| blob | f0080e385687dae0675a8f6bc917603434ef9c96 |
1 % \iffalse meta-comment
2 %
3 % Copyright 1993-2016
4 % The LaTeX3 Project and any individual authors listed elsewhere
5 % in this file.
6 %
7 % This file is part of the LaTeX base system.
8 % -------------------------------------------
9 %
10 % It may be distributed and/or modified under the
11 % conditions of the LaTeX Project Public License, either version 1.3c
12 % of this license or (at your option) any later version.
13 % The latest version of this license is in
14 % http://www.latex-project.org/lppl.txt
15 % and version 1.3c or later is part of all distributions of LaTeX
16 % version 2005/12/01 or later.
17 %
18 % This file has the LPPL maintenance status "maintained".
19 %
20 % The list of all files belonging to the LaTeX base distribution is
21 % given in the file `manifest.txt'. See also `legal.txt' for additional
22 % information.
23 %
24 % The list of derived (unpacked) files belonging to the distribution
25 % and covered by LPPL is defined by the unpacking scripts (with
26 % extension .ins) which are part of the distribution.
27 %
28 % \fi
29 % \iffalse
30 %%% From File: ltmath.dtx
31 %
32 %<leqno>\ProvidesFile{leqno.clo}
33 %<fleqn>\ProvidesFile{fleqn.clo}
34 %<leqno,fleqn> [2016/12/29 v1.2a Standard LaTeX option
35 %<leqno> (left equation numbers)]
36 %<fleqn> (flush left equations)]
37 %
38 %<*driver>
39 % \fi
40 \ProvidesFile{ltmath.dtx}
41 [2016/12/29 v1.2a LaTeX Kernel (Math Setup)]
42 % \iffalse
43 %</driver>
44 %
45 %<*driver>
46 \documentclass{ltxdoc}
47 \GetFileInfo{ltmath.dtx}
48 \title{\filename}
49 \date{\filedate}
50 \author{%
51 Johannes Braams\and
52 David Carlisle\and
53 Alan Jeffrey\and
54 Leslie Lamport\and
55 Frank Mittelbach\and
56 Chris Rowley\and
57 Rainer Sch\"opf}
58 \begin{document}
59 \MaintainedByLaTeXTeam{latex}
60 \maketitle
61 \DocInput{\filename}
62 \end{document}
63 %</driver>
64 % \fi
65 %
66 %
67 % \changes{v1.1b}{1996/07/26}{Removed \cs{global} before
68 % \cs{@ignoretrue} in various places.}
69 % \changes{v1.1c}{1998/08/17}{(RmS) Minor documentation fixes.}
70 % \changes{v1.1g}{2005/11/10}{(MH) Minor documentation fixes.}
71 %
72 % \section{Math setup}
73 %
74 % This file contains a lot of the original plain \TeX{} code, as well
75 % as the \LaTeX{} environments for math. It still needs sorting out.
76 %
77 % \StopEventually{}
78 %
79 % \begin{macrocode}
80 %<*2ekernel>
81 \message{math definitions,}
82 % \end{macrocode}
83 %
84 %
85 %
86 % \subsection{Math commands based on plain \TeX}
87 %
88 % \subsubsection{The log-like functions}
89 %
90 % \changes{1.0m}{1994/10/29}{ASAJ: Added \cs{DeclareMathOperator}.}
91 % \changes{v1.0o}{1994/11/17}
92 % {\cs{@tempa} to \cs{reserved@a}}
93 % \changes{1.0q}{1994/11/30}{ASAJ: \cs{DeclareMathOperator} moved to
94 % AMS\LaTeX.}
95 % \changes{v1.0r}{1995/05/07}{Use \cs{hb@xt@}}
96 % \changes{v1.0r}{1995/05/21}{Update some plain macros}
97 % \changes{v1.0t}{1995/06/28}{minor doc edits}
98 %
99 % \begin{macro}{\log}
100 % The standard operators:
101 % \begin{macrocode}
102 \def\log{\mathop{\operator@font log}\nolimits}
103 \def\lg{\mathop{\operator@font lg}\nolimits}
104 \def\ln{\mathop{\operator@font ln}\nolimits}
105 \def\lim{\mathop{\operator@font lim}}
106 \def\limsup{\mathop{\operator@font lim\,sup}}
107 \def\liminf{\mathop{\operator@font lim\,inf}}
108 \def\sin{\mathop{\operator@font sin}\nolimits}
109 \def\arcsin{\mathop{\operator@font arcsin}\nolimits}
110 \def\sinh{\mathop{\operator@font sinh}\nolimits}
111 \def\cos{\mathop{\operator@font cos}\nolimits}
112 \def\arccos{\mathop{\operator@font arccos}\nolimits}
113 \def\cosh{\mathop{\operator@font cosh}\nolimits}
114 \def\tan{\mathop{\operator@font tan}\nolimits}
115 \def\arctan{\mathop{\operator@font arctan}\nolimits}
116 \def\tanh{\mathop{\operator@font tanh}\nolimits}
117 \def\cot{\mathop{\operator@font cot}\nolimits}
118 \def\coth{\mathop{\operator@font coth}\nolimits}
119 \def\sec{\mathop{\operator@font sec}\nolimits}
120 \def\csc{\mathop{\operator@font csc}\nolimits}
121 \def\max{\mathop{\operator@font max}}
122 \def\min{\mathop{\operator@font min}}
123 \def\sup{\mathop{\operator@font sup}}
124 \def\inf{\mathop{\operator@font inf}}
125 \def\arg{\mathop{\operator@font arg}\nolimits}
126 \def\ker{\mathop{\operator@font ker}\nolimits}
127 \def\dim{\mathop{\operator@font dim}\nolimits}
128 \def\hom{\mathop{\operator@font hom}\nolimits}
129 \def\det{\mathop{\operator@font det}}
130 \def\exp{\mathop{\operator@font exp}\nolimits}
131 \def\Pr{\mathop{\operator@font Pr}}
132 \def\gcd{\mathop{\operator@font gcd}}
133 \def\deg{\mathop{\operator@font deg}\nolimits}
134 % \end{macrocode}
135 % \end{macro}
136 %
137 % \begin{macro}{\bmod}
138 % And some operators have to be done by hand:
139 % \begin{macrocode}
140 \def\bmod{%
141 \nonscript\mskip-\medmuskip\mkern5mu%
142 \mathbin{\operator@font mod}\penalty900\mkern5mu%
143 \nonscript\mskip-\medmuskip}
144 % \end{macrocode}
145 % \end{macro}
146 %
147 % \begin{macro}{\pmod}
148 % \begin{macrocode}
149 \def\pmod#1{%
150 \allowbreak\mkern18mu({\operator@font mod}\,\,#1)}
151 % \end{macrocode}
152 % \end{macro}
153 %
154 % \subsubsection{Biggggg}
155 %
156 % \begin{macro}{\big}
157 % Variants on |\big| and friends for use with delimiters:
158 % \begin{macrocode}
159 \def\bigl{\mathopen\big}
160 \def\bigm{\mathrel\big}
161 \def\bigr{\mathclose\big}
162 \def\Bigl{\mathopen\Big}
163 \def\Bigm{\mathrel\Big}
164 \def\Bigr{\mathclose\Big}
165 \def\biggl{\mathopen\bigg}
166 \def\biggm{\mathrel\bigg}
167 \def\biggr{\mathclose\bigg}
168 \def\Biggl{\mathopen\Bigg}
169 \def\Biggm{\mathrel\Bigg}
170 \def\Biggr{\mathclose\Bigg}
171 % \end{macrocode}
172 % \end{macro}
173 %
174 % \subsubsection{The UNSORTED Rest}
175 %
176 % The other math commands are lifted from plain \TeX.
177 %
178 % \begin{macro}{\jot}
179 % \begin{macrocode}
180 \newdimen\jot
181 \jot=3pt
182 % \end{macrocode}
183 % \end{macro}
184 %
185 % \begin{macro}{\interdisplaylinepenalty}
186 % \begin{macrocode}
187 \newcount\interdisplaylinepenalty
188 \interdisplaylinepenalty=100
189 % \end{macrocode}
190 % \end{macro}
191 %
192 % \begin{macro}{\choose}
193 % \begin{macrocode}
194 \def\choose{\atopwithdelims()}
195 % \end{macrocode}
196 % \end{macro}
197 %
198 % \begin{macro}{\brack}
199 % \begin{macrocode}
200 \def\brack{\atopwithdelims[]}
201 % \end{macrocode}
202 % \end{macro}
203 %
204 % \begin{macro}{\brace}
205 % \begin{macrocode}
206 \def\brace{\atopwithdelims\{\}}
207 % \end{macrocode}
208 % \end{macro}
209 %
210 % \begin{macro}{\mathpalette}
211 % \begin{macrocode}
212 \def\mathpalette#1#2{%
213 \mathchoice
214 {#1\displaystyle{#2}}%
215 {#1\textstyle{#2}}%
216 {#1\scriptstyle{#2}}%
217 {#1\scriptscriptstyle{#2}}}
218 % \end{macrocode}
219 % \end{macro}
220 %
221 % \begin{macro}{\root}
222 % \changes{v1.1d}{1997/01/08}
223 % {(DPC) Remove spurious space tokens from
224 % plain \TeX\ definition /2359}
225 % \begin{macro}{\rootbox}
226 % \begin{macro}{\r@@t}
227 % \changes{v1.0r}{1995/05/21}{Use \cs{sqrtsign} instead of
228 % \cs{sqrt}}
229 % \begin{macrocode}
230 \newbox\rootbox
231 % \end{macrocode}
232 %
233 % \begin{macrocode}
234 \def\root#1\of{%
235 \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}%
236 \mathpalette\r@@t}
237 % \end{macrocode}
238 %
239 % \begin{macrocode}
240 \def\r@@t#1#2{%
241 \setbox\z@\hbox{$\m@th#1\sqrtsign{#2}$}%
242 \dimen@\ht\z@ \advance\dimen@-\dp\z@
243 \mkern5mu\raise.6\dimen@\copy\rootbox
244 \mkern-10mu\box\z@}
245 % \end{macrocode}
246 % \end{macro}
247 % \end{macro}
248 % \end{macro}
249 %
250 % \begin{macro}{\phantom}
251 % \changes{v1.0p}{1994/11/18}
252 % {(DPC) use \cs{expandafter} instead of \cs{next}}
253 % \changes{v1.0p}{1994/11/18}
254 % {(DPC) colour support}
255 % \begin{macro}{\hphantom}
256 % \begin{macro}{\vphantom}
257 % \begin{macrocode}
258 \newif\ifv@
259 \newif\ifh@
260 % \end{macrocode}
261 %
262 % \begin{macrocode}
263 \def\vphantom{\v@true\h@false\ph@nt}
264 % \end{macrocode}
265 %
266 % \begin{macrocode}
267 \def\hphantom{\v@false\h@true\ph@nt}
268 % \end{macrocode}
269 %
270 % \begin{macrocode}
271 \def\phantom{\v@true\h@true\ph@nt}
272 % \end{macrocode}
273 %
274 % \begin{macrocode}
275 \def\ph@nt{%
276 \ifmmode
277 \expandafter\mathpalette\expandafter\mathph@nt
278 \else
279 \expandafter\makeph@nt
280 \fi}
281 % \end{macrocode}
282 %
283 % \begin{macrocode}
284 \def\makeph@nt#1{%
285 \setbox\z@\hbox{\color@begingroup#1\color@endgroup}\finph@nt}
286 % \end{macrocode}
287 %
288 % \begin{macrocode}
289 \def\mathph@nt#1#2{%
290 \setbox\z@\hbox{$\m@th#1{#2}$}\finph@nt}
291 % \end{macrocode}
292 %
293 % \begin{macrocode}
294 \def\finph@nt{%
295 \setbox\tw@\null
296 \ifv@ \ht\tw@\ht\z@ \dp\tw@\dp\z@\fi
297 \ifh@ \wd\tw@\wd\z@\fi \box\tw@}
298 % \end{macrocode}
299 % \end{macro}
300 % \end{macro}
301 % \end{macro}
302 %
303 % \begin{macro}{\mathstrut}
304 % \begin{macrocode}
305 \def\mathstrut{\vphantom(}
306 % \end{macrocode}
307 % \end{macro}
308 %
309 % \begin{macro}{\smash}
310 % \changes{v1.0p}{1994/11/18}
311 % {(DPC) use \cs{expandafter} instead of \cs{next}}
312 % \changes{v1.0p}{1994/11/18}
313 % {(DPC) colour support}
314 % \begin{macrocode}
315 \def\smash{%
316 \relax % \relax, in case this comes first in \halign
317 \ifmmode
318 \expandafter\mathpalette\expandafter\mathsm@sh
319 \else
320 \expandafter\makesm@sh
321 \fi}
322 % \end{macrocode}
323 %
324 % \begin{macrocode}
325 \def\makesm@sh#1{%
326 \setbox\z@\hbox{\color@begingroup#1\color@endgroup}\finsm@sh}
327 \def\mathsm@sh#1#2{%
328 \setbox\z@\hbox{$\m@th#1{#2}$}\finsm@sh}
329 \def\finsm@sh{\ht\z@\z@ \dp\z@\z@ \box\z@}
330 % \end{macrocode}
331 % \end{macro}
332 %
333 % \begin{macro}{\buildrel}
334 % \begin{macrocode}
335 \def\buildrel#1\over#2{\mathrel{\mathop{\kern\z@#2}\limits^{#1}}}
336 % \end{macrocode}
337 % \end{macro}
338 %
339 %
340 % \begin{macro}{\cases}
341 % \changes{LaTeX2.09}{1991/08/14}
342 % {(RmS) inserted extra braces around entry for NFSS}
343 % \begin{macrocode}
344 \def\cases#1{\left\{\,\vcenter{\normalbaselines\m@th
345 \ialign{$##\hfil$&\quad{##}\hfil\crcr#1\crcr}}\right.}
346 % \end{macrocode}
347 % \end{macro}
348 %
349 % \begin{macro}{\matrix}
350 % \begin{macrocode}
351 \def\matrix#1{\null\,\vcenter{\normalbaselines\m@th
352 \ialign{\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr
353 \mathstrut\crcr\noalign{\kern-\baselineskip}
354 #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}
355 % \end{macrocode}
356 % \end{macro}
357 %
358 % \begin{macro}{\pmatrix}
359 % \begin{macrocode}
360 \def\pmatrix#1{\left(\matrix{#1}\right)}
361 % \end{macrocode}
362 % \end{macro}
363 %
364 %
365 % \begin{macro}{\bordermatrix}
366 % \changes{LaTeX2e}{1994/01/25}{Removed \cs{p@renwd}.}
367 % \begin{macrocode}
368 \def\bordermatrix#1{\begingroup \m@th
369 \@tempdima 8.75\p@
370 \setbox\z@\vbox{%
371 \def\cr{\crcr\noalign{\kern2\p@\global\let\cr\endline}}%
372 \ialign{$##$\hfil\kern2\p@\kern\@tempdima&\thinspace\hfil$##$\hfil
373 &&\quad\hfil$##$\hfil\crcr
374 \omit\strut\hfil\crcr\noalign{\kern-\baselineskip}%
375 #1\crcr\omit\strut\cr}}%
376 \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
377 \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
378 \setbox\tw@\hbox{$\kern\wd\@ne\kern-\@tempdima\left(\kern-\wd\@ne
379 \global\setbox\@ne\vbox{\box\@ne\kern2\p@}%
380 \vcenter{\kern-\ht\@ne\unvbox\z@\kern-\baselineskip}\,\right)$}%
381 \null\;\vbox{\kern\ht\@ne\box\tw@}\endgroup}
382 % \end{macrocode}
383 % \end{macro}
384 %
385 % \begin{macro}{\openup}
386 % \begin{macrocode}
387 \def\openup{\afterassignment\@penup\dimen@}
388 % \end{macrocode}
389 %
390 % \begin{macrocode}
391 \def\@penup{\advance\lineskip\dimen@
392 \advance\baselineskip\dimen@
393 \advance\lineskiplimit\dimen@}
394 % \end{macrocode}
395 % \end{macro}
396 %
397 % \begin{macro}{\displaylines}
398 % \begin{macrocode}
399 \newif\ifdt@p
400 % \end{macrocode}
401 %
402 % \begin{macrocode}
403 \def\displ@y{\global\dt@ptrue\openup\jot\m@th
404 \everycr{\noalign{\ifdt@p \global\dt@pfalse \ifdim\prevdepth>-1000\p@
405 \vskip-\lineskiplimit \vskip\normallineskiplimit \fi
406 \else \penalty\interdisplaylinepenalty \fi}}}
407 % \end{macrocode}
408 %
409 % \begin{macrocode}
410 \def\@lign{\tabskip\z@skip\everycr{}} % restore inside \displ@y
411 % \end{macrocode}
412 %
413 % \begin{macrocode}
414 \def\displaylines#1{\displ@y \tabskip\z@skip
415 \halign{\hb@xt@\displaywidth{$\@lign\hfil\displaystyle##\hfil$}\crcr
416 #1\crcr}}
417 % \end{macrocode}
418 % \end{macro}
419 %
420 % \changes{v1.0r}{1995/05/21}{Remove \cs{mathhexbox} from this file}
421 %
422 % \begin{macro}{\sp}
423 % \begin{macro}{\sb}
424 % \begin{macrocode}
425 \let\sp=^
426 \let\sb=_
427 % \end{macrocode}
428 % \end{macro}
429 % \end{macro}
430 %
431 % \begin{macro}{\>}
432 % \begin{macro}{\;}
433 % \begin{macro}{\!}
434 % \begin{macrocode}
435 %\def\,{\mskip\thinmuskip} % already defined in ltspace
436 \def\>{\mskip\medmuskip}
437 \def\;{\mskip\thickmuskip}
438 \def\!{\mskip-\thinmuskip}
439 % \end{macrocode}
440 % \end{macro}
441 % \end{macro}
442 % \end{macro}
443 %
444 % \begin{macro}{\*}
445 % \begin{macrocode}
446 \def\*{\discretionary{\thinspace\the\textfont2\char2}{}{}}
447 % \end{macrocode}
448 % \end{macro}
449 %
450 % \begin{macro}{\:}
451 % Nickname for the medium space since |\>| is not available inside
452 % \texttt{tabbing}.
453 % \begin{macrocode}
454 \let\:=\>
455 % \end{macrocode}
456 % \end{macro}
457 %
458 % \begin{macro}{\active@math@prime}
459 % \changes{v1.1e}{1999/10/09}{Macro added, see PR 3104.}
460 % This is the definition of the active math prime.
461 % \begin{macrocode}
462 \def\active@math@prime{^\bgroup\prim@s}
463 % \end{macrocode}
464 % \end{macro}
465 %
466 % \begin{macro}{\prime@s}
467 % \changes{v1.0p}{1994/11/18}
468 % {(DPC) use \cs{@let@token} instead of \cs{next}
469 % and \cs{expandafter} instead of \cs{nxt}}
470 % \changes{v1.1e}{1999/10/09}{Introduce \cs{active@math@prime}.}
471 % \begin{macrocode}
472 {\catcode`\'=\active \global\let'\active@math@prime}
473 % \end{macrocode}
474 %
475 % \begin{macrocode}
476 \def\prim@s{%
477 \prime\futurelet\@let@token\pr@m@s}
478 % \end{macrocode}
479 %
480 % \begin{macrocode}
481 \def\pr@m@s{%
482 \ifx'\@let@token
483 \expandafter\pr@@@s
484 \else
485 \ifx^\@let@token
486 \expandafter\expandafter\expandafter\pr@@@t
487 \else
488 \egroup
489 \fi
490 \fi}
491 % \end{macrocode}
492 %
493 % \begin{macrocode}
494 \def\pr@@@s#1{\prim@s}
495 % \end{macrocode}
496 %
497 % \begin{macrocode}
498 \def\pr@@@t#1#2{#2\egroup}
499 % \end{macrocode}
500 % \end{macro}
501 %
502 % \changes{v1.0i}{1994/05/17}{Replaced \cs{let} by \cs{gdef}, for
503 % indirect definition.}
504 % \begin{macrocode}
505 {\catcode`\_=\active \gdef_{\_}} % _ in math is
506 % either subscript or \_
507 % \end{macrocode}
508 %
509 %
510 % \changes{v1.0m}{1994/10/29}{ASAJ: Removed \cs{dag}, \cs{ddag}.}
511 % \changes{v1.0m}{1994/10/29}{ASAJ: Renamed \cs{S} and \cs{P} to
512 % \cs{mathsection} and \cs{mathparagraph} and made them
513 % \cs{mathchardef}s.}
514 % \changes{v1.0m}{1994/10/29}{ASAJ: Added \cs{mathellipsis},
515 % \cs{mathdollar} and \cs{mathsterling}.}
516 % \changes{v1.0n}{1994/10/30}{ASAJ: Moved the new commands to ltoutenc.}
517 %
518 % \subsection{Math Environments}
519 %
520 % \changes{1.0m}{1994/10/29}{ASAJ: Tidied up documentation.}
521 %
522 % \begin{macro}{\(}
523 % \begin{macro}{\)}
524 % Produces |$...$| with checks that |\(| isn't used in math mode, and
525 % that |\)| is only used in math mode begun with |\(|.
526 % \changes{v1.1h}{2015/01/08}{Make Robust (latexrelease)}
527 % \begin{macrocode}
528 %</2ekernel>
529 %<latexrelease>\IncludeInRelease{2015/01/01}{\(}{Make \( robust}%
530 %<*2ekernel|latexrelease>
531 \DeclareRobustCommand\({%
532 \relax\ifmmode\@badmath\else$\fi}%
533 \DeclareRobustCommand\){%
534 \relax\ifmmode\ifinner$\else\@badmath\fi\else \@badmath\fi}%
535 %</2ekernel|latexrelease>
536 %<latexrelease>\EndIncludeInRelease
537 %<latexrelease>\IncludeInRelease{0000/00/00}{\(}{Make \( robust}%
538 %<latexrelease>\def\({%
539 %<latexrelease> \relax\ifmmode\@badmath\else$\fi}%
540 %<latexrelease>\expandafter\let\csname\string( \endcsname\@undefined
541 %<latexrelease>\def\){%
542 %<latexrelease> \relax\ifmmode\ifinner$\else\@badmath\fi\else \@badmath\fi}%
543 %<latexrelease>\expandafter\let\csname\string) \endcsname\@undefined
544 %<latexrelease>\EndIncludeInRelease
545 %<*2ekernel>
546 % \end{macrocode}
547 % \end{macro}
548 % \end{macro}
549 %
550 % \begin{macro}{\[}
551 % \changes{v1.1g}{2005/11/10}
552 % {(MH) Fixed potential problem in \cs{[} (pr/3399).}
553 % \begin{macro}{\]}
554 % Produces |$$...$$| with checks that |\[| isn't used in math mode,
555 % and that |\]| is only used in display math mode (though there is no
556 % real test that this display math started with |\[| and not with |$$|).
557 % \changes{v1.1h}{2015/01/08}{Make Robust (latexrelease)}
558 % \begin{macrocode}
559 %</2ekernel>
560 %<latexrelease>\IncludeInRelease{2015/01/01}{\[}{Make \[ robust}%
561 %<*2ekernel|latexrelease>
562 \DeclareRobustCommand\[{%
563 \relax\ifmmode
564 \@badmath
565 \else
566 \ifvmode
567 \nointerlineskip
568 \makebox[.6\linewidth]{}%
569 \fi
570 $$%%$$ BRACE MATCH HACK
571 \fi
572 }%
573 % \end{macrocode}
574 %
575 % \begin{macrocode}
576 \DeclareRobustCommand\]{%
577 \relax\ifmmode
578 \ifinner
579 \@badmath
580 \else
581 $$%%$$ BRACE MATCH HACK
582 \fi
583 \else
584 \@badmath
585 \fi
586 \ignorespaces
587 }%
588 % \end{macrocode}
589 %
590 % \begin{macrocode}
591 %</2ekernel|latexrelease>
592 %<latexrelease>\EndIncludeInRelease
593 %<latexrelease>\IncludeInRelease{0000/00/00}{\[}{Make \[ robust}%
594 %<latexrelease>\def\[{%
595 %<latexrelease> \relax\ifmmode
596 %<latexrelease> \@badmath
597 %<latexrelease> \else
598 %<latexrelease> \ifvmode
599 %<latexrelease> \nointerlineskip
600 %<latexrelease> \makebox[.6\linewidth]{}%
601 %<latexrelease> \fi
602 %<latexrelease> $$%%$$ BRACE MATCH HACK
603 %<latexrelease> \fi
604 %<latexrelease>}%
605 %<latexrelease>\expandafter\let\csname\string[ \endcsname\@undefined
606 % \end{macrocode}
607 %
608 % \begin{macrocode}
609 %<latexrelease>\def\]{%
610 %<latexrelease> \relax\ifmmode
611 %<latexrelease> \ifinner
612 %<latexrelease> \@badmath
613 %<latexrelease> \else
614 %<latexrelease> $$%%$$ BRACE MATCH HACK
615 %<latexrelease> \fi
616 %<latexrelease> \else
617 %<latexrelease> \@badmath
618 %<latexrelease> \fi
619 %<latexrelease> \ignorespaces
620 %<latexrelease>}%
621 %<latexrelease>\expandafter\let\csname\string] \endcsname\@undefined
622 %<latexrelease>\EndIncludeInRelease
623 %<*2ekernel>
624 % \end{macrocode}
625 % \end{macro}
626 % \end{macro}
627 %
628 % \begin{environment}{math}
629 % \begin{environment}{displaymath}
630 % Disguises for |\(...\)| and |\[...\]|.
631 % \begin{macrocode}
632 \let\math=\(
633 \let\endmath=\)
634 % \end{macrocode}
635 %
636 % \begin{macrocode}
637 \def\displaymath{\[}
638 \def\enddisplaymath{\]\@ignoretrue}
639 % \end{macrocode}
640 % \end{environment}
641 % \end{environment}
642 %
643 %
644 % \begin{environment}{equation}
645 % \changes{LaTeX2.09}{1992/01/10}{RmS: put \cs{hbox} around \cs{@eqnnum}
646 % to typeset the equation number in text mode
647 % (as in the eqnarray env.)}
648 % \begin{macro}{\c@equation}
649 % Numbered equations, using the counter |\c@equation|.
650 % \emph{Note}: The document style must define |\theequation| etc., and
651 % do the appropriate |\@addtoreset|. It should also redefine |\@eqnnum|
652 % if another format for the equation number is desired other than the
653 % standard (...), or to move the equation numbers to the flushleft.
654 % (See comment on the |\def| of |\@eqnnum|.)
655 % \begin{macrocode}
656 \@definecounter{equation}
657 \def\equation{$$\refstepcounter{equation}}
658 \def\endequation{\eqno \hbox{\@eqnnum}$$\@ignoretrue}
659 % \end{macrocode}
660 % \end{macro}
661 % \end{environment}
662 %
663 % \begin{macro}{\@eqnnum}
664 % \changes{LaTeX2.09}{1991/09/29}{RmS: \cs{reset@font} added.}
665 % \changes{v1.0l}{1994/10/23}{Added \cs{normalcolor} since \cs{eqno}
666 % introduces a subgroup of the displayed math group}
667 %
668 % Produces the equation number for equation and
669 % eqnarray environments. The following definition is for
670 % flushright numbers; for flushleft numbers, see leqno.clo.
671 % The equation number is set in black roman type even
672 % if an eqnarray environment appears in an italic environment.
673 % \changes{v1.0s}{1995/05/26}{Removed \cs{rmfamily} (PR 1578),
674 % replaced \cs{reset@font} with \cs{normalfont}}
675 % \begin{macrocode}
676 \def\@eqnnum{{\normalfont \normalcolor (\theequation)}}
677 % \end{macrocode}
678 % \end{macro}
679 %
680 % \begin{macro}{\stackrel}
681 % A disguise for plain \TeX's buildrel.
682 % \begin{macrocode}
683 \def\stackrel#1#2{\mathrel{\mathop{#2}\limits^{#1}}}
684 % \end{macrocode}
685 % \end{macro}
686 %
687 % \changes{v0.9g}{1993/12/11}{Added a group around the first argument
688 % of \cs{frac} to prevent
689 % changes (for example font changes) from modifying the contents of
690 % the second argument.}
691 %
692 % \begin{macro}{\frac}
693 % A disguise for plain \TeX's |\over|.
694 % \begin{macrocode}
695 \def\frac#1#2{{\begingroup#1\endgroup\over#2}}
696 % \end{macrocode}
697 % \end{macro}
698 %
699 % \begin{macro}{\sqrt}
700 % \changes{v1.0y}{1995/10/16}{(DPC) Make robust /1808}
701 % \begin{macro}{\@sqrt}
702 % Add an optional argument to plain's |\sqrt| to give the $n$th root
703 % of an expression $\sqrt[n]{e}$.
704 % \changes{v1.0r}{1995/05/21}{Use \cs{sqrtsign}}
705 % \begin{macrocode}
706 \DeclareRobustCommand\sqrt{\@ifnextchar[\@sqrt\sqrtsign}
707 \def\@sqrt[#1]{\root #1\of}
708 % \end{macrocode}
709 % \end{macro}
710 % \end{macro}
711 %
712 % \changes{LaTeX2.09}{1985/11/04}{produce warning message if line
713 % extends into margin. Doesn't warn about formula
714 % overprinting equation number.}
715 % \changes{LaTeX2.09}{1993/11/02}{RmS:
716 % Corrected description of \cs{@eqnsel}, moved \cs{@eqnsel}
717 % accordingly and removed extra \cs{tabskip} assignment.}
718 % \changes{LaTeX2e}{1993/11/03}{RmS: Initialized \cs{everycr} to empty}
719 % \changes{v0.9i}{1993/12/16}
720 % {use \cs{refstepcounter} instead of shortcut}
721 % \changes{v0.9o}{1994/01/13}{correcting 0.9i}
722 %
723 % \begin{environment}{eqnarray}
724 % \begin{macro}{\@eqcnt}
725 % \begin{macro}{\@eqpen}
726 % \begin{macro}{\if@eqnsw}
727 % \begin{macro}{\@eqnsel}
728 % Here's the eqnarray environment:
729 % Default is for left-hand side of equations to be flushright.
730 % To make them flushleft, |\let\@eqnsel = \hfil|.
731 % \begin{macrocode}
732 \newcount\@eqcnt
733 \newcount\@eqpen
734 \newif\if@eqnsw\@eqnswtrue
735 \newskip\@centering
736 \@centering = 0pt plus 1000pt
737 % \end{macrocode}
738 % To get a proper \cs{@currentlabel} we have to redefine it for the
739 % whole display. Note that we can't use \cs{refstepcounter} as this
740 % results in |\@currentlabel| getting restored at the wrong and
741 % thus always writing the first label to the \texttt{.aux} file.
742 % \begin{macrocode}
743 \def\eqnarray{%
744 \stepcounter{equation}%
745 \def\@currentlabel{\p@equation\theequation}%
746 \global\@eqnswtrue
747 \m@th
748 \global\@eqcnt\z@
749 \tabskip\@centering
750 \let\\\@eqncr
751 $$\everycr{}\halign to\displaywidth\bgroup
752 \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
753 &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
754 &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
755 $\displaystyle{##}$\hfil\tabskip\@centering
756 &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
757 \tabskip\z@skip
758 \cr
759 }
760 % \end{macrocode}
761 %
762 % \begin{macrocode}
763 \def\endeqnarray{%
764 \@@eqncr
765 \egroup
766 \global\advance\c@equation\m@ne
767 $$\@ignoretrue
768 }
769 % \end{macrocode}
770 %
771 % \begin{macrocode}
772 \let\@eqnsel=\relax
773 % \end{macrocode}
774 % \end{macro}
775 % \end{macro}
776 % \end{macro}
777 % \end{macro}
778 % \end{environment}
779 %
780 % \begin{macro}{\nonumber}
781 % Switches off equation numbering.
782 % \begin{macrocode}
783 \def\nonumber{\global\@eqnswfalse}
784 % \end{macrocode}
785 % \end{macro}
786 %
787 % \begin{macro}{\@eqncr}
788 % \begin{macro}{\@xeqncr}
789 % \begin{macro}{\@yeqncr}
790 % \changes{v1.0y}{1995/10/16}{(DPC) Use \cs{@testopt} /1911}
791 % \begin{macrocode}
792 \def\@eqncr{%
793 {\ifnum0=`}\fi
794 \@ifstar{%
795 \global\@eqpen\@M\@yeqncr
796 }{%
797 \global\@eqpen\interdisplaylinepenalty \@yeqncr
798 }%
799 }
800 % \end{macrocode}
801 %
802 % \begin{macrocode}
803 \def\@yeqncr{\@testopt\@xeqncr\z@skip}
804 % \end{macrocode}
805 %
806 % \begin{macrocode}
807 \def\@xeqncr[#1]{%
808 \ifnum0=`{\fi}%
809 \@@eqncr
810 \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}%
811 }
812 % \end{macrocode}
813 %
814 % \end{macro}
815 % \end{macro}
816 % \end{macro}
817 %
818 % \begin{macro}{\@@eqncr}
819 % \changes{v0.9i}{1993/12/16}{use \cs{refstepcounter} instead of shortcut}
820 % \changes{v0.9o}{1994/01/13}{correcting 0.9i}
821 %
822 % \begin{macrocode}
823 \def\@@eqncr{\let\reserved@a\relax
824 \ifcase\@eqcnt \def\reserved@a{& & &}\or \def\reserved@a{& &}%
825 \or \def\reserved@a{&}\else
826 \let\reserved@a\@empty
827 \@latex@error{Too many columns in eqnarray environment}\@ehc\fi
828 \reserved@a \if@eqnsw\@eqnnum\stepcounter{equation}\fi
829 \global\@eqnswtrue\global\@eqcnt\z@\cr}
830 % \end{macrocode}
831 % \end{macro}
832 %
833 % \begin{environment}{eqnarray*}
834 % \begin{macro}{\@seqncr}
835 % Here's the eqnarray* environment:
836 % \begin{macrocode}
837 \let\@seqncr=\@eqncr
838 % \end{macrocode}
839 %
840 % \begin{macrocode}
841 \@namedef{eqnarray*}{\def\@eqncr{\nonumber\@seqncr}\eqnarray}
842 % \end{macrocode}
843 %
844 % \begin{macrocode}
845 \@namedef{endeqnarray*}{\nonumber\endeqnarray}
846 % \end{macrocode}
847 % \end{macro}
848 % \end{environment}
849 %
850 % \begin{macro}{\lefteqn}
851 % |\lefteqn{FORMULA}| typesets |FORMULA| in display math style
852 % flushleft in a box of width zero.
853 % \changes{v1.0r}{1995/05/21}{Use \cs{rlap}}
854 % \begin{macrocode}
855 \def\lefteqn#1{\rlap{$\displaystyle #1$}}
856 % \end{macrocode}
857 % \end{macro}
858 %
859 % \begin{macro}{\ensuremath}
860 % In math mode, |\ensuremath{text}| is equivalent to text; in LR or
861 % paragraph mode, it is equivalent to |$|text|$|.
862 % |\relax| is not needed
863 % in front of the |\ifmmode| as |\protect| will be |\let| to |\relax|.
864 % This version (due to Donald Arseneau) avoids duplicating its
865 % argument in the `then' and `else' part of the |\ifmath| which is
866 % necessary in nested `tabular' like environments. See amslatex/2104.
867 % \changes{v1.0k}{1994/05/16}
868 % {Use \cs{DeclareRobustCommand} and add extra braces in math mode}
869 % \changes{v1.0l}{1994/10/23}{Remove extra braces: but see p 168 of
870 % Leslie's book}
871 % \changes{v1.1a}{1996/03/25}{Reimplement for amslatex/2104}
872 % \begin{macrocode}
873 \DeclareRobustCommand{\ensuremath}{%
874 \ifmmode
875 \expandafter\@firstofone
876 \else
877 \expandafter\@ensuredmath
878 \fi}
879 % \end{macrocode}
880 % \end{macro}
881 %
882 % \begin{macro}{\@ensuredmath}
883 % \changes{v1.1a}{1996/03/25}{Macro added for amslatex/2104}
884 % \changes{v1.1c}{1996/11/09}{Made long, as it was before. /2104}
885 % The |\relax| stops |\ensuremath{}| starting display math.
886 % \begin{macrocode}
887 \long\def\@ensuredmath#1{$\relax#1$}
888 % \end{macrocode}
889 % \end{macro}
890 %
891 % \begin{macrocode}
892 %</2ekernel>
893 % \end{macrocode}
894 %
895 %
896 %
897 % \subsection{External options to the standard document classes}
898 %
899 % \changes{v1.0u}{1995/08/09}
900 % {Added code for class options leqno and fleqn}
901 %
902 % \subsubsection{Left equation numbering}
903 %
904 % \begin{macro}{\@eqnnum}
905 % To put the equation number on the left side of an equation we
906 % have to use a little trick. The number is shifted |\displaywidth|
907 % to the left inside a box of (approximately) zero width. This
908 % fails when the quation is too wide, the equation number than may
909 % overprint the equation itself.
910 % \changes{v1.2y classes}{1995/01/12}{Added \cs{normalcolor}}
911 % \changes{v1.3c classes}{1995/05/25}
912 % {replace \cs{reset@font}\cs{rmfamily} with \cs{normalfont}
913 % (PR 1578)}
914 % \begin{macrocode}
915 %<*leqno>
916 \renewcommand\@eqnnum{\hb@xt@.01\p@{}%
917 \rlap{\normalfont\normalcolor
918 \hskip -\displaywidth(\theequation)}}
919 %</leqno>
920 % \end{macrocode}
921 % \end{macro}
922 %
923 % \subsubsection{Flush left equations}
924 %
925 % To get the displayed math environments to print the contents
926 % flush left (with an indentation) we have to redefine all of
927 % \LaTeXe's displayed math environments.
928 %
929 % \begin{macro}{\mathindent}
930 % The amount of indentation of the equations is stored in a register.
931 % \begin{macrocode}
932 %<*fleqn>
933 \newdimen\mathindent
934 % \end{macrocode}
935 % The setting of |\mathindent| has to be deferred until the class
936 % file has been processed, because |\leftmargini| is still 0pt
937 % wide at the moment \texttt{fleqn.clo} is read in.
938 % \changes{v1.0n classes}
939 % {1994/01/19}{Deferred setting of \cs{mathindent}}
940 % \changes{v1.2t classes}
941 % {1994/06/22}{Set \cs{mathindent} at the end of the
942 % class instead of at begin document}
943 % \begin{macrocode}
944 \AtEndOfClass{\mathindent\leftmargini}
945 % \end{macrocode}
946 % \end{macro}
947 %
948 % \begin{macro}{\[}
949 % Begin display math;
950 % \begin{macrocode}
951 \IncludeInRelease{2015/01/01}{\[}{Make \[ robust}%
952 \DeclareRobustCommand\[{\relax
953 \ifmmode\@badmath
954 \else
955 \begin{trivlist}%
956 \@beginparpenalty\predisplaypenalty
957 \@endparpenalty\postdisplaypenalty
958 \item[]\leavevmode
959 \hb@xt@\linewidth\bgroup $\m@th\displaystyle %$
960 \hskip\mathindent\bgroup
961 \fi}
962 \EndIncludeInRelease
963 % \end{macrocode}
964 %
965 % \begin{macrocode}
966 \IncludeInRelease{0000/00/00}{\[}{Make \[ robust}%
967 \renewcommand\[{\relax
968 \ifmmode\@badmath
969 \else
970 \begin{trivlist}%
971 \@beginparpenalty\predisplaypenalty
972 \@endparpenalty\postdisplaypenalty
973 \item[]\leavevmode
974 \hb@xt@\linewidth\bgroup $\m@th\displaystyle %$
975 \hskip\mathindent\bgroup
976 \fi}
977 \EndIncludeInRelease
978 % \end{macrocode}
979 % \end{macro}
980 %
981 % \begin{macro}{\]}
982 % end display math;
983 % \begin{macrocode}
984 \IncludeInRelease{2015/01/01}{\]}{Make \] robust}%
985 \DeclareRobustCommand\]{\relax
986 \ifmmode
987 \egroup $\hfil% $
988 \egroup
989 \end{trivlist}%
990 \else \@badmath
991 \fi}
992 \EndIncludeInRelease
993 % \end{macrocode}
994 %
995 % \begin{macrocode}
996 \IncludeInRelease{0000/00/00}{\]}{Make \] robust}%
997 \renewcommand\]{\relax
998 \ifmmode
999 \egroup $\hfil% $
1000 \egroup
1001 \end{trivlist}%
1002 \else \@badmath
1003 \fi}
1004 \EndIncludeInRelease
1005 % \end{macrocode}
1006 % \end{macro}
1007 %
1008 % \begin{environment}{equation}
1009 % The \textsf{equation} environment
1010 % \begin{macrocode}
1011 \renewenvironment{equation}%
1012 {\@beginparpenalty\predisplaypenalty
1013 \@endparpenalty\postdisplaypenalty
1014 \refstepcounter{equation}%
1015 \trivlist \item[]\leavevmode
1016 \hb@xt@\linewidth\bgroup $\m@th% $
1017 \displaystyle
1018 \hskip\mathindent}%
1019 {$\hfil % $
1020 \displaywidth\linewidth\hbox{\@eqnnum}%
1021 \egroup
1022 \endtrivlist}
1023 % \end{macrocode}
1024 % \end{environment}
1025 %
1026 % \begin{environment}{eqnarray}
1027 % The \textsf{eqnarray} environment
1028 % \begin{macrocode}
1029 \renewenvironment{eqnarray}{%
1030 \stepcounter{equation}%
1031 \def\@currentlabel{\p@equation\theequation}%
1032 \global\@eqnswtrue\m@th
1033 \global\@eqcnt\z@
1034 \tabskip\mathindent
1035 \let\\=\@eqncr
1036 \setlength\abovedisplayskip{\topsep}%
1037 \ifvmode
1038 \addtolength\abovedisplayskip{\partopsep}%
1039 \fi
1040 % \end{macrocode}
1041 % When the documentclass uses a non-zero |\parskip| setting the
1042 % |\topsep| might have a negative value to compensate for
1043 % that. Therefore we add |\parskip| to |\abovedisplayskip|.
1044 % \changes{v1.2v classes}{1994/11/10}{Added value of \cs{parskip} to
1045 % \cs{abovedisplayskip} to compensate for negative \cs{topsep}}
1046 % \begin{macrocode}
1047 \addtolength\abovedisplayskip{\parskip}%
1048 \setlength\belowdisplayskip{\abovedisplayskip}%
1049 \setlength\belowdisplayshortskip{\abovedisplayskip}%
1050 \setlength\abovedisplayshortskip{\abovedisplayskip}%
1051 $$\everycr{}\halign to\linewidth% $$
1052 \bgroup
1053 \hskip\@centering
1054 $\displaystyle\tabskip\z@skip{##}$\@eqnsel&%
1055 \global\@eqcnt\@ne \hskip \tw@\arraycolsep \hfil${##}$\hfil&%
1056 \global\@eqcnt\tw@ \hskip \tw@\arraycolsep
1057 $\displaystyle{##}$\hfil \tabskip\@centering&%
1058 \global\@eqcnt\thr@@
1059 \hb@xt@\z@\bgroup\hss##\egroup\tabskip\z@skip\cr}%
1060 {\@@eqncr
1061 \egroup
1062 \global\advance\c@equation\m@ne$$% $$
1063 \@ignoretrue
1064 }
1065 %</fleqn>
1066 % \end{macrocode}
1067 % \end{environment}
1068 %
1069 %
1070 %
1071 % \Finale
1072 %