¸Š ^|\over|ďĽ\xref{\over}ďĽ‰ć–ĺ…¶ä»–ç›¸ĺ…łĺ‘˝ä»¤ć—¶ďĽŚ
ć­¤çĽ–ç»„ć€§č´¨ĺ°±ĺľćś‰ç”¨ďĽŚĺ›&nbsp;ä¸şä˝&nbsp;ć—&nbsp;éś€ĺś¨ |\over| ćž„é€&nbsp;çš„ĺ†ĺĽŹä¸¤čľąĺŠ&nbsp;ä¸ŠčŠ±ć‹¬ĺŹ·ă€‚

%If you want a left delimiter but not a right delimiter, you can use `|.|' in
%place of the delimiter you don't want and it will turn into empty space
%(of width ^|\nulldelimiterspace|).
%\example
%$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
%  \qquad \left\uparrow q_1\atop q_2\right.$$
%|
%\dproduces
%$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
%  \qquad \left\uparrow q_1\atop q_2\right.$$
%\endexample
%\enddesc
ĺ¦‚ćžśä˝&nbsp;éś€č¦ĺ·¦ĺ®šç•Śç¬¦ä˝†ä¸Ťéś€č¦ĺŹłĺ®šç•Śç¬¦ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąç”¨ `|.|' ä»Łć›żä˝&nbsp;ä¸Ťéś€č¦çš„ĺ®šç•Śç¬¦ďĽŚ
čż™ć&nbsp;·ĺ®ĺ°±ĺŹćä¸€ä¸Şç©şç™˝ďĽĺ®˝ĺş¦ä¸ş ^|\nulldelimiterspace|ďĽ‰ă€‚
\example
$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
  \qquad \left\uparrow q_1\atop q_2\right.$$
|
\dproduces
$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
  \qquad \left\uparrow q_1\atop q_2\right.$$
\endexample
\enddesc

%\begindesc
%\cts delimiter {\&lt;number&gt;}
%\explain
%This command produces a delimiter whose characteristics are given by
%\&lt;number&gt;.  \&lt;number&gt; is normally written in hexadecimal notation.
%You can use the |\delimiter| command instead of a character in any context
%where \TeX\ expects a delimiter (although the command is rarely used
%outside of a macro definition).
%Suppose that \&lt;number&gt; is the hexadecimal number $cs_1s_2s_3
%l_1l_2l_3$.  Then \TeX\ takes the delimiter to have
%\minref{class} $c$, small variant
%$s_1s_2s_3$, and large variant $l_1l_2l_3$.  Here $s_1s_2s_3$ indicates
%the math character found in position $s_2s_3$ of family $s_1$, and
%similarly for $l_1l_2l_3$.  This is the same convention as the one
%used for ^|\mathcode| (\xref\mathcode).
%\example
%\def\vert{\delimiter "026A30C} % As in plain TeX.
%|
%\endexample
%\enddesc
\begindesc
\cts delimiter {\&lt;number&gt;}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ç”¨ \&lt;number&gt; ĺ»ç”»ĺ…¶ç‰ąć€§çš„ĺ®šç•Śç¬¦ă€‚\&lt;number&gt; é€šĺ¸¸ç”¨ĺŤĺ…­čż›ĺ¶čˇ¨ç¤şă€‚
ĺś¨ \TeX\ éś€č¦ĺ®šç•Śç¬¦çš„ä»»ä˝•ĺś°ć–ąä˝&nbsp;é˝ĺŹŻä»Ąç”¨ |\delimiter| ĺ‘˝ä»¤ä»Łć›żä¸€ä¸Şĺ­—ç¬¦%
ďĽĺ°˝ç®ˇć­¤ĺ‘˝ä»¤ĺľĺ°‘ĺś¨ĺ®Źĺ®šäą‰äą‹ĺ¤–çš„ĺś°ć–ąä˝żç”¨ďĽ‰ă€‚
ĺ‡č®ľ \&lt;number&gt; ä¸şĺŤĺ…­čż›ĺ¶ć•° $cs_1s_2s_3l_1l_2l_3$ă€‚
ĺ™ \TeX\ çźĄé“čŻĄĺ®šç•Śç¬¦ĺ±žäşŽç¬¬$c$\minref{ç±»}ďĽŚ
ĺ°ŹĺŹ·ĺŹä˝“ä¸ş $s_1s_2s_3$, č€Śĺ¤§ĺŹ·ĺŹä˝“ä¸ş $l_1l_2l_3$ă€‚
čż™é‡Ś $s_1s_2s_3$ čˇ¨ç¤şç¬¬ $s_1$ ć—Źä˝Ťç˝® $s_2s_3$ çš„ć•°ĺ­¦ĺ­—ç¬¦ďĽŚ
$l_1l_2l_3$ ç±»äĽĽă€‚čż™é‡Śä˝żç”¨ä¸Ž ^|\mathcode|ďĽ\xref\mathcode ďĽ‰ä¸€ć&nbsp;·çš„çş¦ĺ®šă€‚
\example
\def\vert{\delimiter "026A30C} % As in plain TeX.
|
\endexample
\enddesc

%\begindesc
%\margin{{\tt\\delcode} was explained in two places.  The
%combined explanation is now in `General operations'.}
%\cts delimiterfactor {\param{number}}
%\cts delimitershortfall {\param{number}}
%\explain
%^^{delimiters//height of}
%These parameters together tell \TeX\ how the height of a \minref{delimiter}
%should be related to the vertical size of the subformula
%with which the delimiter is associated.
%|\delimiterfactor| gives the minimum
%ratio of the delimiter size to the vertical size of the subformula, and
%|\delimitershortfall| gives the maximum by which the height of the
%delimiter will be reduced from that of the vertical size of the subformula.
\begindesc
\margin{{\tt\\delcode} was explained in two places.  The
combined explanation is now in `General operations'.}
\cts delimiterfactor {\param{number}}
\cts delimitershortfall {\param{number}}
\explain
^^{ĺ®šç•Śç¬¦//ĺ®šç•Śç¬¦é«ĺş¦}
čż™ä¸¤ä¸ŞĺŹ‚ć•°ĺ…±ĺŚçˇ®ĺ®šäş†\minref{ĺ®šç•Śç¬¦}é«ĺş¦ä¸Žĺ…¶ä¸­ĺ­ĺ…¬ĺĽŹçš„ç«–ç›´ĺ°şĺŻ¸çš„ĺ…łçł»ă€‚
|\delimiterfactor| ç»™ĺ‡şĺ®šç•Śç¬¦é«ĺş¦ç›¸ĺŻąĺ­ĺ…¬ĺĽŹç«–ç›´ĺ°şĺŻ¸çš„ćś€ĺ°ŹćŻ”äľ‹ďĽŚ
č€Ś |\delimitershortfall| ç»™ĺ‡şĺ®šç•Śç¬¦é«ĺş¦ç›¸ĺŻąĺ­ĺ…¬ĺĽŹç«–ç›´ĺ°şĺŻ¸çš„ćś€ĺ¤§ĺ·®č·ťă€‚

%Suppose that the \minref{box} containing the subformula
%has height $h$ and depth $d$, and let $y=2\,\max(h,d)$.
%Let the value of |\delimiterfactor| be $f$ and the value of
%|\delimitershortfall| be $\delta$.
%Then \TeX\ takes the minimum delimiter size to be at least $y \cdot
%f/1000$ and at least $y-\delta$.  In particular, if |\delimiterfactor|
%is exactly $1000$ then \TeX\ will try to make a delimiter at least as tall
%as the formula to which it is attached.
%See \knuth{page~152 and page~446 (Rule 19)}
%for the exact details of how \TeX\ uses these parameters.
%\PlainTeX\ sets |\delimiter!-factor| to $901$ and
%|\delimiter!-shortfall| to |5pt|.
%\enddesc
ĺ‡č®ľĺŚ…ĺ«ĺ­ĺ…¬ĺĽŹçš„\minref{ç›’ĺ­}çš„é«ĺş¦ä¸ş $h$ ć·±ĺş¦ä¸ş $d$ďĽŚ
ä¸”ä»¤ $y=2\,\max(h,d)$ă€‚
č®ľ |\delimiterfactor| çš„ĺ€Ľä¸ş $f$ďĽŚ|\delimitershortfall| çš„ĺ€Ľä¸ş $\delta$ă€‚
ĺ™ \TeX\ é€‰ĺŹ–çš„ĺ®šç•Śç¬¦é«ĺş¦č‡łĺ°‘ä¸ş $y \cdot f/1000$ďĽŚä¸”č‡łĺ°‘ä¸ş $y-\delta$ă€‚
ç‰ąĺ«ĺś°ďĽŚĺ¦‚ćžś |\delimiterfactor| ć°ĺĄ˝ä¸ş $1000$ďĽŚ
ĺ™ \TeX\ ĺ°†čŻ•çť€ç”źćä¸€ä¸Şč‡łĺ°‘ĺ’Śĺ…¶ä¸­çš„ĺ­ĺ…¬ĺĽŹä¸€ć&nbsp;·é«çš„ĺ®šç•Śç¬¦ă€‚
č§\knuth{ç¬¬~152~éˇµĺ’Śç¬¬~446~éˇµďĽč§„ĺ™19ďĽ‰}ä¸­ \TeX\ ĺ¦‚ä˝•ä˝żç”¨čż™äş›ĺŹ‚ć•°çš„ç»†čŠ‚ă€‚
\PlainTeX\ č®ľĺ®š |\delimiter!-factor| ä¸ş $901$ďĽŚ
|\delimiter!-shortfall| ä¸ş |5pt|ă€‚
\enddesc

%\see |\delcode| (\xref\delcode), |\vert|, |\Vert|,
%and |\backslash| (\xref\vert).
%\eix^^{delimiters}
\see |\delcode|ďĽ\xref\delcode )ă€|\vert|ă€|\Vert| ĺ’Ś |\backslash|ďĽ\xref\vert ďĽ‰ă€‚
\eix^^{ĺ®šç•Śç¬¦}

%==========================================================================
%\subsection {Matrices}
\subsection {çź©éµ}

%\begindesc
%\cts matrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts pmatrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts bordermatrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\explain
%Each of these three commands produces a ^{matrix}.
%The elements of each row of the input matrix
%are separated by `|&amp;|' and each row in turn is ended
%by |\cr|.
%(This is the same form that is used for an
%\minref{alignment}.)
%The commands differ in the following ways:
%\ulist\compact
%\li |\matrix| produces a matrix without any surrounding or inserted
%\minref{delimiter}s.
%\li |\pmatrix| produces a matrix surrounded by parentheses.
%\li |\bordermatrix| produces a matrix in which the first row and the first
%column are treated as labels.  (The first element of the first row is
%usually left blank.)  The rest of the matrix is enclosed in
%parentheses.
%\endulist
%\TeX\ can make the parentheses for |\pmatrix| and |\bordermatrix| as large as
%they need to be by inserting vertical extensions.  If you want a matrix
%to be surrounded by delimiters other than parentheses, you should use
%|\matrix| in conjunction with |\left| and |\right| (\xref \left).
\begindesc
\cts matrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts pmatrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts bordermatrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\explain
čż™ä¸‰ä¸Şĺ‘˝ä»¤ćŻŹä¸Şé˝ćŽ’ĺŤ°ä¸€ä¸Ş^{çź©éµ}ďĽŚ
čľ“ĺ…Ąçź©éµć—¶ĺ„čˇŚçš„ĺ…ç´&nbsp;äą‹é—´ç”¨ `|&amp;|' ĺ†éš”ďĽŚč€Śĺ„čˇŚç”¨ |\cr| ç»“ĺ°ľă€‚%
ďĽčż™é‡Śä˝żç”¨ä¸Ž\minref{éµĺ—}ä¸€ć&nbsp;·çš„ĺ˝˘ĺĽŹă€‚ďĽ‰%
čż™äş›ĺ‘˝ä»¤äą‹é—´çš„ĺŚşĺ«ĺ¦‚ä¸‹ďĽš
\ulist\compact
\li |\matrix| ćŽ’ĺŤ°ä¸€ä¸Şĺ››ĺ‘¨ç©şç™˝ä¸Ťĺ¸¦\minref{ĺ®šç•Śç¬¦}çš„çź©éµă€‚
\li |\pmatrix| ćŽ’ĺŤ°ä¸€ä¸Şä¸¤čľąĺ¸¦ĺś†ć‹¬ĺŹ·çš„çź©éµă€‚
\li |\bordermatrix| ćŽ’ĺŤ°ä¸€ä¸Şĺ°†ç¬¬ä¸€čˇŚĺ’Śç¬¬ä¸€ĺ—č§†ä¸şć&nbsp;‡ĺŹ·çš„çź©éµă€‚%
ďĽç¬¬ä¸€čˇŚçš„ç¬¬ä¸€ä¸Şĺ…ç´&nbsp;é€šĺ¸¸ä¸şç©şç™˝ă€‚ďĽ‰%
çź©éµçš„ĺ…¶ä»–ĺ…ç´&nbsp;č˘«ĺś†ć‹¬ĺŹ·ĺŚ…ĺ«ă€‚
\endulist
é€ščż‡ĺ˘žĺŠ&nbsp;ç«–ç›´ĺ»¶äĽ¸ďĽŚ\TeX\ č˝ĺ¤źä¸ş |\pmatrix| ĺ’Ś |\bordermatrix| ĺ¶ä˝śč¶łĺ¤źĺ¤§çš„ĺś†ć‹¬ĺŹ·ă€‚
ĺ¦‚ćžśä˝&nbsp;éś€č¦ç”¨ä¸ŤĺŚäşŽĺś†ć‹¬ĺŹ·çš„ĺ®šç•Śç¬¦ĺŚ…ĺ›´çź©éµďĽŚä˝&nbsp;ĺş”ĺ˝“ĺ°†
|\matrix| ä¸Ž |\left| ĺ’Ś |\right|ďĽ\xref\left ďĽ‰ĺčµ·ćťĄä˝żç”¨ă€‚

%\example
%$$\displaylines{
%   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
%\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
%           r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
%           r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
%           r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
%|
%\dproduces
%$$\displaylines{
%   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
%\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
%   r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
%   r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
%   r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
%\endexample
%\enddesc
\example
$$\displaylines{
   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
           r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
           r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
           r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
|
\dproduces
$$\displaylines{
   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
   r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
   r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
   r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
\endexample
\enddesc

%==========================================================================
%\subsection {Roots and radicals}
\subsection {ć&nbsp;ąĺŹ·ä¸Žć&nbsp;ąć•°}

%\begindesc
%\easy\cts sqrt {\&lt;argument&gt;}
%\explain
%This command produces the notation for the square root of \&lt;argument&gt;.
%\example
%$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
%|
%\dproduces
%$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
%\endexample
%\enddesc
\begindesc
\easy\cts sqrt {\&lt;argument&gt;}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ° \&lt;argument&gt; çš„ĺąłć–ąć&nbsp;ąă€‚
\example
$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
|
\dproduces
$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
\endexample
\enddesc

%\begindesc
%\easy\cts root {\&lt;argument$_1$&gt; {\bt \\of} \&lt;argument$_2$&gt;}
%\explain
%This command produces the notation for a root of \&lt;argument$_2$&gt;, where the
%root is given by \&lt;argument$_1$&gt;.
%\example
%$\root \alpha \of {r \cos \theta}$
%|
%\produces
%$\root \alpha \of {r \cos \theta}$
%\endexample
%\enddesc
\begindesc
\easy\cts root {\&lt;argument$_1$&gt; {\bt \\of} \&lt;argument$_2$&gt;}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ° \&lt;argument$_2$&gt; çš„ \&lt;argument$_1$&gt; ć¬ˇć&nbsp;ąĺŹ·ă€‚
\example
$\root \alpha \of {r \cos \theta}$
|
\produces
$\root \alpha \of {r \cos \theta}$
\endexample
\enddesc

%\begindesc
%\cts radical {\&lt;number&gt;}
%\explain
%This command produces a radical sign
%whose characteristics are given by
%\&lt;number&gt;.  It uses the same representation as the delimiter code
%^^{delimiter codes}
%in the ^|\delcode| command (\xref \delcode).
\begindesc
\cts radical {\&lt;number&gt;}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ç”¨ \&lt;number&gt; ĺ»ç”»ĺ…¶ç‰ąć€§çš„ć&nbsp;ąć•°ç¬¦ĺŹ·ă€‚
ĺ®ä˝żç”¨çš„ĺ®šç•Śç&nbsp;čˇ¨ç¤şćł•ä¸Ž ^|\delcode| ĺ‘˝ä»¤ďĽ\xref\delcode ďĽ‰çš„ç›¸ĺŚă€‚
^^{ĺ®šç•Śç&nbsp;}

%\example
%\def\sqrt{\radical "270370} % as in plain TeX
%|
%\endexample
%\enddesc
\example
\def\sqrt{\radical "270370} % as in plain TeX
|
\endexample
\enddesc


%==========================================================================
%\section {Equation numbers}
\section {ć–ąç¨‹çĽ–ĺŹ·}

%\begindesc
%\easy\cts eqno {}
%\cts leqno {}
%\explain
%These commands attach an equation number to a displayed formula.
%|\eqno| puts the equation number on the right and |\leqno| puts it on
%the left.
%The commands must be given at the end of the formula.
%If you have a multiline display and you want to number more than one
%of the lines, use the |\eq!-alignno| or |\leq!-alignno| command
%(\xref \eqalignno).
\begindesc
\easy\cts eqno {}
\cts leqno {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤ç»™é™ĺ—ĺ…¬ĺĽŹĺŠ&nbsp;ä¸Šć–ąç¨‹çĽ–ĺŹ·ă€‚
|\eqno| ĺ°†çĽ–ĺŹ·ć”ľĺś¨ĺŹłäľ§ďĽŚč€Ś|\leqno| ĺ°†çĽ–ĺŹ·ć”ľĺś¨ĺ·¦äľ§ă€‚
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺż…éˇ»ć”ľĺś¨ĺ…¬ĺĽŹćś«ĺ°ľă€‚
ĺ¦‚ćžśä˝&nbsp;ćś‰ä¸Şĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹďĽŚč€Śä˝&nbsp;ĺ¸Śćś›ç»™ä¸Ťć­˘ä¸€čˇŚçĽ–ĺŹ·ďĽŚ
ä˝&nbsp;ĺŹŻä»Ąç”¨ |\eq!-alignno| ć– |\leq!-alignno| ĺ‘˝ä»¤ďĽ\xref\eqalignno ďĽ‰ă€‚

%These commands are valid only in display math mode.
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺŹŞč˝ĺś¨é™ĺ—ć•°ĺ­¦ć¨ˇĺĽŹä¸­ä˝żç”¨ă€‚

%\example
%$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
%|
%\produces
%$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
%\endexample
%\example
%$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
%\endexample
%\enddesc
\example
$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
|
\produces
$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
\endexample
\example
$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
\endexample
\enddesc


%==========================================================================
%\section {Multiline displays}
\section {ĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹ}

%\begindesc
%\bix^^{displays//multiline}
%\cts displaylines
%   {{\bt \rqbraces{\&lt;line&gt;\ths\\cr$\ldots$\&lt;line&gt;\ths\\cr}}}
%\explain
%This command produces a multiline math display in which each line is
%centered independently of the other lines.
%You can use the |\noalign| command (\xref \noalign) to change the amount
%of space between two lines of a multiline display.
\begindesc
\bix^^{é™ĺ—ĺ…¬ĺĽŹ//ĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹ}
\cts displaylines
   {{\bt \rqbraces{\&lt;line&gt;\ths\\cr$\ldots$\&lt;line&gt;\ths\\cr}}}
\explain
ć­¤ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸€ä¸Şĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹďĽŚĺ…¶ä¸­çš„ĺ„čˇŚç‹¬ç«‹ĺś°ĺ±…ä¸­ć”ľç˝®ă€‚
ä˝&nbsp;ĺŹŻä»Ąä˝żç”¨ |\noalign| ĺ‘˝ä»¤ďĽ\xref\noalign ďĽ‰ć”ąĺŹĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹä¸­ä¸¤čˇŚçš„é—´éš”ă€‚

%If you want to attach equation numbers to some or all of the equations
%in a multiline math display, you should use |\eqalignno| or
%|\leqalignno|.
%\example
%$$\displaylines{(x+a)^2 = x^2+2ax+a^2\cr
%                (x+a)(x-a) = x^2-a^2\cr}$$
%|
%\dproduces\centereddisplays
%$$\displaylines{
%(x+a)^2 = x^2+2ax+a^2\cr
%(x+a)(x-a) = x^2-a^2\cr
%}$$
%\endexample
%\enddesc
ĺ¦‚ćžśä˝&nbsp;ĺ¸Śćś›ç»™ĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹçš„ćźä¸Şć–ćźäş›ć–ąç¨‹ć·»ĺŠ&nbsp;çĽ–ĺŹ·ďĽŚ
ä˝&nbsp;ĺş”ĺ˝“ä˝żç”¨|\eqalignno| ć– |\leqalignno|ă€‚
\example
$$\displaylines{(x+a)^2 = x^2+2ax+a^2\cr
                (x+a)(x-a) = x^2-a^2\cr}$$
|
\dproduces\centereddisplays
$$\displaylines{
(x+a)^2 = x^2+2ax+a^2\cr
(x+a)(x-a) = x^2-a^2\cr
}$$
\endexample
\enddesc

%\begindesc
%\cts eqalign {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts eqalignno {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts leqalignno {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\explain
%^^{equation numbers}
%These commands produce a multiline math display
%in which certain corresponding parts of the lines are lined up vertically.
%The |\eqalignno| and |\leqalignno| commands also let you
%provide equation numbers for some or all of the lines.
%|\eqalignno| puts the equation numbers on the right and
%|\leqalignno| puts them on the left.
\begindesc
\cts eqalign {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts eqalignno {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts leqalignno {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\explain
^^{ĺ…¬ĺĽŹçĽ–ĺŹ·}
čż™äş›ĺ‘˝ä»¤ćŽ’ĺŤ°ä¸€ä¸Şĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹďĽŚĺ…¶ä¸­ćźäş›čˇŚçš„ĺŻąĺş”é¨ĺ†ç«–ç›´ĺŻąé˝ă€‚
|\eqalignno| ĺ’Ś |\leqalignno| ĺ‘˝ä»¤čżĺ…č®¸ä˝&nbsp;ç»™ćźä¸Şć–ćźäş›čˇŚć·»ĺŠ&nbsp;ć–ąç¨‹çĽ–ĺŹ·ă€‚
|\eqalignno| ĺ°†ć–ąç¨‹çĽ–ĺŹ·ć”ľĺś¨ĺŹłäľ§ďĽŚ
č€Ś |\leqalignno| ĺ°†çĽ–ĺŹ·ć”ľĺś¨ĺ·¦äľ§ă€‚

%Each line in the display is ended by |\cr|.  Each of the parts to be aligned
%(most often an equals sign) is preceded by
%`|&amp;|'.  An `|&amp;|' also precedes each equation number, which comes at the
%end of a line.
%You can put more than one of these commands in a single display in order
%to produce several groups of equations.  In this case, only the rightmost
%or leftmost group can be produced by |\eqalignno| or |\leqalignno|.
é™ĺ—ĺ…¬ĺĽŹçš„ćŻŹčˇŚç”¨ |\cr| ç»“ĺ°ľă€‚
ĺ„čˇŚéś€č¦ĺŻąé˝çš„ĺ„é¨ĺ†ďĽĺ¤šĺŤŠćŻç­‰ĺŹ·ďĽ‰ĺ‰Ťéť˘ĺŠ&nbsp;ä¸Š `|&amp;|'ă€‚
ć–ąç¨‹çĽ–ĺŹ·ć”ľĺś¨ĺ…¬ĺĽŹćś«ĺ°ľďĽŚĺ®çš„ĺ‰Ťéť˘äąźč¦ĺŠ&nbsp;ä¸Š `|&amp;|'ă€‚
ä˝&nbsp;ĺŹŻä»Ąĺś¨ĺŤ•ä¸Şé™ĺ—ĺ…¬ĺĽŹä¸­ĺ¤šć¬ˇä˝żç”¨čż™äş›ĺ‘˝ä»¤ä»ĄćŽ’ĺŤ°ĺ¤šç»„ć–ąç¨‹ă€‚
ĺś¨čż™ç§Ťć…ĺ˝˘ä¸­ďĽŚ
ĺŹŞćś‰ćś€ĺŹłčľąć–ćś€ĺ·¦čľąçš„é‚Łç»„ć–ąç¨‹ĺŹŻä»Ąç”¨ |\eqalignno| ć– |\leqalignno| çĽ–ĺŹ·ă€‚

%You can use the |\noalign| command (\xref \noalign) to change the amount
%of space between two lines of a multiline display.
%\example
%$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
%         f_3(t) &amp;= t^2-1\cr}\right\}
%  \left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
%|
%\dproduces
%$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
%   f_3(t) &amp;= t^2-1\cr}\right\}
%\left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
%\nextexample
%$$\eqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
%   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
%   &amp;=E(x^2)-\mu^2\cr}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\eqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
%   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
%   &amp;=E(x^2)-\mu^2\cr}$$
%\nextexample
%$$\leqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
%   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\leqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
%   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
%\nextexample
%$$\eqalignno{
%  &amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
%  &amp;(x+a)(x-a) = x^2-a^2\cr}$$
%% same effect as \displaylines but with an equation number
%|
%\dproduces
%$$\eqalignno{
%&amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
%&amp;(x+a)(x-a) = x^2-a^2\cr
%}$$
%% same effect as \displaylines but with an equation number
ä˝&nbsp;ĺŹŻä»Ąä˝żç”¨ |\noalign| ĺ‘˝ä»¤ďĽ\xref\noalign ďĽ‰ć”ąĺŹĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹä¸­ä¸¤čˇŚçš„é—´éš”ă€‚
\example
$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
         f_3(t) &amp;= t^2-1\cr}\right\}
  \left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
|
\dproduces
$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
   f_3(t) &amp;= t^2-1\cr}\right\}
\left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
\nextexample
$$\eqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
   &amp;=E(x^2)-\mu^2\cr}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\eqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
   &amp;=E(x^2)-\mu^2\cr}$$
\nextexample
$$\leqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\leqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
\nextexample
$$\eqalignno{
  &amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
  &amp;(x+a)(x-a) = x^2-a^2\cr}$$
% same effect as \displaylines but with an equation number
|
\dproduces
$$\eqalignno{
&amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
&amp;(x+a)(x-a) = x^2-a^2\cr
}$$
% same effect as \displaylines but with an equation number

%\eix^^{displays//multiline}
%\endexample
%\enddesc
\eix^^{é™ĺ—ĺ…¬ĺĽŹ//ĺ¤ščˇŚé™ĺ—ĺ…¬ĺĽŹ}
\endexample
\enddesc


%==========================================================================
%\section {Fonts in math formulas}
\section {ć•°ĺ­¦ĺ…¬ĺĽŹĺ­—ä˝“}

%\begindesc
%^^{fonts}
%\xrdef{mathfonts}
%%
%\easy\ctsx cal {use calligraphic uppercase font}
%\ctsx mit {use math italic font}
%\ctsx oldstyle {use old style digit font}
%\explain
%These commands cause \TeX\ to typeset the following text in the
%specified font.  You can only use them in \minref{math mode}.
%The |\mit| command is useful for producing slanted capital ^{Greek letters}.
%You can also use the commands given in
%\headcit{Selecting fonts}{selfont} to change fonts in math mode.
%\example
%${\cal XYZ} \quad
%{\mit AaBb\Gamma \Delta \Sigma} \quad
%{\oldstyle 0123456789}$
%|
%\produces
%${\cal XYZ} \quad
%{\mit AaBb\Gamma \Delta \Sigma} \quad
%{\oldstyle 0123456789}$
%\endexample
%\enddesc
\begindesc
^^{ĺ­—ä˝“}
\xrdef{mathfonts}
%
\easy\ctsx cal {use calligraphic uppercase font}
\ctsx mit {use math italic font}
\ctsx oldstyle {use old style digit font}
\explain
čż™äş›ĺ‘˝ä»¤č®© \TeX\ ç”¨ćŚ‡ĺ®šçš„ĺ­—ä˝“ćŽ’ç‰äą‹ĺŽçš„ć–‡ćś¬ă€‚
ä˝&nbsp;ĺŹŞč˝ĺś¨\minref{ć•°ĺ­¦ć¨ˇĺĽŹ}ä¸­ä˝żç”¨ĺ®ä»¬ă€‚
|\mit| ĺ‘˝ä»¤ĺŹŻç”¨äşŽćŽ’ĺŤ°ć–śä˝“ĺ¤§ĺ†™^{ĺ¸Śč…Šĺ­—ćŻŤ}ă€‚
ä˝&nbsp;čżĺŹŻä»Ąç”¨\headcit{é€‰ć‹©ĺ­—ä˝“}{selfont}ä¸­çš„é‚Łäş›ĺ‘˝ä»¤ć”ąĺŹć•°ĺ­¦ć¨ˇĺĽŹä¸­çš„ĺ­—ä˝“ă€‚
\example
${\cal XYZ} \quad
{\mit AaBb\Gamma \Delta \Sigma} \quad
{\oldstyle 0123456789}$
|
\produces
${\cal XYZ} \quad
{\mit AaBb\Gamma \Delta \Sigma} \quad
{\oldstyle 0123456789}$
\endexample
\enddesc

%^^{type styles}
%\begindesc
%\ctsx itfam {family for italic type}
%\ctsx bffam {family for boldface type}
%\ctsx slfam {family for slanted type}
%\ctsx ttfam {family for typewriter type}
%\explain
%These commands define type families \minrefs{family} for use in
%\minref{math mode}.  Their principal use is in defining the
%|\it|, |\bf|, |\sl|, and |\tt| commands so that they work in math mode.
%\enddesc
^^{ĺ­—ä˝“éŁŽć&nbsp;Ľ}
\begindesc
\ctsx itfam {family for italic type}
\ctsx bffam {family for boldface type}
\ctsx slfam {family for slanted type}
\ctsx ttfam {family for typewriter type}
\explain
čż™äş›ĺ‘˝ä»¤ĺ®šäą‰ĺ‡&nbsp;ç§Ťç”¨äşŽ\minref{ć•°ĺ­¦ć¨ˇĺĽŹ}çš„ĺ­—ä˝“ć—Ź\minrefs{ć—Ź}ă€‚
ĺ®ä»¬ä¸»č¦ç”¨ĺś¨ |\it|ă€|\bf|ă€|\sl| ĺ’Ś |\tt| ĺ‘˝ä»¤çš„ĺ®šäą‰ä¸­ďĽŚä˝żčż™äş›ĺ‘˝ä»¤č˝ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹä¸­ä˝żç”¨ă€‚
\enddesc

%\begindesc
%\cts fam {\param{number}}
%\explain
%When \TeX\ is in \minref{math mode}, it ordinarily typesets a character
%using the font family ^^{class} given in its \minref{mathcode}.
%^^{family//given by \b\tt\\fam\e}
%However, when \TeX\ is in math mode and encounters a character whose
%\minref{class} is $7$ (Variable), it typesets that character using
%the font \minref{family} given by the value of |\fam|, provided that the
%value of |\fam| is between $0$ and $15$.
%If the value of |\fam| isn't in that range, \TeX\ uses the family in
%the character's mathcode as in the ordinary case.
%\TeX\ sets |\fam| to $-1$ whenever it enters math mode.
%Outside of math mode, |\fam| has no effect.
\begindesc
\cts fam {\param{number}}
\explain
ĺś¨\minref{ć•°ĺ­¦ć¨ˇĺĽŹ}ć—¶ďĽŚ\TeX\ é€šĺ¸¸ç”¨ĺ­—ç¬¦çš„\minref{ć•°ĺ­¦ç&nbsp;}ćŚ‡ĺ®šçš„ĺ­—ä˝“ć—ŹćŽ’ç‰čŻĄĺ­—ç¬¦ă€‚
^^{ç±»}^^{ć—Ź//ç”¨ \b\tt\\fam\e ç»™ĺ‡ş}
ä˝†ćŻďĽŚĺ¦‚ćžś \TeX\ ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹä¸­é‡ĺ°ç¬¬ $7$ \minref{ç±»}ďĽĺŹé‡ŹďĽ‰ĺ­—ç¬¦ďĽŚ
ĺ®ĺ°†ç”¨ç”± |\fam| çš„ĺ€Ľç»™ĺ‡şçš„ĺ­—ä˝“\minref{ć—Ź}ćŽ’ç‰čŻĄĺ­—ç¬¦ďĽŚ
ĺŹŞč¦ |\fam| çš„ĺ€Ľĺś¨ $0$ ĺ’Ś $15$ äą‹é—´ă€‚
ĺ¦‚ćžś |\fam| çš„ĺ€Ľä¸Ťĺś¨čŻĄčŚĺ›´ĺ†…ďĽŚ
\TeX\ ĺ°±ĺŹé€šĺ¸¸ć…ĺ˝˘é‚Łć&nbsp;·ä˝żç”¨ĺ­—ç¬¦çš„ć•°ĺ­¦ç&nbsp;ćŚ‡ĺ®šçš„ĺ­—ä˝“ć—Źă€‚
\TeX\ ĺś¨čż›ĺ…Ąć•°ĺ­¦ć¨ˇĺĽŹć—¶č®ľĺ®š |\fam| ä¸ş $-1$ă€‚
ĺś¨ć•°ĺ­¦ć¨ˇĺĽŹäą‹ĺ¤–ďĽŚ|\fam| ć—&nbsp;ä»»ä˝•ć•ćžśă€‚

%By assigning a value to
%|\fam| you can change the way that \TeX\ typesets ordinary
%characters such as variables.
%For instance, by setting |\fam| to |\ttfam|, you cause \TeX\ to typeset
%variables using a typewriter font.
%\PlainTeX\ defines |\tt| as a \minref{macro} that, among other things,
%sets |\fam| to |\ttfam|.
%\example
%\def\bf{\fam\bffam\tenbf} % As in plain TeX.
%|
%\endexample
%\enddesc
é€ščż‡čµ‹äş |\fam| ä¸ŤĺŚçš„ĺ€ĽďĽŚä˝&nbsp;č˝č®© \TeX\ ç”¨ä¸ŤĺŚć–ąĺĽŹćŽ’ç‰ć™®é€šĺ­—ç¬¦ďĽŚćŻ”ĺ¦‚ĺŹé‡Źă€‚
ä¸ľä¸Şäľ‹ĺ­ďĽŚč®ľĺ®šäş† |\fam| ä¸ş |\ttfam| ďĽŚä˝&nbsp;ĺŹŻä»Ąč®© \TeX\ ç”¨ć‰“ĺ­—ćśşĺ­—ä˝“ćŽ’ç‰ĺŹé‡Źă€‚
\PlainTeX\ ĺś¨ĺ®šäą‰ |\tt| \minref{ĺ®Ź}ć—¶ďĽŚé™¤äş†ĺ…¶ä»–č®ľĺ®šäą‹ĺ¤–ďĽŚ
čżč®ľĺ®š |\fam| ç­‰äşŽ |\ttfam|ă€‚
\example
\def\bf{\fam\bffam\tenbf} % As in plain TeX.
|
\endexample
\enddesc

%\begindesc
%\cts textfont {\&lt;family&gt;\param{fontname}}
%\cts scriptfont {\&lt;family&gt;\param{fontname}}
%\cts scriptscriptfont {\&lt;family&gt;\param{fontname}}
%\explain
%^^{text style}
%^^{script style}
%^^{scriptscript style}
%Each of these parameters specifies the font that \TeX\ is to use for
%typesetting the indicated \minref{style} in the indicated \minref{family}.
%These choices have no effect outside of \minref{math mode}.
%\example
%\scriptfont2 = \sevensy % As in plain TeX.
%|
%\endexample
%\enddesc
\begindesc
\cts textfont {\&lt;family&gt;\param{fontname}}
\cts scriptfont {\&lt;family&gt;\param{fontname}}
\cts scriptscriptfont {\&lt;family&gt;\param{fontname}}
\explain
^^{ć–‡ćś¬ć&nbsp;·ĺĽŹ}
^^{ć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ}
^^{ĺ°Źć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹ}
čż™ä¸‰ä¸ŞĺŹ‚ć•°ĺ†ĺ«é€‰ć‹© \TeX\ ćŽ’ç‰ćŚ‡ĺ®š\minref{ć—Ź}çš„ćŚ‡ĺ®š\minref{ć&nbsp;·ĺĽŹ}ć—¶ć‰€ç”¨çš„ĺ­—ä˝“ă€‚
čż™äş›é€‰ć‹©ĺś¨\minref{ć•°ĺ­¦ć¨ˇĺĽŹ}äą‹ĺ¤–ć—&nbsp;ä»»ä˝•ć•ćžśă€‚
\example
\scriptfont2 = \sevensy % As in plain TeX.
|
\endexample
\enddesc

%\see ``Type styles'' (\xref{seltype}).
\see ``ĺ­—ä˝“éŁŽć&nbsp;Ľ''ďĽ\xref{seltype}ďĽ‰ă€‚


%==========================================================================
%\section {Constructing math symbols}
\section {ćž„é€&nbsp;ć•°ĺ­¦ç¬¦ĺŹ·}

%==========================================================================
%\subsection {Making delimiters bigger}
\subsection {ĺ˘žĺ¤§ĺ®šç•Śç¬¦}

%\begindesc
%\makecolumns 16/4:
%\easy\cts big {}
%\cts bigl {}
%\cts bigm {}
%\cts bigr {}
%\cts Big {}
%\cts Bigl {}
%\cts Bigm {}
%\cts Bigr {}
%\cts bigg {}
%\cts biggl {}
%\cts biggm {}
%\cts biggr {}
%\cts Bigg {}
%\cts Biggl {}
%\cts Biggm {}
%\cts Biggr {}
%\explain
%^^{delimiters//enlarging}
%These commands make \minref{delimiter}s bigger than their normal size.
%The commands in the four columns
%produce successively larger sizes.  The difference between |\big|,
%|\bigl|, |\bigr|, and |bigm| has to do with the \minref{class} of the
%enlarged delimiter:
%\ulist\compact
%\li |\big| produces an ordinary symbol.
%\li |\bigl| produces an opening symbol.
%\li |\bigr| produces a closing symbol.
%\li |\bigm| produces a relation symbol.
%\endulist
%\noindent
%\TeX\ uses the class of a symbol in order to decide how much space to put
%around that symbol.
\begindesc
\makecolumns 16/4:
\easy\cts big {}
\cts bigl {}
\cts bigm {}
\cts bigr {}
\cts Big {}
\cts Bigl {}
\cts Bigm {}
\cts Bigr {}
\cts bigg {}
\cts biggl {}
\cts biggm {}
\cts biggr {}
\cts Bigg {}
\cts Biggl {}
\cts Biggm {}
\cts Biggr {}
\explain
^^{ĺ®šç•Śç¬¦//ĺ˘žĺ¤§ĺ®šç•Śç¬¦}
čż™äş›ĺ‘˝ä»¤č®©\minref{ĺ®šç•Śç¬¦}ćŻ”ĺ®ä»¬çš„ć­Łĺ¸¸ĺ°şĺŻ¸čżĺ¤§ă€‚
čż™ĺ››ć&nbsp;Źä¸­çš„ĺ‘˝ä»¤ç”źćäľťć¬ˇĺ˘žĺ¤§çš„ĺ°şĺŻ¸ă€‚|\big|ă€|\bigl|ă€|\bigr|
ĺ’Ś |\bigm| çš„ĺŚşĺ«ĺś¨äşŽĺ˘žĺ¤§çš„ĺ®šç•Śç¬¦ć‰€ĺ±žçš„\minref{ç±»}ďĽš
\ulist\compact
\li |\big| ç”źćä¸€ä¸Şć™®é€šç¬¦ĺŹ·ă€‚
\li |\bigl| ç”źćä¸€ä¸ŞĺĽ€ç¬¦ĺŹ·ă€‚
\li |\bigr| ç”źćä¸€ä¸Şé—­ç¬¦ĺŹ·ă€‚
\li |\bigm| ç”źćä¸€ä¸Şĺ…łçł»ç¬¦ĺŹ·ă€‚
\endulist
\noindent
\TeX\ ä»Žĺ­—ç¬¦ć‰€ĺ±žçš„ç±»çˇ®ĺ®šč¦ĺś¨čŻĄĺ­—ç¬¦ä¸¤čľąç•™ä¸‹ĺ¤šĺ¤§çš„ç©şć&nbsp;Ľă€‚

%These commands, unlike |\left| and |\right|,
%do \emph{not} define a group.

%\example
%$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
%   \biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
%[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
%   \biggl[x\biggr] \quad \Biggl[x\Biggr]$$
%|
%\dproduces
%$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
%\biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
%[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
%\biggl[x\biggr] \quad \Biggl[x\Biggr]$$
%\endexample
%\enddesc
\example
$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
   \biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
   \biggl[x\biggr] \quad \Biggl[x\Biggr]$$
|
\dproduces
$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
\biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
\biggl[x\biggr] \quad \Biggl[x\Biggr]$$
\endexample
\enddesc

%==========================================================================
%\subsection {Parts of large symbols}
\subsection {ĺ¤§ç¬¦ĺŹ·çš„ä¸€é¨ĺ†}

%\begindesc
%\cts downbracefill {}
%\cts upbracefill {}
%\explain
%These commands respectively produce upward-pointing
%and downward-pointing extensible ^{horizontal braces}. ^^{braces}
%\TeX\ will make the braces as wide as necessary.
%These commands
%are used in the definitions of ^|\overbrace| and ^|\underbrace|
%(\xref \overbrace).
%\example
%$$\hbox to 1in{\downbracefill} \quad
%   \hbox to 1in{\upbracefill}$$
%|
%\dproduces
%$$\hbox to 1in{\downbracefill} \quad
%   \hbox to 1in{\upbracefill}$$
%\endexample
%\enddesc
\begindesc
\cts downbracefill {}
\cts upbracefill {}
\explain
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺ†ĺ«ćŽ’ĺŤ°ćśťä¸Šĺ’Śćśťä¸‹çš„ĺŹŻäĽ¸ĺ±•^{ć°´ĺąłčŠ±ć‹¬ĺŹ·}ă€‚^^{čŠ±ć‹¬ĺŹ·}
\TeX\ ĺ°†č®©čŠ±ć‹¬ĺŹ·č¶łĺ¤źĺ®˝ă€‚
čż™ä¸¤ä¸Şĺ‘˝ä»¤ç”¨äşŽĺ®šäą‰ ^|\overbrace| ĺ’Ś ^|\underbrace|ďĽ\xref\overbrace ďĽ‰ă€‚
\example
$$\hbox to 1in{\downbracefill} \quad
   \hbox to 1in{\upbracefill}$$
|
\dproduces
$$\hbox to 1in{\downbracefill} \quad
   \hbox to 1in{\upbracefill}$$
\endexample
\enddesc

%\begindesc
%\cts arrowvert {}
%\cts Arrowvert {}
%\cts lmoustache {}
%\cts rmoustache {}
%\cts bracevert {}
%\explain
%These commands produce portions of certain large
%delimiters
%^^{delimiters//parts of}
%and can themselves be used as delimiters.
%They refer to characters in the ^|cmex10| math font.
%\example
%$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
%  \Big\lmoustache \cdots \Big\rmoustache \cdots
%  \Big\bracevert \cdots$$
%|
%\dproduces
%$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
%  \Big\lmoustache \cdots \Big\rmoustache \cdots
%  \Big\bracevert \cdots$$
%\endexample
%\enddesc
\begindesc
\cts arrowvert {}
\cts Arrowvert {}
\cts lmoustache {}
\cts rmoustache {}
\cts bracevert {}
\explain
čż™äş›ĺ‘˝ä»¤ćŽ’ĺŤ°ćźäş›ĺ¤§ĺ®šç•Śç¬¦çš„ä¸€é¨ĺ†ďĽŚ
^^{ĺ®šç•Śç¬¦//ĺ®šç•Śç¬¦çš„ä¸€é¨ĺ†}
ćŠŠĺ®ä»¬äąźç”¨ä˝śĺ®šç•Śç¬¦ă€‚
ĺ®ä»¬ĺŹ–č‡Ş ^|cmex10| ć•°ĺ­¦ĺ­—ä˝“ä¸­çš„ĺ­—ç¬¦ă€‚
\example
$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
  \Big\lmoustache \cdots \Big\rmoustache \cdots
  \Big\bracevert \cdots$$
|
\dproduces
$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
  \Big\lmoustache \cdots \Big\rmoustache \cdots
  \Big\bracevert \cdots$$
\endexample
\enddesc


%==========================================================================
%\section {Aligning parts of a formula}
\section {ĺŻąé˝é¨ĺ†ĺ…¬ĺĽŹ}

%==========================================================================
%\subsection {Aligning accents}
\subsection {ĺŻąé˝ć•°ĺ­¦é‡Ťéźł}

%\begindesc
%\bix^^{accents//aligning}
%\cts skew {\&lt;number&gt; \&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
%\explain
%This command shifts the accent \&lt;argument$_1$&gt; by
%\&lt;number&gt; \minref{mathematical unit}s to the right of its normal position
%with respect to \&lt;argu\-ment$_2$&gt;.
%The most common use of this command is for
%modifying the position of an accent that's over
%another accent.
%\example
%$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
%  \skew 4\tilde{\hat x}$$
%|
%\dproduces
%$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
%  \skew 4\tilde{\hat x}$$
%\endexample
%\enddesc
\begindesc
\bix^^{é‡Ťéźł//ĺŻąé˝é‡Ťéźł}
\cts skew {\&lt;number&gt; \&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
\explain
ć­¤ĺ‘˝ä»¤ĺ°†é‡Ťéźł \&lt;argument$_1$&gt; ç›¸ĺŻą \&lt;argu\-ment$_2$&gt;
ä»Žĺ®çš„ć­Łĺ¸¸ä˝Ťç˝®ĺľ€ĺŹłç§»ĺŠ¨ \&lt;number&gt; ä¸Ş\minref{ć•°ĺ­¦ĺŤ•ä˝Ť}ă€‚
ć­¤ĺ‘˝ä»¤ĺ¸¸ç”¨äşŽč°ć•´ĺś¨ĺ…¶ä»–é‡Ťéźłäą‹ä¸Šçš„é‡Ťéźłçš„ä˝Ťç˝®ă€‚
\example
$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
  \skew 4\tilde{\hat x}$$
|
\dproduces
$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
  \skew 4\tilde{\hat x}$$
\endexample
\enddesc

%\begindesc
%\cts skewchar {\&lt;font&gt;\param{number}}
%\explain
%The |\skewchar| of a font
%is the character in the font whose kerns,
%as defined in the font's metrics file, determine the positions
%of math accents. That is, suppose that \TeX\ is applying a math accent
%to the character `|x|'.  \TeX\ checks if the character pair
%`|x\skewchar|' has a kern; if so, it moves the accent by the amount of
%that kern. The complete algorithm that \TeX\ uses to position math
%accents (which involves many more things) is in \knuth{Appendix~G}.
\begindesc
\cts skewchar {\&lt;font&gt;\param{number}}
\explain
ĺ­—ä˝“çš„ |\skewchar| ćŻĺ­—ä˝“ä¸­çš„ćźä¸Şĺ­—ç¬¦ďĽŚ
ĺ®ĺś¨ĺ­—ä˝“ĺş¦é‡Źć–‡ä»¶ä¸­ĺ®šäą‰çš„ç´§ćŽ’çˇ®ĺ®šäş†ć•°ĺ­¦é‡Ťéźłçš„ä˝Ťç˝®ă€‚
äąźĺ°±ćŻčŻ´ďĽŚĺ‡č®ľ \TeX\ č¦ç»™ĺ­—ç¬¦ `|x|' ĺŠ&nbsp;ä¸Šć•°ĺ­¦é‡ŤéźłďĽŚ
ĺ™ \TeX\ ćŁ€ćźĄĺ­—ç¬¦ĺŻą `|x\skewchar|' ćŻĺ¦ćś‰ä¸Şç´§ćŽ’ďĽ›
ĺ¦‚ćžśćś‰ďĽŚĺ®ĺ°±ä»ĄčŻĄç´§ćŽ’çš„ĺ€Ľç§»ĺŠ¨čŻĄé‡Ťéźłă€‚
\TeX\ ć”ľç˝®ć•°ĺ­¦é‡Ťéźłçš„ĺ®Ść•´ç®—ćł•ďĽčż™ć¶‰ĺŹŠĺ°ĺľĺ¤šäş‹ć…ďĽ‰ĺś¨\knuth{é™„ĺ˝•~G}ä¸­ćŹŹčż°ă€‚

%If the value of |\skewchar| is not in the range $0$--$255$,
%\TeX\ takes the kern value to be zero.
ĺ¦‚ćžś |\skewchar| çš„ĺ€Ľä¸Ťĺś¨ $0$--$255$ çš„čŚĺ›´ĺ†…ďĽŚ\TeX\ ĺ°†ç´§ćŽ’çš„ĺ€Ľĺ˝“ä˝śé›¶ă€‚

%Note that \&lt;font&gt; is a control sequence
%that names a font, not a \&lt;font\-name&gt; that names font files.
%Beware:
%an assignment to |\skewchar| is \emph{not} undone at the end
%of a group.
%If you want to change |\skewchar| locally, you'll need to
%save and restore its original value explicitly.
%\enddesc
ćł¨ć„Ź \&lt;font&gt; ćŻä¸€ä¸ŞćŽ§ĺ¶ĺşŹĺ—ďĽŚĺ®ćŻĺ­—ä˝“çš„ĺŤç§°ďĽŚč€Śä¸ŤćŻĺ­—ä˝“ć–‡ä»¶çš„ĺŤç§° \&lt;font\-name&gt;ă€‚
ĺ°ŹĺżďĽšĺŻą |\skewchar| çš„čµ‹ĺ€Ľĺś¨çĽ–ç»„ç»“ćťźć—¶\emph{ĺą¶ä¸ŤäĽš}čżĺŽźă€‚
ĺ¦‚ćžśä˝&nbsp;ćłĺ±€é¨ć”ąĺŹ|\skewchar|ďĽŚä˝&nbsp;éś€č¦ćľĺĽŹĺś°äżťĺ­ĺ’ŚčżĺŽźĺ®çš„ĺŽźĺ§‹ĺ€Ľă€‚
\enddesc

%\begindesc
%\cts defaultskewchar {\param{number}}
%\explain
%When \TeX\ reads the metrics file
%^^{metrics file//default skew character in}
%for a font in response to a
%^|\font| command, it sets the font's ^|\skewchar| to
%|\default!-skewchar|.
%If the value of |\default!-skewchar| is
%not in the range $0$--$255$, \TeX\ does not assign any
%skew characters by default.
%\PlainTeX\ sets |\defaultskewchar| to $-1$, and it's usually best
%to leave it there.
%\margin{Misleading example deleted.}
%\eix^^{accents//aligning}
%\enddesc
\begindesc
\cts defaultskewchar {\param{number}}
\explain
ĺś¨ć‰§čˇŚ ^|\font| ĺ‘˝ä»¤čŻ»ĺŹ–ĺ­—ä˝“çš„ĺş¦é‡Źć–‡ä»¶ć—¶ďĽŚ
^^{ĺş¦é‡Źć–‡ä»¶//ĺ…¶ä¸­çš„é»č®¤ć–śĺ­—ç¬¦}
\TeX\ č®ľĺ®ščŻĄĺ­—ä˝“çš„ ^|\skewchar| ç­‰äşŽ |\default!-skewchar|ă€‚
ĺ¦‚ćžś |\default!-skewchar| çš„ĺ€Ľä¸Ťĺś¨ $0$--$255$ çš„čŚĺ›´ĺ†…ďĽŚ
\TeX\ é»č®¤ĺ°±ä¸Ťč®ľĺ®š |\skewchar| çš„ĺ€Ľă€‚
\PlainTeX\ č®ľĺ®š |\defaultskewchar| ç­‰äşŽ $-1$ďĽŚä¸€č¬ä¸Ťéś€č¦ć”ąĺŠ¨ĺ®ă€‚
\margin{Misleading example deleted.}
\eix^^{é‡Ťéźł//ĺŻąé˝é‡Ťéźł}
\enddesc

%==========================================================================
%\subsection {Aligning material vertically}
\subsection {ç«–ç›´ĺŻąé˝ç´&nbsp;ćť}

%\begindesc
%\cts vcenter {\rqbraces{\&lt;vertical mode material&gt;}}
%\ctsbasic {\\vcenter to \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
%\ctsbasic {\\vcenter spread \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
%\explain
%Every math formula has an invisible
%``^{axis}'' that \TeX\ treats as a kind of
%horizontal centering line for that formula.
%For instance, the axis of a formula consisting of a
%fraction is at the center of the fraction bar.
%The |\vcenter| command tells \TeX\ to place the \&lt;vertical mode material&gt;
%in a \minref{vbox} and to center the vbox
%with respect to the axis of the formula it is currently constructing.
\begindesc
\cts vcenter {\rqbraces{\&lt;vertical mode material&gt;}}
\ctsbasic {\\vcenter to \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
\ctsbasic {\\vcenter spread \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
\explain
ćŻŹä¸Şć•°ĺ­¦ĺ…¬ĺĽŹé˝ćś‰ä¸€ä¸Şä¸ŤĺŹŻč§çš„``^{č˝´çşż}''ďĽŚ\TeX\ ĺ°†ĺ®ä˝śä¸şčŻĄĺ…¬ĺĽŹçš„ć°´ĺąłä¸­ĺżçşżă€‚
ä¸ľä¸Şäľ‹ĺ­ďĽŚç”±ĺ†ĺĽŹç»„ćçš„ĺ…¬ĺĽŹçš„č˝´çşżĺ°±ĺś¨ĺ†ć•°çşżçš„ä¸­ĺżă€‚
|\vcenter| ĺ‘˝ä»¤č®© \TeX\ ĺ°† \&lt;vertical mode material&gt; ć”ľĺ…Ą\minref{ç«–ç›´ç›’ĺ­}ä¸­ďĽŚ
ĺą¶ĺ°†čŻĄç«–ç›´ç›’ĺ­ä¸Žĺ˝“ĺ‰Ťĺ…¬ĺĽŹçš„č˝´çşżĺ±…ä¸­ĺŻąé˝ă€‚

%The first form of the command
%centers the material as given.  The second and third
%forms expand or shrink the material vertically as in the |\vbox| command
%(\xref \vbox).
ć­¤ĺ‘˝ä»¤çš„ç¬¬ä¸€ç§Ťĺ˝˘ĺĽŹĺ¦‚ä¸Šć‰€čż°ĺ±…ä¸­ć”ľç˝®ç´&nbsp;ćťă€‚
ĺŽä¸¤ç§Ťĺ˝˘ĺĽŹç«–ç›´ć‰©ĺ±•ć–ć”¶çĽ©ç´&nbsp;ćťďĽŚĺ¦‚ĺŚ |\vbox| ĺ‘˝ä»¤ďĽ\xref\vbox ďĽ‰ă€‚

%\example
%$${n \choose k} \buildrel \rm def \over \equiv \&gt;
%\vcenter{\hsize 1.5 in \noindent the number of
%combinations of $n$ things taken $k$ at a time}$$
%|
%\dproduces
%$${n \choose k} \buildrel \rm def \over \equiv \&gt;
%\vcenter{\hsize 1.5 in \noindent the number of
%combinations of $n$ things taken $k$ at a time}$$
%\endexample
%\enddesc
\example
$${n \choose k} \buildrel \rm def \over \equiv \&gt;
\vcenter{\hsize 1.5 in \noindent the number of
combinations of $n$ things taken $k$ at a time}$$
|
\dproduces
$${n \choose k} \buildrel \rm def \over \equiv \&gt;
\vcenter{\hsize 1.5 in \noindent the number of
combinations of $n$ things taken $k$ at a time}$$
\endexample
\enddesc


%==========================================================================
%\section {Producing spaces}
\section {ç”źćé—´éš”}

%==========================================================================
%\subsection {Fixed-width math spaces}
\subsection {ĺ›şĺ®šĺ®˝ĺş¦ć•°ĺ­¦é—´éš”}

%\begindesc
%\bix^^{space//in math formulas}
%\ctspecial ! \ctsxrdef{@shriek}
%\ctspecial , \ctsxrdef{@comma}
%\ctspecial &gt; \ctsxrdef{@greater}
%\ctspecial ; \ctsxrdef{@semi}
%\explain
%These commands produce various amounts of ^{extra space} in formulas.  They
%are defined in terms of \minref{mathematical unit}s, so \TeX\ adjusts
%the amount of space according to the current \minref{style}.
%\ulist
%\li |\!!| produces a negative thin space, i.e., it reduces the space
%between its neighboring subformulas by the amount of a thin space.
%\li |\,| produces a thin space.
%\li |\&gt;| produces a medium space.
%\li |\;| produces a thick space.
%\endulist
%\example
%$$00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
%{\scriptstyle 00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
%|
%\dproduces
%$$00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
%{\scriptstyle 00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
%\endexample
%\enddesc
\begindesc
\bix^^{é—´éš”//ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„é—´éš”}
\ctspecial ! \ctsxrdef{@shriek}
\ctspecial , \ctsxrdef{@comma}
\ctspecial &gt; \ctsxrdef{@greater}
\ctspecial ; \ctsxrdef{@semi}
\explain
čż™äş›ĺ‘˝ä»¤ĺś¨ĺ…¬ĺĽŹä¸­ç”źćĺ„ç§Ťĺ¤§ĺ°Źçš„^{é˘ťĺ¤–é—´éš”}ă€‚
ĺ®ä»¬ä˝żç”¨\minref{ć•°ĺ­¦ĺŤ•ä˝Ť}ćťĄĺ®šäą‰ďĽŚ
ĺ›&nbsp;ć­¤ \TeX\ äĽšć&nbsp;ąćŤ®ĺ˝“ĺ‰Ť\minref{ć&nbsp;·ĺĽŹ}č°ć•´é—´éš”çš„ĺ¤§ĺ°Źă€‚
\ulist
\li |\!!| ç”źćč´źçš„ç»†ĺ°Źé—´éš”ďĽŚĺŤłĺ®č®©ç›¸é‚»ĺ­ĺ…¬ĺĽŹçš„é—´éš”ĺ‡ŹĺŽ»čŻĄç»†ĺ°Źé—´éš”çš„ĺ¤§ĺ°Źă€‚
\li |\,| ç”źćç»†ĺ°Źé—´éš”ă€‚
\li |\&gt;| ç”źćä¸­ç­‰é—´éš”ă€‚
\li |\;| ç”źćčľĺ¤§é—´éš”ă€‚
\endulist
\example
$$00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
{\scriptstyle 00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
|
\dproduces
$$00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
{\scriptstyle 00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
\endexample
\enddesc

%\begindesc
%\cts thinmuskip {\param{muglue}}
%\cts medmuskip {\param{muglue}}
%\cts thickmuskip {\param{muglue}}
%\explain
%These parameters define thin, medium, and thick spaces in
%math mode.
%\example
%$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
%   \quad0\mskip\thickmuskip0$
%|
%\produces
%$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
%   \quad0\mskip\thickmuskip0$
%\endexample
%\enddesc
\begindesc
\cts thinmuskip {\param{muglue}}
\cts medmuskip {\param{muglue}}
\cts thickmuskip {\param{muglue}}
\explain
čż™äş›ĺŹ‚ć•°ĺ®šäą‰äş†ć•°ĺ­¦ć¨ˇĺĽŹä¸­ç»†ĺ°Źă€ä¸­ç­‰ĺ’Śčľĺ¤§é—´éš”çš„ĺ¤§ĺ°Źă€‚
\example
$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
   \quad0\mskip\thickmuskip0$
|
\produces
$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
   \quad0\mskip\thickmuskip0$
\endexample
\enddesc

%\begindesc
%\cts jot {\param{dimen}}
%\explain
%This parameter defines a distance that is equal to three points (unless
%you change it).
%The |\jot| is a convenient unit of measure for opening up \hbox{math displays}.
%\enddesc
\begindesc
\cts jot {\param{dimen}}
\explain
ć­¤ĺŹ‚ć•°ĺ®šäą‰ä¸şä¸‰ä¸Şç‚ąçš„č·ťç¦»ďĽé™¤éťžä˝&nbsp;ć”ąĺŹäş†ĺ®ďĽ‰ă€‚
ĺś¨ç”¨ |\openup| ĺ‘˝ä»¤ĺ†ĺĽ€é™ĺ—ĺ…¬ĺĽŹĺ„čˇŚć—¶ďĽŚ|\jot| ćŻä¸€ä¸Şĺ®žç”¨çš„ĺş¦é‡ŹĺŤ•ä˝Ťă€‚
\footnote{čŻ‘ćł¨ďĽšä¸‹éť˘çš„äľ‹ĺ­ä¸şčŻ‘č€…ć‰€ĺŠ&nbsp;ă€‚čŻ·ĺŹ‚é… |\openup| ĺ‘˝ä»¤ďĽ\xref\openup ďĽ‰ă€‚}
\example
$$\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
$$\openup2\jot\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
|
\produces
$$\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
$$\openup2\jot\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
\endexample
\enddesc

%==========================================================================
%\subsection {Variable-width math spaces}
\subsection {ĺŹŻĺŹĺ®˝ĺş¦ć•°ĺ­¦é—´éš”}

%\begindesc
%\cts mkern {\&lt;mudimen&gt;}
%\explain
%^^{kerns//in math formulas}
%This command
%produces a \minref{kern}, i.e., blank space, of width \&lt;mudimen&gt;.
%The kern is measured
%in \minref{mathematical unit}s, which vary according to the style.
%Aside from its unit of measurement, this command behaves just like
%|\kern| (\xref \kern) does in horizontal mode.
\begindesc
\cts mkern {\&lt;mudimen&gt;}
\explain
^^{ç´§ćŽ’//ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„ç´§ćŽ’}
ć­¤ĺ‘˝ä»¤ç”źćä¸€ä¸Şĺ®˝ĺş¦ä¸ş \&lt;mudimen&gt; çš„\minref{ç´§ćŽ’}ďĽŚĺŤłç©şç™˝é—´éš”ă€‚
čŻĄç´§ćŽ’ç”¨\minref{ć•°ĺ­¦ĺŤ•ä˝Ť}čˇ¨ç¤şďĽŚĺ›&nbsp;ć­¤ĺś¨ä¸ŤĺŚć&nbsp;·ĺĽŹä¸­ćś‰ä¸ŤĺŚçš„ĺ°şĺŻ¸ă€‚
é™¤äş†ä˝żç”¨ć•°ĺ­¦ĺŤ•ä˝Ťĺ¤–ďĽŚć­¤ĺ‘˝ä»¤ä¸Žć°´ĺąłć¨ˇĺĽŹçš„|\kern|ďĽ\xref\kern ďĽ‰çš„čˇ¨çŽ°ç±»äĽĽă€‚

%\example
%$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
%|
%\produces
%$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
%\endexample
%\enddesc
\example
$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
|
\produces
$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
\endexample
\enddesc

%\begindesc
%\cts mskip {\&lt;mudimen$_1$&gt; {\bt plus} \&lt;mudimen$_2$&gt; {\bt minus}
%   \&lt;mudimen$_3$&gt;}
%\explain
%^^{glue}
%This command produces horizontal \minref{glue}
%that has natural width \&lt;mu\-dimen$_1$&gt;, stretch \&lt;mudimen$_2$&gt;,
%and shrink \&lt;mudimen$_3$&gt;.
%The glue is measured in \minref{mathematical unit}s, which vary according
%to the style.  Aside from its units of measurement, this command behaves
%just like |\hskip| (\xref \hskip).
\begindesc
\cts mskip {\&lt;mudimen$_1$&gt; {\bt plus} \&lt;mudimen$_2$&gt; {\bt minus}
   \&lt;mudimen$_3$&gt;}
\explain
^^{ç˛čżž}
ć­¤ĺ‘˝ä»¤ç”źćä¸€ä¸Şć°´ĺął\minref{ç˛čżž}ďĽŚĺ®çš„č‡Şç„¶ĺ®˝ĺş¦ä¸ş \&lt;mu\-dimen$_1$&gt;ďĽŚ
äĽ¸é•żé‡Źä¸ş \&lt;mudimen$_2$&gt;ďĽŚć”¶çĽ©é‡Źä¸ş \&lt;mudimen$_3$&gt;ă€‚
čŻĄç˛čżžç”¨\minref{ć•°ĺ­¦ĺŤ•ä˝Ť}čˇ¨ç¤şďĽŚĺ›&nbsp;ć­¤ĺ°†éšŹçť€ć&nbsp;·ĺĽŹçš„ĺŹĺŚ–č€ŚĺŹĺŚ–ă€‚
é™¤äş†ä˝żç”¨ć•°ĺ­¦ĺŤ•ä˝Ťĺ¤–ďĽŚć­¤ĺ‘˝ä»¤ä¸Ž |\hskip|ďĽ\xref\hskip ďĽ‰çš„čˇ¨çŽ°ç±»äĽĽă€‚

%\example
%$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
%|
%\produces
%$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
%\endexample
%\enddesc
\example
$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
|
\produces
$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
\endexample
\enddesc

%\begindesc
%\cts nonscript {}
%\explain
%When \TeX\ is currently typesetting in script or scriptscript
%\minref{style} and encounters this command
%immediately in front of glue or a kern,
%it cancels the glue or kern.
%|\nonscript| has no effect in the other styles.
\begindesc
\cts nonscript {}
\explain
ĺś¨ćŽ’ç‰ć&nbsp;‡ĺŹ·ć–ĺ°Źć&nbsp;‡ĺŹ·\minref{ć&nbsp;·ĺĽŹ}ć—¶ďĽŚĺ¦‚ćžś \TeX\ ĺś¨ç˛čżžć–ç´§ćŽ’č·źĺ‰Ťé‡ĺ°ć­¤ĺ‘˝ä»¤ďĽŚ
ĺ®ĺ°±ä¸˘ĺĽčŻĄç˛čżžć–ç´§ćŽ’ă€‚|\nonscript| ĺś¨ĺ…¶ä»–ć&nbsp;·ĺĽŹä¸­ć—&nbsp;ä»»ä˝•ć•ćžśă€‚

%This command provides a way of ``tightening up'' the spacing in
%script and scriptscript styles, which generally are set in smaller type.
%It is of little use outside of macro definitions.
%\example
%\def\ab{a\nonscript\; b}
%$\ab^{\ab}$
%|
%\produces
%\def\ab{a\nonscript\; b}
%$\ab^{\ab}$
%\endexample
%\enddesc
ć­¤ĺ‘˝ä»¤ćŹäľ›ä¸€ç§Ť``ć”¶ç´§''ć&nbsp;‡ĺŹ·ĺ’Śĺ°Źć&nbsp;‡ĺŹ·ć&nbsp;·ĺĽŹä¸­çš„é—´éš”çš„ć–ąćł•ďĽ›
é€šĺ¸¸ç”¨ĺ°ŹĺŹ·ĺ­—ä˝“ćŽ’ç‰čż™ä¸¤ä¸Şć&nbsp;·ĺĽŹă€‚ĺś¨ĺ®Źĺ®šäą‰äą‹ĺ¤–çš„ĺś°ć–ąďĽŚć­¤ĺ‘˝ä»¤ĺľĺ°‘ç”¨ĺ°ă€‚
\example
\def\ab{a\nonscript\; b}
$\ab^{\ab}$
|
\produces
\def\ab{a\nonscript\; b}
$\ab^{\ab}$
\endexample
\enddesc

%\see |\kern| (\xref\kern), |\hskip| (\xref\hskip).
%\eix^^{space//in math formulas}
\see |\kern|ďĽ\xref\kern ďĽ‰ĺ’Ś |\hskip|ďĽ\xref\hskip ďĽ‰ă€‚
\eix^^{é—´éš”//ć•°ĺ­¦ĺ…¬ĺĽŹä¸­çš„é—´éš”}

%==========================================================================
%\subsection {Spacing parameters for displays}
\subsection {é™ĺ—ĺ…¬ĺĽŹçš„é—´éš”ĺŹ‚ć•°}

%\begindesc
%\bix^^{displays//spacing parameters for}
%\cts displaywidth {\param{dimen}}
%\explain
%This parameter specifies the maximum width that
%\TeX\ allows for a math display.  If \TeX\ cannot fit the display
%into a space of this width, it sets an overfull \minref{hbox}
%and complains.
%\TeX\ sets the value of |\displaywidth| when it encounters the `|$$|'
%that starts the display.  This initial value is
%|\hsize| (\xref \hsize) unless it's overridden by changes to the
%paragraph shape.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\bix^^{é™ĺ—ĺ…¬ĺĽŹ//é™ĺ—ĺ…¬ĺĽŹçš„é—´éš”ĺŹ‚ć•°}
\cts displaywidth {\param{dimen}}
\explain
ć­¤ĺŹ‚ć•°ćŚ‡ĺ®š \TeX\ ĺŻąé™ĺ—ĺ…¬ĺĽŹć‰€ĺ…č®¸çš„ćś€ĺ¤§ĺ®˝ĺş¦ă€‚
ĺ¦‚ćžś \TeX\ ć—&nbsp;ćł•ĺ°†é™ĺ—ĺ…¬ĺĽŹć”ľĺ…Ąčż™ć&nbsp;·ĺ®˝çš„ç©şé—´ä¸­ďĽŚ
ĺ®ĺ°†ç”źćä¸€ä¸Şčż‡ć»ˇçš„\minref{ć°´ĺąłç›’ĺ­}ĺą¶ç»™ĺ‡şč­¦ĺ‘Šă€‚
\TeX\ ĺś¨é‡ĺ° `|$$|' ĺĽ€ĺ§‹é™ĺ—ĺ…¬ĺĽŹć—¶ĺ°±č®ľĺ®š |\displaywidth| çš„ĺ€Ľă€‚
ĺ®çš„ĺťĺ§‹ĺ€Ľä¸ş |\hsize|ďĽ\xref\hsize ďĽ‰ďĽŚé™¤éťžć®µč˝ĺ˝˘çŠ¶ć”ąĺŹäş†ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„čŻ´ćŽă€‚
\enddesc

%\begindesc
%\cts displayindent {\param{dimen}}
%\explain
%This parameter specifies the space by which \TeX\ indents a
%math display.
%\TeX\ sets the value of |\displayindent| when it encounters the `|$$|'
%that starts the display.  Usually this initial value is zero,
%but if the paragraph shape indicates that the display should
%be shifted by an amount $s$,
%\TeX\ will set |\displayindent| to $s$.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts displayindent {\param{dimen}}
\explain
ć­¤ĺŹ‚ć•°ćŚ‡ĺ®š \TeX\ ĺŻąé™ĺ—ĺ…¬ĺĽŹçš„çĽ©čż›é‡Źă€‚
\TeX\ ĺś¨é‡ĺ° `|$$|' ĺĽ€ĺ§‹é™ĺ—ĺ…¬ĺĽŹć—¶ĺ°±č®ľĺ®š |\displayindent| çš„ĺ€Ľă€‚
é€šĺ¸¸ĺ®çš„ĺťĺ§‹ĺ€Ľä¸şé›¶ďĽŚä˝†ĺ¦‚ćžść®µč˝ĺ˝˘çŠ¶čˇ¨ćŽčŻĄé™ĺ—ĺ…¬ĺĽŹéś€č¦ç§»ĺŠ¨č·ťç¦» $s$ďĽŚ
\TeX\ ĺ°±č®ľĺ®š |\displayindent| ç­‰äşŽ $s$ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚
\enddesc

%\begindesc
%\cts predisplaysize {\param{dimen}}
%\explain
%\TeX\ sets this parameter to the width of the line preceding
%a math display.
%\TeX\ uses |\predisplaysize| to determine whether or not
%the display starts to
%the left of where the previous line ends, i.e., whether or not it visually
%overlaps the previous line.
%If there is overlap, it uses the |\abovedisplayskip| and
%|\belowdisplayskip| glue in setting the display;
%otherwise it uses the |\abovedisplay!-shortskip| and
%|\belowdisplay!-shortskip| glue.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts predisplaysize {\param{dimen}}
\explain
\TeX\ č®ľĺ®šć­¤ĺŹ‚ć•°ç­‰äşŽé™ĺ—ĺ…¬ĺĽŹäą‹ĺ‰Ťçš„ć–‡ćś¬čˇŚçš„ĺ®˝ĺş¦ă€‚
\TeX\ ĺ©ç”¨ |\predisplaysize| çˇ®ĺ®šćŻĺ¦č®©é™ĺ—ĺ…¬ĺĽŹçš„čµ·ĺ§‹ç‚ąä˝ŤäşŽĺ‰Ťä¸€čˇŚç»“ĺ°ľĺ¤„çš„ĺ·¦čľąďĽŚ
ĺŤłĺ®ĺś¨ĺ¤–č§‚ä¸ŠćŻĺ¦ĺŹŻč˝ä¸Žĺ‰Ťä¸€čˇŚé‡ŤĺŹ&nbsp;ă€‚ĺ¦‚ćžśäĽšćś‰é‡ŤĺŹ&nbsp;ďĽŚ
\TeX\ ĺś¨ćŽ’ç‰é™ĺ—ĺ…¬ĺĽŹć—¶ä˝żç”¨|\abovedisplayskip| ĺ’Ś |\belowdisplayskip| ç˛čżžďĽ›
ĺ¦ĺ™ \TeX\ ä˝żç”¨ |\abovedisplay!-shortskip| ĺ’Ś |\belowdisplay!-shortskip| ç˛čżžă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚
\enddesc

%\begindesc
%\cts abovedisplayskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts before a display when the display starts to
%the left of where the previous line ends, i.e., when it visually
%overlaps the previous line.
%\PlainTeX\ sets |\abovedisplayskip| to |12pt plus3pt minus9pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts abovedisplayskip {\param{glue}}
\explain
ć­¤ĺ‘˝ä»¤ćŚ‡ĺ®šĺ˝“é™ĺ—ĺ…¬ĺĽŹçš„čµ·ĺ§‹ç‚ąä˝ŤäşŽĺ‰Ťä¸€čˇŚç»“ĺ°ľĺ¤„çš„ĺ·¦čľąć—¶ďĽŚ
ĺŤłĺ®ĺś¨ĺ¤–č§‚ä¸ŠĺŹŻč˝ä¸Žĺ‰Ťä¸€čˇŚćś‰é‡ŤĺŹ&nbsp;ć—¶ďĽŚ
\TeX\ ĺś¨é™ĺ—ĺ…¬ĺĽŹäą‹ĺ‰ŤćŹ’ĺ…Ąçš„ç«–ç›´ç˛čżžçš„ĺ¤§ĺ°Źă€‚
\PlainTeX\ č®ľĺ®š |\abovedisplayskip| ç­‰äşŽ |12pt plus3pt minus9pt|ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚
\enddesc

%\begindesc
%\cts belowdisplayskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts after a display when the display starts to
%the left of where the previous line ends, i.e., when it visually
%overlaps the previous line.
%\PlainTeX\ sets |\belowdisplay!-skip| to |12pt plus3pt minus9pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts belowdisplayskip {\param{glue}}
\explain
ć­¤ĺ‘˝ä»¤ćŚ‡ĺ®šĺ˝“é™ĺ—ĺ…¬ĺĽŹçš„čµ·ĺ§‹ç‚ąä˝ŤäşŽĺ‰Ťä¸€čˇŚç»“ĺ°ľĺ¤„çš„ĺ·¦čľąć—¶ďĽŚ
ĺŤłĺ®ĺś¨ĺ¤–č§‚ä¸ŠĺŹŻč˝ä¸Žĺ‰Ťä¸€čˇŚćś‰é‡ŤĺŹ&nbsp;ć—¶ďĽŚ
\TeX\ ĺś¨é™ĺ—ĺ…¬ĺĽŹäą‹ĺŽćŹ’ĺ…Ąçš„ç«–ç›´ç˛čżžçš„ĺ¤§ĺ°Źă€‚
\PlainTeX\ č®ľĺ®š |\belowdisplay!-skip| ç­‰äşŽ |12pt plus3pt minus9pt|ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚
\enddesc

%\begindesc
%\cts abovedisplayshortskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts before a math display
%when the display starts to
%the right of where the previous line ends, i.e., when it does not visually
%overlap the previous line.
%\PlainTeX\ sets |\abovedisplay!-shortskip| to |0pt plus3pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts abovedisplayshortskip {\param{glue}}
\explain
ć­¤ĺ‘˝ä»¤ćŚ‡ĺ®šĺ˝“é™ĺ—ĺ…¬ĺĽŹçš„čµ·ĺ§‹ç‚ąä˝ŤäşŽĺ‰Ťä¸€čˇŚç»“ĺ°ľĺ¤„çš„ĺŹłčľąć—¶ďĽŚ
ĺŤłĺ®ĺś¨ĺ¤–č§‚ä¸Šä¸ŤäĽšä¸Žĺ‰Ťä¸€čˇŚćś‰é‡ŤĺŹ&nbsp;ć—¶ďĽŚ
\TeX\ ĺś¨é™ĺ—ĺ…¬ĺĽŹäą‹ĺ‰ŤćŹ’ĺ…Ąçš„ç«–ç›´ç˛čżžçš„ĺ¤§ĺ°Źă€‚
\PlainTeX\ č®ľĺ®š |\abovedisplay!-shortskip| ç­‰äşŽ |0pt plus3pt|ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚
\enddesc

%\begindesc
%\cts belowdisplayshortskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts after a display
%when the display starts to
%the right of where the previous line ends, i.e., when it does not visually
%overlap the previous line.
%\PlainTeX\ sets |\belowdisplay!-shortskip| to |7pt plus3pt minus4pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
\begindesc
\cts belowdisplayshortskip {\param{glue}}
\explain
ć­¤ĺ‘˝ä»¤ćŚ‡ĺ®šĺ˝“é™ĺ—ĺ…¬ĺĽŹçš„čµ·ĺ§‹ç‚ąä˝ŤäşŽĺ‰Ťä¸€čˇŚç»“ĺ°ľĺ¤„çš„ĺŹłčľąć—¶ďĽŚ
ĺŤłĺ®ĺś¨ĺ¤–č§‚ä¸Šä¸ŤäĽšä¸Žĺ‰Ťä¸€čˇŚćś‰é‡ŤĺŹ&nbsp;ć—¶ďĽŚ
\TeX\ ĺś¨é™ĺ—ĺ…¬ĺĽŹäą‹ĺŽćŹ’ĺ…Ąçš„ç«–ç›´ç˛čżžçš„ĺ¤§ĺ°Źă€‚
\PlainTeX\ č®ľĺ®š |\belowdisplay!-shortskip| ç­‰äşŽ |7pt plus3pt minus4pt|ă€‚
č§\knuth{ç¬¬~188--189~éˇµ}ä¸­ĺŻąć­¤ĺŹ‚ć•°çš„ć›´ä»”ç»†çš„ä»‹ç»Ťă€‚

%\eix^^{displays//spacing parameters for}
%\enddesc
\eix^^{é™ĺ—ĺ…¬ĺĽŹ//é™ĺ—ĺ…¬ĺĽŹçš„é—´éš”ĺŹ‚ć•°}
\enddesc


%==========================================================================
\subsection {ĺ…¶ä»–çš„ć•°ĺ­¦é—´éš”ĺŹ‚ć•°}

%\begindesc
%\cts mathsurround {\param{dimen}}
%\explain
%This parameter specifies the amount of space that \TeX\
%inserts before and after a math formula in text mode (i.e., a formula
%surrounded by single |$|'s).  See \knuth{page~162} for further details about
%its behavior.
%\PlainTeX\ leaves |\mathsurround| at |0pt|.
%\enddesc
\begindesc
\cts mathsurround {\param{dimen}}
\explain
ć­¤ĺŹ‚ć•°ćŚ‡ĺ®š \TeX\ ĺś¨ć–‡ĺ†…ć•°ĺ­¦ĺ…¬ĺĽŹďĽĺŤłć”ľĺś¨ä¸¤ä¸Ş|$|äą‹é—´çš„ĺ…¬ĺĽŹďĽ‰ä¸¤čľąćŹ’ĺ…Ąçš„é—´éš”çš„ĺ¤§ĺ°Źă€‚
č§\knuth{ç¬¬~162~éˇµ}ĺŻąć­¤čˇŚä¸şçš„čż›ä¸€ć­Ąč§Łé‡Šă€‚
\PlainTeX\ č®ľĺ®š |\mathsurround| ä¸ş |0pt|ă€‚
\enddesc

%\begindesc
%\cts nulldelimiterspace {\param{dimen}}
%\explain
%^^{delimiters//null, space for}
%This parameter specifies the width of the
%space produced by a null \minref{delimiter}.
%\PlainTeX\ sets |\nulldelimiterspace| to |1.2pt|.
%\enddesc
\begindesc
\cts nulldelimiterspace {\param{dimen}}
\explain
^^{ĺ®šç•Śç¬¦//ç©şĺ®šç•Śç¬¦çš„é—´éš”}
ć­¤ĺŹ‚ć•°ćŚ‡ĺ®šç©ş\minref{ĺ®šç•Śç¬¦}ç”źćçš„é—´éš”çš„ĺ¤§ĺ°Źă€‚
\PlainTeX\ č®ľĺ®š |\null!-delimiterspace| ç­‰äşŽ |1.2pt|ă€‚
\enddesc

%\begindesc
%\cts scriptspace {\param{dimen}}
%\explain
%This parameter specifies the amount of space that \TeX\
%inserts before and after a subscript or superscript.
%The |\nonscript| command (\xref\nonscript) ^^|\nonscript|
%after a subscript or superscript cancels this space.
%\PlainTeX\ sets |\script!-space| to |0.5pt|.
%\enddesc
\begindesc
\cts scriptspace {\param{dimen}}
\explain
ć­¤ĺŹ‚ć•°ćŚ‡ĺ®š \TeX\ ĺś¨ä¸Šć&nbsp;‡ć–ä¸‹ć&nbsp;‡ĺ‰ŤĺŽćŹ’ĺ…Ąçš„é—´éš”çš„ĺ¤§ĺ°Źă€‚
ä¸Šć&nbsp;‡ć–ä¸‹ć&nbsp;‡äą‹ĺŽçš„ |\nonscript| ĺ‘˝ä»¤ďĽ\xref\nonscript ďĽ‰^^|\nonscript|
ĺŹŻä»ĄĺŹ–ć¶ć­¤é—´éš”ă€‚
\PlainTeX\ č®ľĺ®š |\script!-space| ç­‰äşŽ |0.5pt|ă€‚
\enddesc


%==========================================================================
%\section {Categorizing math constructs}
\section {ĺ†ç±»ć•°ĺ­¦ç»“ćž„}

%\begindesc
%\makecolumns 7/2:
%\cts mathord {}
%\cts mathop {}
%\cts mathbin {}
%\cts mathrel {}
%\cts mathopen {}
%\cts mathclose {}
%\cts mathpunct {}
%\explain
%These commands tell \TeX\ to treat the construct that follows as belonging
%to a particular ^{class} (see \knuth{page~154} for the definition
%of the classes).  They are listed here in the order of the class numbers,
%from $0$ to $6$.  Their primary
%effect is to adjust the spacing around the construct
%to be whatever it is for the specified class.
\begindesc
\makecolumns 7/2:
\cts mathord {}
\cts mathop {}
\cts mathbin {}
\cts mathrel {}
\cts mathopen {}
\cts mathclose {}
\cts mathpunct {}
\explain
čż™äş›ĺ‘˝ä»¤č®© \TeX\ ćŠŠéšŹĺŽçš„ç»“ćž„ĺ˝’ĺ…ĄćŚ‡ĺ®šçš„^{ç±»}ďĽč§\knuth{ç¬¬~154~éˇµ}ĺŻąç±»çš„ĺ®šäą‰ďĽ‰ă€‚
ĺ®ä»¬ćŚ‰ç…§ç±»çĽ–ĺŹ·çš„ĺ¤§ĺ°ŹéˇşĺşŹćŽ’ĺ—ďĽŚä»Ž $0$ ĺ° $6$ă€‚
ĺ®ä»¬ä¸»č¦ç”¨äşŽćŚ‰ç…§ćŚ‡ĺ®šçš„ç±»č°ć•´čŻĄç»“ćž„ä¸¤čľąçš„é—´éš”ĺ¤§ĺ°Źă€‚
%\example
%$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
%% By treating minmax as a math operator, we can get TeX to
%% put something underneath it.
%|
%\produces
%$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
%\endexample
%\enddesc
\example
$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
% By treating minmax as a math operator, we can get TeX to
% put something underneath it.
|
\produces
$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
\endexample
\enddesc

%\begindesc
%\cts mathinner {}
%\explain
%This command tells \TeX\ to treat the construct that follows
%as an ``inner formula'', e.g., a fraction, for spacing purposes.
%It resembles the class commands given just above.
%\enddesc
\begindesc
\cts mathinner {}
\explain
ć­¤ĺ‘˝ä»¤č®© \TeX\ ĺ°†éšŹĺŽçš„ç»“ćž„č§†ä¸ş``ĺ†…é¨ĺ…¬ĺĽŹ''ďĽŚćŻ”ĺ¦‚ĺ†ĺĽŹďĽŚĺą¶ćŤ®ć­¤č°ć•´é—´éš”ă€‚
ĺ®ä¸Žä¸Šéť˘ĺšćŹĺ°çš„ç±»ĺ‘˝ä»¤ç±»äĽĽă€‚
\enddesc

%==========================================================================
%\section {Special actions for math formulas}
\section {ç‰ąć®Šĺ¤„ç†ć•°ĺ­¦ĺ…¬ĺĽŹ}

%\begindesc
%\cts everymath {\param{token list}}
%\cts everydisplay {\param{token list}}
%\explain
%^^{displays//actions for every display}
%These parameters specify \minref{token} lists that \TeX\ inserts
%at the start of every text math or display math formula, respectively.
%You can
%take special actions at the start of each math formula by
%assigning those actions to |\everymath| or
%|\everydisplay|.  Don't forget that if you want both kinds of formulas to
%be affected, you need to set \emph{both} parameters.
%\example
%\everydisplay={\heartsuit\quad}
%\everymath = {\clubsuit}
%$3$ is greater than $2$ for large values of $3$.
%$$4&gt;3$$
%|
%\produces
%\everydisplay={\heartsuit\quad}
%\everymath = {\clubsuit}
%$3$ is greater than $2$ for large values of $3$.
%$$4&gt;3$$
%\endexample
%\enddesc
\begindesc
\cts everymath {\param{token list}}
\cts everydisplay {\param{token list}}
\explain
^^{é™ĺ—ĺ…¬ĺĽŹ//ä˝śç”¨ĺ°ćŻŹä¸Şé™ĺ—ĺ…¬ĺĽŹ}
čż™ä¸¤ä¸Şĺ‘˝ä»¤ĺ†ĺ«ćŚ‡ĺ®š \TeX\ ĺś¨ćŻŹä¸Şć–‡ĺ†…ĺ…¬ĺĽŹć–é™ĺ—ĺ…¬ĺĽŹĺĽ€ĺ¤´ćŹ’ĺ…Ąçš„\minref{č®°ĺŹ·}ĺ—ă€‚
ä˝&nbsp;ĺŹŻä»Ąĺ©ç”¨ |\everymath| ć– |\everydisplay| ĺś¨ćŻŹä¸Şć•°ĺ­¦ĺ…¬ĺĽŹĺĽ€ĺ¤´ä˝śç‰ąć®Šĺ¤„ç†ă€‚
ä˝&nbsp;ĺŠˇĺż…ć¸…ćĄšďĽŚč‹Ąä˝&nbsp;éś€č¦ĺŚć—¶ĺ¤„ç†ä¸¤ç§Ťĺ…¬ĺĽŹďĽŚä˝&nbsp;ĺż…éˇ»\emph{ĺŚć—¶}č®ľĺ®ščż™ä¸¤ä¸ŞĺŹ‚ć•°ă€‚
\example
\everydisplay={\heartsuit\quad}
\everymath = {\clubsuit}
$3$ is greater than $2$ for large values of $3$.
$$4&gt;3$$
|
\produces
\everydisplay={\heartsuit\quad}
\everymath = {\clubsuit}
$3$ is greater than $2$ for large values of $3$.
$$4&gt;3$$
\endexample
\enddesc

%\enddescriptions
%\eix^^{math}
%\endchapter
%\byebye
\enddescriptions
\eix^^{ć•°ĺ­¦}

\ifoldeplain\else\ifcompletebook\else
\vskip4em{\sectionfonts\leftline{ćś¬ç«&nbsp;ç´˘ĺĽ•}}
\readindexfile{i}
\fi\fi

\endchapter
\byebye
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