1 % This is similar to the plain TeX format, with neither fonts nor hyphens.
3 % This is the plain TeX format that's described in The TeXbook.
4 % N.B.: A version number is defined at the very end of this file;
5 % please change that number whenever the file is modified!
6 % And don't modify the file unless you change its name:
7 % Everybody's "plain.tex" file should be the same, worldwide.
9 % Unlimited copying and redistribution of this file are permitted as long
10 % as this file is not modified. Modifications are permitted, but only if
11 % the resulting file is not named plain.tex.
13 \catcode`\
{=
1 % left brace is begin-group character
14 \catcode`\
}=
2 % right brace is end-group character
15 \catcode`\$=
3 % dollar sign is math shift
16 \catcode`\&=
4 % ampersand is alignment tab
17 \catcode`\#=
6 % hash mark is macro parameter character
18 \catcode`\^=
7 \catcode`\^^K=
7 % circumflex and uparrow are for superscripts
19 \catcode`
\_=
8 \catcode`\^^A=
8 % underline and downarrow are for subscripts
20 \catcode`\^^I=
10 % ascii tab is a blank space
21 \chardef\active=
13 \catcode`\~=
\active % tilde is active
22 \catcode`\^^L=
\active \outer\def^^L
{\par} % ascii form-feed is "\outer\par"
24 \message{Preloading the plain format: codes,
}
26 % We had to define the \catcodes right away, before the message line,
27 % since \message uses the { and } characters.
28 % When INITEX (the TeX initializer) starts up,
29 % it has defined the following \catcode values:
30 % \catcode`\^^@=9 % ascii null is ignored
31 % \catcode`\^^M=5 % ascii return is end-line
32 % \catcode`\\=0 % backslash is TeX escape character
33 % \catcode`\%=14 % percent sign is comment character
34 % \catcode`\ =10 % ascii space is blank space
35 % \catcode`\^^?=15 % ascii delete is invalid
36 % \catcode`\A=11 ... \catcode`\Z=11 % uppercase letters
37 % \catcode`\a=11 ... \catcode`\z=11 % lowercase letters
38 % all others are type 12 (other)
40 % Here is a list of the characters that have been specially catcoded:
41 \def\dospecials{\do\
\do\\
\do\
{\do\
}\do\$
\do\&
%
42 \do\#
\do\^
\do\^^K
\do\_\do\^^A
\do\%
\do\~
}
43 % (not counting ascii null, tab, linefeed, formfeed, return, delete)
44 % Each symbol in the list is preceded by \do, which can be defined
45 % if you want to do something to every item in the list.
47 % We make @ signs act like letters, temporarily, to avoid conflict
48 % between user names and internal control sequences of plain format.
51 % INITEX sets up \mathcode x=x, for x=0..255, except that
52 % \mathcode x=x+"7100, for x = `A to `Z and `a to `z;
53 % \mathcode x=x+"7000, for x = `0 to `9.
54 % The following changes define internal codes as recommended
55 % in Appendix C of The TeXbook:
56 \mathcode`\^^@="
2201 % \cdot
57 \mathcode`\^^A="
3223 % \downarrow
58 \mathcode`\^^B="
010B
% \alpha
59 \mathcode`\^^C="
010C
% \beta
60 \mathcode`\^^D="
225E
% \land
61 \mathcode`\^^E="
023A
% \lnot
62 \mathcode`\^^F="
3232 % \in
63 \mathcode`\^^G="
0119 % \pi
64 \mathcode`\^^H="
0115 % \lambda
65 \mathcode`\^^I="
010D
% \gamma
66 \mathcode`\^^J="
010E
% \delta
67 \mathcode`\^^K="
3222 % \uparrow
68 \mathcode`\^^L="
2206 % \pm
69 \mathcode`\^^M="
2208 % \oplus
70 \mathcode`\^^N="
0231 % \infty
71 \mathcode`\^^O="
0140 % \partial
72 \mathcode`\^^P="
321A
% \subset
73 \mathcode`\^^Q="
321B
% \supset
74 \mathcode`\^^R="
225C
% \cap
75 \mathcode`\^^S="
225B
% \cup
76 \mathcode`\^^T="
0238 % \forall
77 \mathcode`\^^U="
0239 % \exists
78 \mathcode`\^^V="
220A
% \otimes
79 \mathcode`\^^W="
3224 % \leftrightarrow
80 \mathcode`\^^X="
3220 % \leftarrow
81 \mathcode`\^^Y="
3221 % \rightarrow
82 \mathcode`\^^Z="
8000 % \ne
83 \mathcode`\^^
[="
2205 % \diamond
84 \mathcode`\^^\="
3214 % \le
85 \mathcode`\^^
]="
3215 % \ge
86 \mathcode`\^^^="
3211 % \equiv
87 \mathcode`\^^_="
225F
% \lor
88 \mathcode`\ ="
8000 % \space
90 \mathcode`\'="
8000 % ^\prime
93 \mathcode`\*="
2203 % \ast
106 \mathcode`\\="
026E
% \backslash
108 \mathcode`
\_="
8000 % \_
112 \mathcode`\^^?="
1273 % \smallint
114 % INITEX sets \uccode`x=`X and \uccode `X=`X for all letters x,
115 % and \lccode`x=`x, \lccode`X=`x; all other values are zero.
116 % No changes to those tables are needed in plain TeX format.
118 % INITEX sets \sfcode x=1000 for all x, except that \sfcode`X=999
119 % for uppercase letters. The following changes are needed:
120 \sfcode`\)=
0 \sfcode`\'=
0 \sfcode`\
]=
0
121 % The \nonfrenchspacing macro will make further changes to \sfcode values.
123 % Finally, INITEX sets all \delcode values to -1, except \delcode`.=0
133 % N.B. { and } should NOT get delcodes; otherwise parameter grouping fails!
135 % To make the plain macros more efficient in time and space,
136 % several constant values are declared here as control sequences.
137 % If they were changed, anything could happen; so they are private symbols.
143 \mathchardef\@cclvi=
256
145 \mathchardef\@M=
10000
146 \mathchardef\@MM=
20000
148 % Allocation of registers
150 % Here are macros for the automatic allocation of \count, \box, \dimen,
151 % \skip, \muskip, and \toks registers, as well as \read and \write
152 % stream numbers, \fam codes, \language codes, and \insert numbers.
156 % When a register is used only temporarily, it need not be allocated;
157 % grouping can be used, making the value previously in the register return
158 % after the close of the group. The main use of these macros is for
159 % registers that are defined by one macro and used by others, possibly at
160 % different nesting levels. All such registers should be defined through
161 % these macros; otherwise conflicts may occur, especially when two or more
162 % macro packages are being used at once.
164 % The following counters are reserved:
165 % 0 to 9 page numbering
166 % 10 count allocation
167 % 11 dimen allocation
169 % 13 muskip allocation
172 % 16 read file allocation
173 % 17 write file allocation
174 % 18 math family allocation
175 % 19 language allocation
176 % 20 insert allocation
177 % 21 the most recently allocated number
179 % New counters are allocated starting with 23, 24, etc. Other registers are
180 % allocated starting with 10. This leaves 0 through 9 for the user to play
181 % with safely, except that counts 0 to 9 are considered to be the page and
182 % subpage numbers (since they are displayed during output). In this scheme,
183 % \count 10 always contains the number of the highest-numbered counter that
184 % has been allocated, \count 14 the highest-numbered box, etc.
185 % Inserts are given numbers 254, 253, etc., since they require a \count,
186 % \dimen, \skip, and \box all with the same number; \count 20 contains the
187 % lowest-numbered insert that has been allocated. Of course, \box255 is
188 % reserved for \output; \count255, \dimen255, and \skip255 can be used freely.
190 % It is recommended that macro designers always use
191 % \global assignments with respect to registers numbered 1, 3, 5, 7, 9, and
192 % always non-\global assignments with respect to registers 0, 2, 4, 6, 8, 255.
193 % This will prevent ``save stack buildup'' that might otherwise occur.
195 \count10=
22 % allocates \count registers 23, 24, ...
196 \count11=
9 % allocates \dimen registers 10, 11, ...
197 \count12=
9 % allocates \skip registers 10, 11, ...
198 \count13=
9 % allocates \muskip registers 10, 11, ...
199 \count14=
9 % allocates \box registers 10, 11, ...
200 \count15=
9 % allocates \toks registers 10, 11, ...
201 \count16=-
1 % allocates input streams 0, 1, ...
202 \count17=-
1 % allocates output streams 0, 1, ...
203 \count18=
3 % allocates math families 4, 5, ...
204 \count19=
0 % allocates \language codes 1, 2, ...
205 \count20=
255 % allocates insertions 254, 253, ...
206 \countdef\insc@unt=
20 % the insertion counter
207 \countdef\allocationnumber=
21 % the most recent allocation
208 \countdef\m@ne=
22 \m@ne=-
1 % a handy constant
209 \def\wlog{\immediate\write\m@ne
} % write on log file (only)
211 % Here are abbreviations for the names of scratch registers
212 % that don't need to be allocated.
216 \dimendef\dimen@i=
1 % global only
221 % Now, we define \newcount, \newbox, etc. so that you can say \newcount\foo
222 % and \foo will be defined (with \countdef) to be the next counter.
223 % To find out which counter \foo is, you can look at \allocationnumber.
224 % Since there's no \boxdef command, \chardef is used to define a \newbox,
225 % \newinsert, \newfam, and so on.
227 \outer\def\newcount{\alloc@
0\count\countdef\insc@unt
}
228 \outer\def\newdimen{\alloc@
1\dimen\dimendef\insc@unt
}
229 \outer\def\newskip{\alloc@
2\skip\skipdef\insc@unt
}
230 \outer\def\newmuskip{\alloc@
3\muskip\muskipdef\@cclvi
}
231 \outer\def\newbox{\alloc@
4\box\chardef\insc@unt
}
232 \let\newtoks=
\relax % we do this to allow plain.tex to be read in twice
233 \outer\def\newhelp#1#2{\newtoks#1#1\expandafter{\csname#2\endcsname}}
234 \outer\def\newtoks{\alloc@
5\toks\toksdef\@cclvi
}
235 \outer\def\newread{\alloc@
6\read\chardef\sixt@@n
}
236 \outer\def\newwrite{\alloc@
7\write\chardef\sixt@@n
}
237 \outer\def\newfam{\alloc@
8\fam\chardef\sixt@@n
}
238 \outer\def\newlanguage{\alloc@
9\language\chardef\@cclvi
}
239 \def\alloc@
#1#2#3#4#5{\global\advance\count1#1by\@ne
240 \ch@ck
#1#4#2% make sure there's still room
241 \allocationnumber=
\count1#1%
242 \global#3#5=
\allocationnumber
243 \wlog{\string#5=
\string#2\the\allocationnumber}}
244 \outer\def\newinsert#1{\global\advance\insc@unt by
\m@ne
245 \ch@ck0
\insc@unt
\count
246 \ch@ck1
\insc@unt
\dimen
247 \ch@ck2
\insc@unt
\skip
249 \allocationnumber=
\insc@unt
250 \global\chardef#1=
\allocationnumber
251 \wlog{\string#1=
\string\insert\the\allocationnumber}}
252 \def\ch@ck
#1#2#3{\ifnum\count1#1<
#2%
253 \else\errmessage{No room for a new
#3}\fi}
255 % Here are some examples of allocation.
256 \newdimen\maxdimen \maxdimen=
16383.99999pt
% the largest legal <dimen>
257 \newskip\hideskip \hideskip=-
1000pt plus
1fill
% negative but can grow
258 \newskip\centering \centering=
0pt plus
1000pt minus
1000pt
259 \newdimen\p@
\p@=
1pt
% this saves macro space and time
260 \newdimen\z@
\z@=
0pt
% can be used both for 0pt and 0
261 \newskip\z@skip
\z@skip=
0pt plus0pt minus0pt
262 \newbox\voidb@x
% permanently void box register
264 % And here's a different sort of allocation:
265 % For example, \newif\iffoo creates \footrue, \foofalse to go with \iffoo.
266 \outer\def\newif#1{\count@
\escapechar \escapechar\m@ne
267 \expandafter\expandafter\expandafter
268 \def\@if
#1{true
}{\let#1=
\iftrue}%
269 \expandafter\expandafter\expandafter
270 \def\@if
#1{false
}{\let#1=
\iffalse}%
271 \@if
#1{false
}\escapechar\count@
} % the condition starts out false
272 \def\@if
#1#2{\csname\expandafter\if@
\string#1#2\endcsname}
273 {\uccode`
1=`i
\uccode`
2=`f
\uppercase{\gdef\if@
12{}}} % `if' is required
275 % Assign initial values to TeX's parameters
277 \message{parameters,
}
279 % All of TeX's numeric parameters are listed here,
280 % but the code is commented out if no special value needs to be set.
281 % INITEX makes all parameters zero except where noted.
284 \tolerance=
200 % INITEX sets this to 10000
294 \displaywidowpenalty=
50
296 \predisplaypenalty=
10000
297 % \postdisplaypenalty=0
298 % \interlinepenalty=0
299 % \floatingpenalty=0, set during \insert
300 % \outputpenalty=0, set before TeX enters \output
301 \doublehyphendemerits=
10000
302 \finalhyphendemerits=
5000
304 % \looseness=0, cleared by TeX after each paragraph
310 % \tracingparagraphs=0
318 % \lefthyphenmin=2 \righthyphenmin=3 set below
320 % \maxdeadcycles=25 % INITEX does this
321 % \hangafter=1 % INITEX does this, also TeX after each paragraph
323 % \mag=1000 % INITEX does this
324 % \escapechar=`\\ % INITEX does this
325 \defaulthyphenchar=`\-
327 % \endlinechar=`\^^M % INITEX does this
330 % \time=now % TeX does this at beginning of job
331 % \day=now % TeX does this at beginning of job
332 % \month=now % TeX does this at beginning of job
333 % \year=now % TeX does this at beginning of job
344 \splitmaxdepth=
\maxdimen
345 \boxmaxdepth=
\maxdimen
346 % \lineskiplimit=0pt, changed by \normalbaselines
347 \delimitershortfall=
5pt
348 \nulldelimiterspace=
1.2pt
351 % \predisplaysize=0pt, set before TeX enters $$
352 % \displaywidth=0pt, set before TeX enters $$
353 % \displayindent=0pt, set before TeX enters $$
355 % \hangindent=0pt, zeroed by TeX after each paragraph
359 % \baselineskip=0pt, changed by \normalbaselines
360 % \lineskip=0pt, changed by \normalbaselines
361 \parskip=
0pt plus
1pt
362 \abovedisplayskip=
12pt plus
3pt minus
9pt
363 \abovedisplayshortskip=
0pt plus
3pt
364 \belowdisplayskip=
12pt plus
3pt minus
9pt
365 \belowdisplayshortskip=
7pt plus
3pt minus
4pt
373 \parfillskip=
0pt plus
1fil
376 \medmuskip=
4mu plus
2mu minus
4mu
377 \thickmuskip=
5mu plus
5mu
379 % We also define special registers that function like parameters:
380 \newskip\smallskipamount \smallskipamount=
3pt plus
1pt minus
1pt
381 \newskip\medskipamount \medskipamount=
6pt plus
2pt minus
2pt
382 \newskip\bigskipamount \bigskipamount=
12pt plus
4pt minus
4pt
383 \newskip\normalbaselineskip \normalbaselineskip=
12pt
384 \newskip\normallineskip \normallineskip=
1pt
385 \newdimen\normallineskiplimit \normallineskiplimit=
0pt
386 \newdimen\jot \jot=
3pt
387 \newcount\interdisplaylinepenalty \interdisplaylinepenalty=
100
388 \newcount\interfootnotelinepenalty \interfootnotelinepenalty=
100
390 % Definitions for preloaded fonts
392 \def\magstephalf{1095 }
393 \def\magstep#1{\ifcase#1 \@m
\or 1200\or 1440\or 1728\or 2074\or 2488\fi\relax}
395 % Fonts assigned to \preloaded are not part of "plain TeX",
396 % but they are preloaded so that other format packages can use them.
397 % For example, if another set of macros says "\font\ninerm=cmr9",
398 % TeX will not have to reload the font metric information for cmr9.
400 % Macros for setting ordinary text
403 \def\frenchspacing{\sfcode`\.\@m
\sfcode`\?\@m
\sfcode`\!\@m
404 \sfcode`\:\@m
\sfcode`\;\@m
\sfcode`\,\@m
}
405 \def\nonfrenchspacing{\sfcode`\
.3000\sfcode`\?
3000\sfcode`\!
3000%
406 \sfcode`\:
2000\sfcode`\;
1500\sfcode`\,
1250 }
408 \def\normalbaselines{\lineskip\normallineskip
409 \baselineskip\normalbaselineskip \lineskiplimit\normallineskiplimit}
411 \def\^^M
{\
} % control <return> = control <space>
412 \def\^^I
{\
} % same for <tab>
414 \def\lq{`
} \def\rq{'
}
415 \def\lbrack{[} \def\rbrack{]}
417 \let\endgraf=
\par \let\endline=
\cr
423 \let\bgroup=
{ \let\egroup=
}
425 % In \obeylines, we say `\let^^M=\par' instead of `\def^^M{\par}'
426 % since this allows, for example, `\let\par=\cr \obeylines \halign{...'
427 {\catcode`\^^M=
\active % these lines must end with %
428 \gdef\obeylines{\catcode`\^^M
\active \let^^M
\par}%
429 \global\let^^M
\par} % this is in case ^^M appears in a \write
430 \def\obeyspaces{\catcode`\
\active}
431 {\obeyspaces\global\let =
\space}
433 \def\loop#1\repeat{\def\body{#1}\iterate}
434 \def\iterate{\body \let\next\iterate \else\let\next\relax\fi \next}
435 \let\repeat=
\fi % this makes \loop...\if...\repeat skippable
437 \def\thinspace{\kern .16667em
}
438 \def\negthinspace{\kern-
.16667em
}
439 \def\enspace{\kern.5em
}
441 \def\enskip{\hskip.5em
\relax}
442 \def\quad{\hskip1em\relax}
443 \def\qquad{\hskip2em\relax}
445 \def\smallskip{\vskip\smallskipamount}
446 \def\medskip{\vskip\medskipamount}
447 \def\bigskip{\vskip\bigskipamount}
449 \def\nointerlineskip{\prevdepth-
1000\p@
}
450 \def\offinterlineskip{\baselineskip-
1000\p@
451 \lineskip\z@
\lineskiplimit\maxdimen}
453 \def\topglue{\nointerlineskip\vglue-
\topskip\vglue} % for top of page
454 \def\vglue{\afterassignment\vgl@
\skip@=
}
455 \def\vgl@
{\par \dimen@
\prevdepth \hrule height
\z@
456 \nobreak\vskip\skip@
\prevdepth\dimen@
}
457 \def\hglue{\afterassignment\hgl@
\skip@=
}
458 \def\hgl@
{\leavevmode \count@
\spacefactor \vrule width
\z@
459 \nobreak\hskip\skip@
\spacefactor\count@
}
461 \def~
{\penalty\@M \
} % tie
462 \def\slash{/
\penalty\exhyphenpenalty} % a `/' that acts like a `-'
464 \def\break{\penalty-\@M
}
465 \def\nobreak{\penalty \@M
}
466 \def\allowbreak{\penalty \z@
}
468 \def\filbreak{\par\vfil\penalty-
200\vfilneg}
469 \def\goodbreak{\par\penalty-
500 }
470 \def\eject{\par\break}
471 \def\supereject{\par\penalty-\@MM
}
473 \def\removelastskip{\ifdim\lastskip=
\z@
\else\vskip-
\lastskip\fi}
474 \def\smallbreak{\par\ifdim\lastskip<
\smallskipamount
475 \removelastskip\penalty-
50\smallskip\fi}
476 \def\medbreak{\par\ifdim\lastskip<
\medskipamount
477 \removelastskip\penalty-
100\medskip\fi}
478 \def\bigbreak{\par\ifdim\lastskip<
\bigskipamount
479 \removelastskip\penalty-
200\bigskip\fi}
481 \def\line{\hbox to
\hsize}
482 \def\leftline#1{\line{#1\hss}}
483 \def\rightline#1{\line{\hss#1}}
484 \def\centerline#1{\line{\hss#1\hss}}
486 \def\rlap#1{\hbox to
\z@
{#1\hss}}
487 \def\llap#1{\hbox to
\z@
{\hss#1}}
489 \def\m@th
{\mathsurround\z@
}
490 \def\underbar#1{$
\setbox\z@
\hbox{#1}\dp\z@
\z@
491 \m@th
\underline{\box\z@
}$
}
494 \setbox\strutbox=
\hbox{\vrule height8.5pt depth3.5pt width
\z@
}
495 \def\strut{\relax\ifmmode\copy\strutbox\else\unhcopy\strutbox\fi}
497 \def\hidewidth{\hskip\hideskip} % for alignment entries that can stick out
498 \def\ialign{\everycr{}\tabskip\z@skip
\halign} % initialized \halign
500 \def\multispan#1{\omit \mscount#1\relax
501 \loop\ifnum\mscount>\@ne
\sp@n
\repeat}
502 \def\sp@n
{\span\omit\advance\mscount\m@ne
}
504 \newif\ifus@
\newif\if@cr
505 \newbox\tabs \newbox\tabsyet \newbox\tabsdone
507 \def\cleartabs{\global\setbox\tabsyet\null \setbox\tabs\null}
508 \def\settabs{\setbox\tabs\null \futurelet\next\sett@b
}
509 \let\+=
\relax % in case this file is being read in twice
510 \def\sett@b
{\ifx\next\+
\def\nxt{\afterassignment\s@tt@b
\let\nxt}%
511 \else\let\nxt\s@tcols
\fi \let\next\relax \nxt}
512 \def\s@tt@b
{\let\nxt\relax \us@false
\m@ketabbox
}
513 \def\tabalign{\us@true
\m@ketabbox
} % non-\outer version of \+
514 \outer\def\+
{\tabalign}
515 \def\s@tcols
#1\columns{\count@
#1\dimen@
\hsize
516 \loop\ifnum\count@>
\z@ \@nother
\repeat}
517 \def\@nother
{\dimen@ii
\dimen@
\divide\dimen@ii
\count@
518 \setbox\tabs\hbox{\hbox to
\dimen@ii
{}\unhbox\tabs}%
519 \advance\dimen@-
\dimen@ii
\advance\count@
\m@ne
}
521 \def\m@ketabbox
{\begingroup
522 \global\setbox\tabsyet\copy\tabs
523 \global\setbox\tabsdone\null
524 \def\cr{\@crtrue
\crcr\egroup\egroup
525 \ifus@
\unvbox\z@
\lastbox\fi\endgroup
526 \setbox\tabs\hbox{\unhbox\tabsyet\unhbox\tabsdone}}%
527 \setbox\z@
\vbox\bgroup\@crfalse
528 \ialign\bgroup&
\t@bbox##
\t@bb@x
\crcr}
530 \def\t@bbox
{\setbox\z@
\hbox\bgroup}
531 \def\t@bb@x
{\if@cr
\egroup % now \box\z@ holds the column
532 \else\hss\egroup \global\setbox\tabsyet\hbox{\unhbox\tabsyet
533 \global\setbox\@ne
\lastbox}% now \box\@ne holds its size
534 \ifvoid\@ne
\global\setbox\@ne
\hbox to
\wd\z@
{}%
535 \else\setbox\z@
\hbox to
\wd\@ne
{\unhbox\z@
}\fi
536 \global\setbox\tabsdone\hbox{\box\@ne
\unhbox\tabsdone}\fi
539 \def\hang{\hangindent\parindent}
540 \def\textindent#1{\indent\llap{#1\enspace}\ignorespaces}
541 \def\item{\par\hang\textindent}
542 \def\itemitem{\par\indent \hangindent2\parindent \textindent}
543 \def\narrower{\advance\leftskip\parindent
544 \advance\rightskip\parindent}
546 \outer\def\beginsection#1\par{\vskip\z@ plus
.3\vsize\penalty-
250
547 \vskip\z@ plus-
.3\vsize\bigskip\vskip\parskip
548 \message{#1}\leftline{\bf#1}\nobreak\smallskip\noindent}
549 \outer\def\proclaim #1.
#2\par{\medbreak
550 \noindent{\bf#1.
\enspace}{\sl#2\par}%
551 \ifdim\lastskip<
\medskipamount \removelastskip\penalty55\medskip\fi}
553 \def\raggedright{\rightskip\z@ plus2em
\spaceskip.3333em
\xspaceskip.5em
\relax}
554 \def\ttraggedright{\tt\rightskip\z@ plus2em
\relax} % for use with \tt only
567 \chardef\i="
10 \chardef\j="
11 % dotless letters
570 \def\L{\leavevmode\setbox0\hbox{L
}\hbox to
\wd0{\hss\char32L}}
572 \def\leavevmode{\unhbox\voidb@x
} % begins a paragraph, if necessary
573 \def\_{\leavevmode \kern.06em
\vbox{\hrule width
.3em
}}
574 \def\AA{\leavevmode\setbox0\hbox{!
}\dimen@
\ht0\advance\dimen@-
1ex
%
575 \rlap{\raise.67\dimen@
\hbox{\char'
27}}A
}
577 \def\mathhexbox#1#2#3{\leavevmode
578 \hbox{$
\m@th
\mathchar"
#1#2#3$
}}
579 \def\dag{\mathhexbox279}
580 \def\ddag{\mathhexbox27A}
581 \def\S{\mathhexbox278}
582 \def\P{\mathhexbox27B}
583 \def\Orb{\mathhexbox20D}
585 \def\oalign#1{\leavevmode\vtop{\baselineskip\z@skip
\lineskip.25ex
%
586 \ialign{##
\crcr#1\crcr}}} \def\o@lign
{\lineskiplimit\z@
\oalign}
587 \def\ooalign{\lineskiplimit-
\maxdimen \oalign} % chars over each other
588 {\catcode`p=
12 \catcode`t=
12 \gdef\\
#1pt
{#1}} \let\getf@ctor=\\
589 \def\sh@ft
#1{\dimen@
#1\kern\expandafter\getf@ctor
\the\fontdimen1\font
590 \dimen@
} % kern by #1 times the current slant
591 \def\d#1{{\o@lign
{\relax#1\crcr\hidewidth\sh@ft
{-
1ex
}.
\hidewidth}}}
592 \def\b#1{{\o@lign
{\relax#1\crcr\hidewidth\sh@ft
{-
3ex
}%
593 \vbox to
.2ex
{\hbox{\char22}\vss}\hidewidth}}}
594 \def\c#1{{\setbox\z@
\hbox{#1}\ifdim\ht\z@=
1ex
\accent24 #1%
595 \else\ooalign{\unhbox\z@
\crcr\hidewidth\char24\hidewidth}\fi}}
596 \def\copyright{{\ooalign{\hfil\raise.07ex
\hbox{c
}\hfil\crcr\Orb}}}
598 \def\dots{\relax\ifmmode\ldots\else$
\m@th
\ldots\,$
\fi}
599 \def\TeX{T
\kern-
.1667em
\lower.5ex
\hbox{E
}\kern-
.125emX
}
601 \def\`
#1{{\accent18 #1}}
602 \def\'
#1{{\accent19 #1}}
603 \def\v#1{{\accent20 #1}} \let\^^_=
\v
604 \def\u#1{{\accent21 #1}} \let\^^S=
\u
605 \def\=
#1{{\accent22 #1}}
606 \def\^
#1{{\accent94 #1}} \let\^^D=\^
607 \def\.
#1{{\accent95 #1}}
608 \def\H#1{{\accent"
7D
#1}}
609 \def\~
#1{{\accent"
7E
#1}}
610 \def\"
#1{{\accent"
7F
#1}}
611 \def\t#1{{\edef\next{\the\font}\the\textfont1\accent"
7F
\next#1}}
613 \def\hrulefill{\leaders\hrule\hfill}
614 \def\dotfill{\cleaders\hbox{$
\m@th
\mkern1.5mu.
\mkern1.5mu$
}\hfill}
615 \def\rightarrowfill{$
\m@th
\smash-
\mkern-
7mu
%
616 \cleaders\hbox{$
\mkern-
2mu
\smash-
\mkern-
2mu$
}\hfill
617 \mkern-
7mu
\mathord\rightarrow$
}
618 \def\leftarrowfill{$
\m@th
\mathord\leftarrow\mkern-
7mu
%
619 \cleaders\hbox{$
\mkern-
2mu
\smash-
\mkern-
2mu$
}\hfill
621 \mathchardef\braceld="
37A
\mathchardef\bracerd="
37B
622 \mathchardef\bracelu="
37C
\mathchardef\braceru="
37D
623 \def\downbracefill{$
\m@th
\setbox\z@
\hbox{$
\braceld$
}%
624 \braceld\leaders\vrule height
\ht\z@ depth
\z@
\hfill\braceru
625 \bracelu\leaders\vrule height
\ht\z@ depth
\z@
\hfill\bracerd$
}
626 \def\upbracefill{$
\m@th
\setbox\z@
\hbox{$
\braceld$
}%
627 \bracelu\leaders\vrule height
\ht\z@ depth
\z@
\hfill\bracerd
628 \braceld\leaders\vrule height
\ht\z@ depth
\z@
\hfill\braceru$
}
630 \outer\def\bye{\par\vfill\supereject\end}
632 % Macros for math setting
633 \message{math definitions,
}
636 \def\,
{\mskip\thinmuskip}
637 \def\>
{\mskip\medmuskip}
638 \def\;
{\mskip\thickmuskip}
639 \def\!
{\mskip-
\thinmuskip}
640 \def\*
{\discretionary{\thinspace\the\textfont2\char2}{}{}}
641 {\catcode`\'=
\active \gdef'
{^
\bgroup\prim@s
}}
642 \def\prim@s
{\prime\futurelet\next\pr@m@s
}
643 \def\pr@m@s
{\ifx'
\next\let\nxt\pr@@@s
\else\ifx^
\next\let\nxt\pr@@@t
644 \else\let\nxt\egroup\fi\fi \nxt}
645 \def\pr@@@s
#1{\prim@s
} \def\pr@@@t
#1#2{#2\egroup}
646 {\catcode`\^^Z=
\active \gdef^^Z
{\not=
}} % ^^Z is like \ne in math
648 {\catcode`
\_=
\active \global\let_=
\_} % _ in math is either subscript or \_
650 \mathchardef\alpha="
010B
651 \mathchardef\beta="
010C
652 \mathchardef\gamma="
010D
653 \mathchardef\delta="
010E
654 \mathchardef\epsilon="
010F
655 \mathchardef\zeta="
0110
656 \mathchardef\eta="
0111
657 \mathchardef\theta="
0112
658 \mathchardef\iota="
0113
659 \mathchardef\kappa="
0114
660 \mathchardef\lambda="
0115
661 \mathchardef\mu="
0116
662 \mathchardef\nu="
0117
663 \mathchardef\xi="
0118
664 \mathchardef\pi="
0119
665 \mathchardef\rho="
011A
666 \mathchardef\sigma="
011B
667 \mathchardef\tau="
011C
668 \mathchardef\upsilon="
011D
669 \mathchardef\phi="
011E
670 \mathchardef\chi="
011F
671 \mathchardef\psi="
0120
672 \mathchardef\omega="
0121
673 \mathchardef\varepsilon="
0122
674 \mathchardef\vartheta="
0123
675 \mathchardef\varpi="
0124
676 \mathchardef\varrho="
0125
677 \mathchardef\varsigma="
0126
678 \mathchardef\varphi="
0127
679 \mathchardef\Gamma="
7000
680 \mathchardef\Delta="
7001
681 \mathchardef\Theta="
7002
682 \mathchardef\Lambda="
7003
683 \mathchardef\Xi="
7004
684 \mathchardef\Pi="
7005
685 \mathchardef\Sigma="
7006
686 \mathchardef\Upsilon="
7007
687 \mathchardef\Phi="
7008
688 \mathchardef\Psi="
7009
689 \mathchardef\Omega="
700A
691 \mathchardef\aleph="
0240
692 \def\hbar{{\mathchar'
26\mkern-
9muh
}}
693 \mathchardef\imath="
017B
694 \mathchardef\jmath="
017C
695 \mathchardef\ell="
0160
696 \mathchardef\wp="
017D
697 \mathchardef\Re="
023C
698 \mathchardef\Im="
023D
699 \mathchardef\partial="
0140
700 \mathchardef\infty="
0231
701 \mathchardef\prime="
0230
702 \mathchardef\emptyset="
023B
703 \mathchardef\nabla="
0272
704 \def\surd{{\mathchar"
1270}}
705 \mathchardef\top="
023E
706 \mathchardef\bot="
023F
707 \def\angle{{\vbox{\ialign{$
\m@th
\scriptstyle##$
\crcr
708 \not\mathrel{\mkern14mu}\crcr
709 \noalign{\nointerlineskip}
710 \mkern2.5mu
\leaders\hrule height
.34pt
\hfill\mkern2.5mu
\crcr}}}}
711 \mathchardef\triangle="
0234
712 \mathchardef\forall="
0238
713 \mathchardef\exists="
0239
714 \mathchardef\neg="
023A
\let\lnot=
\neg
715 \mathchardef\flat="
015B
716 \mathchardef\natural="
015C
717 \mathchardef\sharp="
015D
718 \mathchardef\clubsuit="
027C
719 \mathchardef\diamondsuit="
027D
720 \mathchardef\heartsuit="
027E
721 \mathchardef\spadesuit="
027F
723 \mathchardef\coprod="
1360
724 \mathchardef\bigvee="
1357
725 \mathchardef\bigwedge="
1356
726 \mathchardef\biguplus="
1355
727 \mathchardef\bigcap="
1354
728 \mathchardef\bigcup="
1353
729 \mathchardef\intop="
1352 \def\int{\intop\nolimits}
730 \mathchardef\prod="
1351
731 \mathchardef\sum="
1350
732 \mathchardef\bigotimes="
134E
733 \mathchardef\bigoplus="
134C
734 \mathchardef\bigodot="
134A
735 \mathchardef\ointop="
1348 \def\oint{\ointop\nolimits}
736 \mathchardef\bigsqcup="
1346
737 \mathchardef\smallint="
1273
739 \mathchardef\triangleleft="
212F
740 \mathchardef\triangleright="
212E
741 \mathchardef\bigtriangleup="
2234
742 \mathchardef\bigtriangledown="
2235
743 \mathchardef\wedge="
225E
\let\land=
\wedge
744 \mathchardef\vee="
225F
\let\lor=
\vee
745 \mathchardef\cap="
225C
746 \mathchardef\cup="
225B
747 \mathchardef\ddagger="
227A
748 \mathchardef\dagger="
2279
749 \mathchardef\sqcap="
2275
750 \mathchardef\sqcup="
2274
751 \mathchardef\uplus="
225D
752 \mathchardef\amalg="
2271
753 \mathchardef\diamond="
2205
754 \mathchardef\bullet="
220F
755 \mathchardef\wr="
226F
756 \mathchardef\div="
2204
757 \mathchardef\odot="
220C
758 \mathchardef\oslash="
220B
759 \mathchardef\otimes="
220A
760 \mathchardef\ominus="
2209
761 \mathchardef\oplus="
2208
762 \mathchardef\mp="
2207
763 \mathchardef\pm="
2206
764 \mathchardef\circ="
220E
765 \mathchardef\bigcirc="
220D
766 \mathchardef\setminus="
226E
% for set difference A\setminus B
767 \mathchardef\cdot="
2201
768 \mathchardef\ast="
2203
769 \mathchardef\times="
2202
770 \mathchardef\star="
213F
772 \mathchardef\propto="
322F
773 \mathchardef\sqsubseteq="
3276
774 \mathchardef\sqsupseteq="
3277
775 \mathchardef\parallel="
326B
776 \mathchardef\mid="
326A
777 \mathchardef\dashv="
3261
778 \mathchardef\vdash="
3260
779 \mathchardef\nearrow="
3225
780 \mathchardef\searrow="
3226
781 \mathchardef\nwarrow="
322D
782 \mathchardef\swarrow="
322E
783 \mathchardef\Leftrightarrow="
322C
784 \mathchardef\Leftarrow="
3228
785 \mathchardef\Rightarrow="
3229
786 \def\neq{\not=
} \let\ne=
\neq
787 \mathchardef\leq="
3214 \let\le=
\leq
788 \mathchardef\geq="
3215 \let\ge=
\geq
789 \mathchardef\succ="
321F
790 \mathchardef\prec="
321E
791 \mathchardef\approx="
3219
792 \mathchardef\succeq="
3217
793 \mathchardef\preceq="
3216
794 \mathchardef\supset="
321B
795 \mathchardef\subset="
321A
796 \mathchardef\supseteq="
3213
797 \mathchardef\subseteq="
3212
798 \mathchardef\in="
3232
799 \mathchardef\ni="
3233 \let\owns=
\ni
800 \mathchardef\gg="
321D
801 \mathchardef\ll="
321C
802 \mathchardef\not="
3236
803 \mathchardef\leftrightarrow="
3224
804 \mathchardef\leftarrow="
3220 \let\gets=
\leftarrow
805 \mathchardef\rightarrow="
3221 \let\to=
\rightarrow
806 \mathchardef\mapstochar="
3237 \def\mapsto{\mapstochar\rightarrow}
807 \mathchardef\sim="
3218
808 \mathchardef\simeq="
3227
809 \mathchardef\perp="
323F
810 \mathchardef\equiv="
3211
811 \mathchardef\asymp="
3210
812 \mathchardef\smile="
315E
813 \mathchardef\frown="
315F
814 \mathchardef\leftharpoonup="
3128
815 \mathchardef\leftharpoondown="
3129
816 \mathchardef\rightharpoonup="
312A
817 \mathchardef\rightharpoondown="
312B
819 \def\joinrel{\mathrel{\mkern-
3mu
}}
820 \def\relbar{\mathrel{\smash-
}} % \smash, because - has the same height as +
821 \def\Relbar{\mathrel=
}
822 \mathchardef\lhook="
312C
\def\hookrightarrow{\lhook\joinrel\rightarrow}
823 \mathchardef\rhook="
312D
\def\hookleftarrow{\leftarrow\joinrel\rhook}
824 \def\bowtie{\mathrel\triangleright\joinrel\mathrel\triangleleft}
825 \def\models{\mathrel|
\joinrel=
}
826 \def\Longrightarrow{\Relbar\joinrel\Rightarrow}
827 \def\longrightarrow{\relbar\joinrel\rightarrow}
828 \def\longleftarrow{\leftarrow\joinrel\relbar}
829 \def\Longleftarrow{\Leftarrow\joinrel\Relbar}
830 \def\longmapsto{\mapstochar\longrightarrow}
831 \def\longleftrightarrow{\leftarrow\joinrel\rightarrow}
832 \def\Longleftrightarrow{\Leftarrow\joinrel\Rightarrow}
833 \def\iff{\;
\Longleftrightarrow\;
}
835 \mathchardef\ldotp="
613A
% ldot as a punctuation mark
836 \mathchardef\cdotp="
6201 % cdot as a punctuation mark
837 \mathchardef\colon="
603A
% colon as a punctuation mark
838 \def\ldots{\mathinner{\ldotp\ldotp\ldotp}}
839 \def\cdots{\mathinner{\cdotp\cdotp\cdotp}}
840 \def\vdots{\vbox{\baselineskip4\p@
\lineskiplimit\z@
841 \kern6\p@
\hbox{.
}\hbox{.
}\hbox{.
}}}
842 \def\ddots{\mathinner{\mkern1mu\raise7\p@
\vbox{\kern7\p@
\hbox{.
}}\mkern2mu
843 \raise4\p@
\hbox{.
}\mkern2mu\raise\p@
\hbox{.
}\mkern1mu}}
845 \def\acute{\mathaccent"
7013 }
846 \def\grave{\mathaccent"
7012 }
847 \def\ddot{\mathaccent"
707F
}
848 \def\tilde{\mathaccent"
707E
}
849 \def\bar{\mathaccent"
7016 }
850 \def\breve{\mathaccent"
7015 }
851 \def\check{\mathaccent"
7014 }
852 \def\hat{\mathaccent"
705E
}
853 \def\vec{\mathaccent"
017E
}
854 \def\dot{\mathaccent"
705F
}
855 \def\widetilde{\mathaccent"
0365 }
856 \def\widehat{\mathaccent"
0362 }
857 \def\overrightarrow#1{\vbox{\m@th
\ialign{##
\crcr
858 \rightarrowfill\crcr\noalign{\kern-
\p@
\nointerlineskip}
859 $
\hfil\displaystyle{#1}\hfil$
\crcr}}}
860 \def\overleftarrow#1{\vbox{\m@th
\ialign{##
\crcr
861 \leftarrowfill\crcr\noalign{\kern-
\p@
\nointerlineskip}
862 $
\hfil\displaystyle{#1}\hfil$
\crcr}}}
863 \def\overbrace#1{\mathop{\vbox{\m@th
\ialign{##
\crcr\noalign{\kern3\p@
}
864 \downbracefill\crcr\noalign{\kern3\p@
\nointerlineskip}
865 $
\hfil\displaystyle{#1}\hfil$
\crcr}}}\limits}
866 \def\underbrace#1{\mathop{\vtop{\m@th
\ialign{##
\crcr
867 $
\hfil\displaystyle{#1}\hfil$
\crcr\noalign{\kern3\p@
\nointerlineskip}
868 \upbracefill\crcr\noalign{\kern3\p@
}}}}\limits}
869 \def\skew#1#2#3{{\muskip\z@
#1mu
\divide\muskip\z@
\tw@
\mkern\muskip\z@
870 #2{\mkern-
\muskip\z@
{#3}\mkern\muskip\z@
}\mkern-
\muskip\z@
}{}}
872 \def\lmoustache{\delimiter"
437A340
} % top from (, bottom from )
873 \def\rmoustache{\delimiter"
537B341
} % top from ), bottom from (
874 \def\lgroup{\delimiter"
462833A
} % extensible ( with sharper tips
875 \def\rgroup{\delimiter"
562933B
} % extensible ) with sharper tips
876 \def\arrowvert{\delimiter"
26A33C
} % arrow without arrowheads
877 \def\Arrowvert{\delimiter"
26B33D
} % double arrow without arrowheads
878 \def\bracevert{\delimiter"
77C33E
} % the vertical bar that extends braces
879 \def\Vert{\delimiter"
26B30D
} \let\|=
\Vert
880 \def\vert{\delimiter"
26A30C
}
881 \def\uparrow{\delimiter"
3222378 }
882 \def\downarrow{\delimiter"
3223379 }
883 \def\updownarrow{\delimiter"
326C33F
}
884 \def\Uparrow{\delimiter"
322A37E
}
885 \def\Downarrow{\delimiter"
322B37F
}
886 \def\Updownarrow{\delimiter"
326D377
}
887 \def\backslash{\delimiter"
26E30F
} % for double coset G\backslash H
888 \def\rangle{\delimiter"
526930B
}
889 \def\langle{\delimiter"
426830A
}
890 \def\rbrace{\delimiter"
5267309 } \let\
}=
\rbrace
891 \def\lbrace{\delimiter"
4266308 } \let\
{=
\lbrace
892 \def\rceil{\delimiter"
5265307 }
893 \def\lceil{\delimiter"
4264306 }
894 \def\rfloor{\delimiter"
5263305 }
895 \def\lfloor{\delimiter"
4262304 }
897 \def\bigl{\mathopen\big}
898 \def\bigm{\mathrel\big}
899 \def\bigr{\mathclose\big}
900 \def\Bigl{\mathopen\Big}
901 \def\Bigm{\mathrel\Big}
902 \def\Bigr{\mathclose\Big}
903 \def\biggl{\mathopen\bigg}
904 \def\biggm{\mathrel\bigg}
905 \def\biggr{\mathclose\bigg}
906 \def\Biggl{\mathopen\Bigg}
907 \def\Biggm{\mathrel\Bigg}
908 \def\Biggr{\mathclose\Bigg}
909 \def\big#1{{\hbox{$
\left#1\vbox to8.5
\p@
{}\right.
\n@space$
}}}
910 \def\Big#1{{\hbox{$
\left#1\vbox to11.5
\p@
{}\right.
\n@space$
}}}
911 \def\bigg#1{{\hbox{$
\left#1\vbox to14.5
\p@
{}\right.
\n@space$
}}}
912 \def\Bigg#1{{\hbox{$
\left#1\vbox to17.5
\p@
{}\right.
\n@space$
}}}
913 \def\n@space
{\nulldelimiterspace\z@
\m@th
}
915 \def\choose{\atopwithdelims()
}
916 \def\brack{\atopwithdelims[]}
917 \def\brace{\atopwithdelims\
{\
}}
919 \def\sqrt{\radical"
270370 }
921 \def\mathpalette#1#2{\mathchoice{#1\displaystyle{#2}}%
922 {#1\textstyle{#2}}{#1\scriptstyle{#2}}{#1\scriptscriptstyle{#2}}}
924 \def\root#1\of{\setbox\rootbox
925 \hbox{$
\m@th
\scriptscriptstyle{#1}$
}\mathpalette\r@@t
}
926 \def\r@@t
#1#2{\setbox\z@
\hbox{$
\m@th
#1\sqrt{#2}$
}\dimen@
\ht\z@
927 \advance\dimen@-
\dp\z@
928 \mkern5mu\raise.6\dimen@
\copy\rootbox \mkern-
10mu
\box\z@
}
929 \newif\ifv@
\newif\ifh@
930 \def\vphantom{\v@true
\h@false
\ph@nt
}
931 \def\hphantom{\v@false
\h@true
\ph@nt
}
932 \def\phantom{\v@true
\h@true
\ph@nt
}
933 \def\ph@nt
{\ifmmode\def\next{\mathpalette\mathph@nt
}%
934 \else\let\next\makeph@nt
\fi\next}
935 \def\makeph@nt
#1{\setbox\z@
\hbox{#1}\finph@nt
}
936 \def\mathph@nt
#1#2{\setbox\z@
\hbox{$
\m@th
#1{#2}$
}\finph@nt
}
937 \def\finph@nt
{\setbox\tw@
\null
938 \ifv@
\ht\tw@
\ht\z@
\dp\tw@
\dp\z@
\fi
939 \ifh@
\wd\tw@
\wd\z@
\fi \box\tw@
}
940 \def\mathstrut{\vphantom(
}
941 \def\smash{\relax % \relax, in case this comes first in \halign
942 \ifmmode\def\next{\mathpalette\mathsm@sh
}\else\let\next\makesm@sh
944 \def\makesm@sh
#1{\setbox\z@
\hbox{#1}\finsm@sh
}
945 \def\mathsm@sh
#1#2{\setbox\z@
\hbox{$
\m@th
#1{#2}$
}\finsm@sh
}
946 \def\finsm@sh
{\ht\z@
\z@
\dp\z@
\z@
\box\z@
}
948 \def\cong{\mathrel{\mathpalette\@vereq
\sim}} % congruence sign
949 \def\@vereq
#1#2{\lower.5\p@
\vbox{\lineskiplimit\maxdimen\lineskip-
.5\p@
950 \ialign{$
\m@th
#1\hfil##
\hfil$
\crcr#2\crcr=
\crcr}}}
951 \def\notin{\mathrel{\mathpalette\c@ncel
\in}}
952 \def\c@ncel
#1#2{\m@th
\ooalign{$
\hfil#1\mkern1mu/
\hfil$
\crcr$
#1#2$
}}
953 \def\rightleftharpoons{\mathrel{\mathpalette\rlh@
{}}}
954 \def\rlh@
#1{\vcenter{\m@th
\hbox{\ooalign{\raise2pt
955 \hbox{$
#1\rightharpoonup$
}\crcr
956 $
#1\leftharpoondown$
}}}}
957 \def\buildrel#1\over#2{\mathrel{\mathop{\kern\z@
#2}\limits^
{#1}}}
958 \def\doteq{\buildrel\textstyle.
\over=
}
960 \def\log{\mathop{\rm log
}\nolimits}
961 \def\lg{\mathop{\rm lg
}\nolimits}
962 \def\ln{\mathop{\rm ln
}\nolimits}
963 \def\lim{\mathop{\rm lim
}}
964 \def\limsup{\mathop{\rm lim\,sup
}}
965 \def\liminf{\mathop{\rm lim\,inf
}}
966 \def\sin{\mathop{\rm sin
}\nolimits}
967 \def\arcsin{\mathop{\rm arcsin
}\nolimits}
968 \def\sinh{\mathop{\rm sinh
}\nolimits}
969 \def\cos{\mathop{\rm cos
}\nolimits}
970 \def\arccos{\mathop{\rm arccos
}\nolimits}
971 \def\cosh{\mathop{\rm cosh
}\nolimits}
972 \def\tan{\mathop{\rm tan
}\nolimits}
973 \def\arctan{\mathop{\rm arctan
}\nolimits}
974 \def\tanh{\mathop{\rm tanh
}\nolimits}
975 \def\cot{\mathop{\rm cot
}\nolimits}
976 \def\coth{\mathop{\rm coth
}\nolimits}
977 \def\sec{\mathop{\rm sec
}\nolimits}
978 \def\csc{\mathop{\rm csc
}\nolimits}
979 \def\max{\mathop{\rm max
}}
980 \def\min{\mathop{\rm min
}}
981 \def\sup{\mathop{\rm sup
}}
982 \def\inf{\mathop{\rm inf
}}
983 \def\arg{\mathop{\rm arg
}\nolimits}
984 \def\ker{\mathop{\rm ker
}\nolimits}
985 \def\dim{\mathop{\rm dim
}\nolimits}
986 \def\hom{\mathop{\rm hom
}\nolimits}
987 \def\det{\mathop{\rm det
}}
988 \def\exp{\mathop{\rm exp
}\nolimits}
989 \def\Pr{\mathop{\rm Pr
}}
990 \def\gcd{\mathop{\rm gcd
}}
991 \def\deg{\mathop{\rm deg
}\nolimits}
993 \def\bmod{\nonscript\mskip-
\medmuskip\mkern5mu
994 \mathbin{\rm mod
}\penalty900\mkern5mu\nonscript\mskip-
\medmuskip}
995 \def\pmod#1{\allowbreak\mkern18mu(
{\rm mod
}\,\,
#1)
}
997 \def\cases#1{\left\
{\,
\vcenter{\normalbaselines\m@th
998 \ialign{$##
\hfil$&
\quad##
\hfil\crcr#1\crcr}}\right.
}
999 \def\matrix#1{\null\,
\vcenter{\normalbaselines\m@th
1000 \ialign{\hfil$##$
\hfil&&
\quad\hfil$##$
\hfil\crcr
1001 \mathstrut\crcr\noalign{\kern-
\baselineskip}
1002 #1\crcr\mathstrut\crcr\noalign{\kern-
\baselineskip}}}\,
}
1003 \def\pmatrix#1{\left(
\matrix{#1}\right)
}
1005 % \setbox0=\hbox{\tenex B} \p@renwd=\wd0 % width of the big left (
1006 \p@renwd=
5pt
% width of the big left (
1007 \def\bordermatrix#1{\begingroup \m@th
1008 \setbox\z@
\vbox{\def\cr{\crcr\noalign{\kern2\p@
\global\let\cr\endline}}%
1009 \ialign{$##$
\hfil\kern2\p@
\kern\p@renwd&
\thinspace\hfil$##$
\hfil
1010 &&
\quad\hfil$##$
\hfil\crcr
1011 \omit\strut\hfil\crcr\noalign{\kern-
\baselineskip}%
1012 #1\crcr\omit\strut\cr}}%
1013 \setbox\tw@
\vbox{\unvcopy\z@
\global\setbox\@ne
\lastbox}%
1014 \setbox\tw@
\hbox{\unhbox\@ne
\unskip\global\setbox\@ne
\lastbox}%
1015 \setbox\tw@
\hbox{$
\kern\wd\@ne
\kern-
\p@renwd
\left(
\kern-
\wd\@ne
1016 \global\setbox\@ne
\vbox{\box\@ne
\kern2\p@
}%
1017 \vcenter{\kern-
\ht\@ne
\unvbox\z@
\kern-
\baselineskip}\,
\right)$
}%
1018 \null\;
\vbox{\kern\ht\@ne
\box\tw@
}\endgroup}
1020 \def\openup{\afterassignment\@penup
\dimen@=
}
1021 \def\@penup
{\advance\lineskip\dimen@
1022 \advance\baselineskip\dimen@
1023 \advance\lineskiplimit\dimen@
}
1024 \def\eqalign#1{\null\,
\vcenter{\openup\jot\m@th
1025 \ialign{\strut\hfil$
\displaystyle{##
}$&$
\displaystyle{{}##
}$
\hfil
1028 \def\displ@y
{\global\dt@ptrue
\openup\jot\m@th
1029 \everycr{\noalign{\ifdt@p
\global\dt@pfalse
\ifdim\prevdepth>-
1000\p@
1030 \vskip-
\lineskiplimit \vskip\normallineskiplimit \fi
1031 \else \penalty\interdisplaylinepenalty \fi}}}
1032 \def\@lign
{\tabskip\z@skip
\everycr{}} % restore inside \displ@y
1033 \def\displaylines#1{\displ@y
\tabskip\z@skip
1034 \halign{\hbox to
\displaywidth{$\@lign
\hfil\displaystyle##
\hfil$
}\crcr
1036 \def\eqalignno#1{\displ@y
\tabskip\centering
1037 \halign to
\displaywidth{\hfil$\@lign
\displaystyle{##
}$
\tabskip\z@skip
1038 &$\@lign
\displaystyle{{}##
}$
\hfil\tabskip\centering
1039 &
\llap{$\@lign##$
}\tabskip\z@skip
\crcr
1041 \def\leqalignno#1{\displ@y
\tabskip\centering
1042 \halign to
\displaywidth{\hfil$\@lign
\displaystyle{##
}$
\tabskip\z@skip
1043 &$\@lign
\displaystyle{{}##
}$
\hfil\tabskip\centering
1044 &
\kern-
\displaywidth\rlap{$\@lign##$
}\tabskip\displaywidth\crcr
1047 % Definitions related to output
1049 \message{output routines,
}
1051 \countdef\pageno=
0 \pageno=
1 % first page is number 1
1052 \newtoks\headline \headline=
{\hfil} % headline is normally blank
1053 \newtoks\footline \footline=
{\hfil} % footline is blank
1054 \newif\ifr@ggedbottom
1055 \def\raggedbottom{\topskip 10\p@ plus60
\p@
\r@ggedbottomtrue
}
1056 \def\normalbottom{\topskip 10\p@
\r@ggedbottomfalse
} % undoes \raggedbottom
1057 \def\folio{\ifnum\pageno<
\z@
\romannumeral-
\pageno \else\number\pageno \fi}
1058 \def\advancepageno{\ifnum\pageno<
\z@
\global\advance\pageno\m@ne
1059 \else\global\advance\pageno\@ne
\fi} % increase |pageno|
1062 \def\footnote#1{\let\@sf
\empty % parameter #2 (the text) is read later
1063 \ifhmode\edef\@sf
{\spacefactor\the\spacefactor}\/
\fi
1064 #1\@sf
\vfootnote{#1}}
1065 \def\vfootnote#1{\insert\footins\bgroup
1066 \interlinepenalty\interfootnotelinepenalty
1067 \splittopskip\ht\strutbox % top baseline for broken footnotes
1068 \splitmaxdepth\dp\strutbox \floatingpenalty\@MM
1069 \leftskip\z@skip
\rightskip\z@skip
\spaceskip\z@skip
\xspaceskip\z@skip
1070 \textindent{#1}\footstrut\futurelet\next\fo@t
}
1071 \def\fo@t
{\ifcat\bgroup\noexpand\next \let\next\f@@t
1072 \else\let\next\f@t
\fi \next}
1073 \def\f@@t
{\bgroup\aftergroup\@foot
\let\next}
1074 \def\f@t
#1{#1\@foot
}
1075 \def\@foot
{\strut\egroup}
1076 \def\footstrut{\vbox to
\splittopskip{}}
1077 \skip\footins=
\bigskipamount % space added when footnote is present
1078 \count\footins=
1000 % footnote magnification factor (1 to 1)
1079 \dimen\footins=
8in
% maximum footnotes per page
1082 \newif\ifp@ge
\newif\if@mid
1083 \def\topinsert{\@midfalse
\p@gefalse\@ins
}
1084 \def\midinsert{\@midtrue\@ins
}
1085 \def\pageinsert{\@midfalse
\p@getrue\@ins
}
1086 \skip\topins=
\z@skip
% no space added when a topinsert is present
1087 \count\topins=
1000 % magnification factor (1 to 1)
1088 \dimen\topins=
\maxdimen % no limit per page
1089 \def\@ins
{\par\begingroup\setbox\z@
\vbox\bgroup} % start a \vbox
1090 \def\endinsert{\egroup % finish the \vbox
1091 \if@mid
\dimen@
\ht\z@
\advance\dimen@
\dp\z@
\advance\dimen@
12\p@
1092 \advance\dimen@
\pagetotal \advance\dimen@-
\pageshrink
1093 \ifdim\dimen@>
\pagegoal\@midfalse
\p@gefalse
\fi\fi
1094 \if@mid
\bigskip\box\z@
\bigbreak
1095 \else\insert\topins{\penalty100 % floating insertion
1096 \splittopskip\z@skip
1097 \splitmaxdepth\maxdimen \floatingpenalty\z@
1098 \ifp@ge
\dimen@
\dp\z@
1099 \vbox to
\vsize{\unvbox\z@
\kern-
\dimen@
}% depth is zero
1100 \else \box\z@
\nobreak\bigskip\fi}\fi\endgroup}
1102 \output{\plainoutput}
1103 \def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}%
1105 \ifnum\outputpenalty>-\@MM
\else\dosupereject\fi}
1106 \def\pagebody{\vbox to
\vsize{\boxmaxdepth\maxdepth \pagecontents}}
1107 \def\makeheadline{\vbox to
\z@
{\vskip-
22.5\p@
1108 \line{\vbox to8.5
\p@
{}\the\headline}\vss}\nointerlineskip}
1109 \def\makefootline{\baselineskip24\p@
\lineskiplimit\z@
\line{\the\footline}}
1110 \def\dosupereject{\ifnum\insertpenalties>
\z@
% something is being held over
1111 \line{}\kern-
\topskip\nobreak\vfill\supereject\fi}
1113 \def\pagecontents{\ifvoid\topins\else\unvbox\topins\fi
1114 \dimen@=
\dp\@cclv
\unvbox\@cclv
% open up \box255
1115 \ifvoid\footins\else % footnote info is present
1119 \ifr@ggedbottom
\kern-
\dimen@
\vfil \fi}
1120 \def\footnoterule{\kern-
3\p@
1121 \hrule width
2truein
\kern 2.6\p@
} % the \hrule is .4pt high
1123 % Miscellaneous macros, and initial values for standard layout
1124 \message{hyphenation
}
1126 \lefthyphenmin=
2 \righthyphenmin=
3 % disallow x- or -xx breaks
1129 \def\magnification{\afterassignment\m@g
\count@
}
1130 \def\m@g
{\mag\count@
1131 \hsize6.5truein
\vsize8.9truein
\dimen\footins8truein}
1133 \def\loggingall{\tracingcommands\tw@
\tracingstats\tw@
1134 \tracingpages\@ne
\tracingoutput\@ne
\tracinglostchars\@ne
1135 \tracingmacros\tw@
\tracingparagraphs\@ne
\tracingrestores\@ne
1136 \showboxbreadth\maxdimen\showboxdepth\maxdimen}
1137 \def\tracingall{\tracingonline\@ne
\loggingall}
1139 \def\showhyphens#1{\setbox0\vbox{\parfillskip\z@skip
\hsize\maxdimen\tenrm
1140 \pretolerance\m@ne
\tolerance\m@ne
\hbadness0\showboxdepth0\
#1}}
1142 \normalbaselines % \rm % select roman font
1143 \nonfrenchspacing % punctuation affects the spacing
1144 \catcode`@=
12 % at signs are no longer letters
1146 % \def\fmtname{plain}\def\fmtversion{3.141592653} % identifies the current format
