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diff --git a/Build/source/texk/tests/texmf/plain.tex b/Build/source/texk/tests/texmf/plain.tex new file mode 100644 index 00000000000..2b72027dff8 --- /dev/null +++ b/Build/source/texk/tests/texmf/plain.tex @@ -0,0 +1,1241 @@ +% This is the plain TeX format that's described in The TeXbook. +% N.B.: A version number is defined at the very end of this file; +% please change that number whenever the file is modified! +% And don't modify the file unless you change its name: +% Everybody's "plain.tex" file should be the same, worldwide. + +% Unlimited copying and redistribution of this file are permitted as long +% as this file is not modified. Modifications are permitted, but only if +% the resulting file is not named plain.tex. + +\catcode`\{=1 % left brace is begin-group character +\catcode`\}=2 % right brace is end-group character +\catcode`\$=3 % dollar sign is math shift +\catcode`\&=4 % ampersand is alignment tab +\catcode`\#=6 % hash mark is macro parameter character +\catcode`\^=7 \catcode`\^^K=7 % circumflex and uparrow are for superscripts +\catcode`\_=8 \catcode`\^^A=8 % underline and downarrow are for subscripts +\catcode`\^^I=10 % ascii tab is a blank space +\chardef\active=13 \catcode`\~=\active % tilde is active +\catcode`\^^L=\active \outer\def^^L{\par} % ascii form-feed is "\outer\par" + +\message{Preloading the plain format: codes,} + +% We had to define the \catcodes right away, before the message line, +% since \message uses the { and } characters. +% When INITEX (the TeX initializer) starts up, +% it has defined the following \catcode values: +% \catcode`\^^@=9 % ascii null is ignored +% \catcode`\^^M=5 % ascii return is end-line +% \catcode`\\=0 % backslash is TeX escape character +% \catcode`\%=14 % percent sign is comment character +% \catcode`\ =10 % ascii space is blank space +% \catcode`\^^?=15 % ascii delete is invalid +% \catcode`\A=11 ... \catcode`\Z=11 % uppercase letters +% \catcode`\a=11 ... \catcode`\z=11 % lowercase letters +% all others are type 12 (other) + +% Here is a list of the characters that have been specially catcoded: +\def\dospecials{\do\ \do\\\do\{\do\}\do\$\do\&% + \do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~} +% (not counting ascii null, tab, linefeed, formfeed, return, delete) +% Each symbol in the list is preceded by \do, which can be defined +% if you want to do something to every item in the list. + +% We make @ signs act like letters, temporarily, to avoid conflict +% between user names and internal control sequences of plain format. +\catcode`@=11 + +% INITEX sets up \mathcode x=x, for x=0..255, except that +% \mathcode x=x+"7100, for x = `A to `Z and `a to `z; +% \mathcode x=x+"7000, for x = `0 to `9. +% The following changes define internal codes as recommended +% in Appendix C of The TeXbook: +\mathcode`\^^@="2201 % \cdot +\mathcode`\^^A="3223 % \downarrow +\mathcode`\^^B="010B % \alpha +\mathcode`\^^C="010C % \beta +\mathcode`\^^D="225E % \land +\mathcode`\^^E="023A % \lnot +\mathcode`\^^F="3232 % \in +\mathcode`\^^G="0119 % \pi +\mathcode`\^^H="0115 % \lambda +\mathcode`\^^I="010D % \gamma +\mathcode`\^^J="010E % \delta +\mathcode`\^^K="3222 % \uparrow +\mathcode`\^^L="2206 % \pm +\mathcode`\^^M="2208 % \oplus +\mathcode`\^^N="0231 % \infty +\mathcode`\^^O="0140 % \partial +\mathcode`\^^P="321A % \subset +\mathcode`\^^Q="321B % \supset +\mathcode`\^^R="225C % \cap +\mathcode`\^^S="225B % \cup +\mathcode`\^^T="0238 % \forall +\mathcode`\^^U="0239 % \exists +\mathcode`\^^V="220A % \otimes +\mathcode`\^^W="3224 % \leftrightarrow +\mathcode`\^^X="3220 % \leftarrow +\mathcode`\^^Y="3221 % \rightarrow +\mathcode`\^^Z="8000 % \ne +\mathcode`\^^[="2205 % \diamond +\mathcode`\^^\="3214 % \le +\mathcode`\^^]="3215 % \ge +\mathcode`\^^^="3211 % \equiv +\mathcode`\^^_="225F % \lor +\mathcode`\ ="8000 % \space +\mathcode`\!="5021 +\mathcode`\'="8000 % ^\prime +\mathcode`\(="4028 +\mathcode`\)="5029 +\mathcode`\*="2203 % \ast +\mathcode`\+="202B +\mathcode`\,="613B +\mathcode`\-="2200 +\mathcode`\.="013A +\mathcode`\/="013D +\mathcode`\:="303A +\mathcode`\;="603B +\mathcode`\<="313C +\mathcode`\=="303D +\mathcode`\>="313E +\mathcode`\?="503F +\mathcode`\[="405B +\mathcode`\\="026E % \backslash +\mathcode`\]="505D +\mathcode`\_="8000 % \_ +\mathcode`\{="4266 +\mathcode`\|="026A +\mathcode`\}="5267 +\mathcode`\^^?="1273 % \smallint + +% INITEX sets \uccode`x=`X and \uccode `X=`X for all letters x, +% and \lccode`x=`x, \lccode`X=`x; all other values are zero. +% No changes to those tables are needed in plain TeX format. + +% INITEX sets \sfcode x=1000 for all x, except that \sfcode`X=999 +% for uppercase letters. The following changes are needed: +\sfcode`\)=0 \sfcode`\'=0 \sfcode`\]=0 +% The \nonfrenchspacing macro will make further changes to \sfcode values. + +% Finally, INITEX sets all \delcode values to -1, except \delcode`.=0 +\delcode`\(="028300 +\delcode`\)="029301 +\delcode`\[="05B302 +\delcode`\]="05D303 +\delcode`\<="26830A +\delcode`\>="26930B +\delcode`\/="02F30E +\delcode`\|="26A30C +\delcode`\\="26E30F +% N.B. { and } should NOT get delcodes; otherwise parameter grouping fails! + +% To make the plain macros more efficient in time and space, +% several constant values are declared here as control sequences. +% If they were changed, anything could happen; so they are private symbols. +\chardef\@ne=1 +\chardef\tw@=2 +\chardef\thr@@=3 +\chardef\sixt@@n=16 +\chardef\@cclv=255 +\mathchardef\@cclvi=256 +\mathchardef\@m=1000 +\mathchardef\@M=10000 +\mathchardef\@MM=20000 + +% Allocation of registers + +% Here are macros for the automatic allocation of \count, \box, \dimen, +% \skip, \muskip, and \toks registers, as well as \read and \write +% stream numbers, \fam codes, \language codes, and \insert numbers. + +\message{registers,} + +% When a register is used only temporarily, it need not be allocated; +% grouping can be used, making the value previously in the register return +% after the close of the group. The main use of these macros is for +% registers that are defined by one macro and used by others, possibly at +% different nesting levels. All such registers should be defined through +% these macros; otherwise conflicts may occur, especially when two or more +% macro packages are being used at once. + +% The following counters are reserved: +% 0 to 9 page numbering +% 10 count allocation +% 11 dimen allocation +% 12 skip allocation +% 13 muskip allocation +% 14 box allocation +% 15 toks allocation +% 16 read file allocation +% 17 write file allocation +% 18 math family allocation +% 19 language allocation +% 20 insert allocation +% 21 the most recently allocated number +% 22 constant -1 +% New counters are allocated starting with 23, 24, etc. Other registers are +% allocated starting with 10. This leaves 0 through 9 for the user to play +% with safely, except that counts 0 to 9 are considered to be the page and +% subpage numbers (since they are displayed during output). In this scheme, +% \count 10 always contains the number of the highest-numbered counter that +% has been allocated, \count 14 the highest-numbered box, etc. +% Inserts are given numbers 254, 253, etc., since they require a \count, +% \dimen, \skip, and \box all with the same number; \count 20 contains the +% lowest-numbered insert that has been allocated. Of course, \box255 is +% reserved for \output; \count255, \dimen255, and \skip255 can be used freely. + +% It is recommended that macro designers always use +% \global assignments with respect to registers numbered 1, 3, 5, 7, 9, and +% always non-\global assignments with respect to registers 0, 2, 4, 6, 8, 255. +% This will prevent ``save stack buildup'' that might otherwise occur. + +\count10=22 % allocates \count registers 23, 24, ... +\count11=9 % allocates \dimen registers 10, 11, ... +\count12=9 % allocates \skip registers 10, 11, ... +\count13=9 % allocates \muskip registers 10, 11, ... +\count14=9 % allocates \box registers 10, 11, ... +\count15=9 % allocates \toks registers 10, 11, ... +\count16=-1 % allocates input streams 0, 1, ... +\count17=-1 % allocates output streams 0, 1, ... +\count18=3 % allocates math families 4, 5, ... +\count19=0 % allocates \language codes 1, 2, ... +\count20=255 % allocates insertions 254, 253, ... +\countdef\insc@unt=20 % the insertion counter +\countdef\allocationnumber=21 % the most recent allocation +\countdef\m@ne=22 \m@ne=-1 % a handy constant +\def\wlog{\immediate\write\m@ne} % write on log file (only) + +% Here are abbreviations for the names of scratch registers +% that don't need to be allocated. + +\countdef\count@=255 +\dimendef\dimen@=0 +\dimendef\dimen@i=1 % global only +\dimendef\dimen@ii=2 +\skipdef\skip@=0 +\toksdef\toks@=0 + +% Now, we define \newcount, \newbox, etc. so that you can say \newcount\foo +% and \foo will be defined (with \countdef) to be the next counter. +% To find out which counter \foo is, you can look at \allocationnumber. +% Since there's no \boxdef command, \chardef is used to define a \newbox, +% \newinsert, \newfam, and so on. + +\outer\def\newcount{\alloc@0\count\countdef\insc@unt} +\outer\def\newdimen{\alloc@1\dimen\dimendef\insc@unt} +\outer\def\newskip{\alloc@2\skip\skipdef\insc@unt} +\outer\def\newmuskip{\alloc@3\muskip\muskipdef\@cclvi} +\outer\def\newbox{\alloc@4\box\chardef\insc@unt} +\let\newtoks=\relax % we do this to allow plain.tex to be read in twice +\outer\def\newhelp#1#2{\newtoks#1#1\expandafter{\csname#2\endcsname}} +\outer\def\newtoks{\alloc@5\toks\toksdef\@cclvi} +\outer\def\newread{\alloc@6\read\chardef\sixt@@n} +\outer\def\newwrite{\alloc@7\write\chardef\sixt@@n} +\outer\def\newfam{\alloc@8\fam\chardef\sixt@@n} +\outer\def\newlanguage{\alloc@9\language\chardef\@cclvi} +\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne + \ch@ck#1#4#2% make sure there's still room + \allocationnumber=\count1#1% + \global#3#5=\allocationnumber + \wlog{\string#5=\string#2\the\allocationnumber}} +\outer\def\newinsert#1{\global\advance\insc@unt by\m@ne + \ch@ck0\insc@unt\count + \ch@ck1\insc@unt\dimen + \ch@ck2\insc@unt\skip + \ch@ck4\insc@unt\box + \allocationnumber=\insc@unt + \global\chardef#1=\allocationnumber + \wlog{\string#1=\string\insert\the\allocationnumber}} +\def\ch@ck#1#2#3{\ifnum\count1#1<#2% + \else\errmessage{No room for a new #3}\fi} + +% Here are some examples of allocation. +\newdimen\maxdimen \maxdimen=16383.99999pt % the largest legal <dimen> +\newskip\hideskip \hideskip=-1000pt plus 1fill % negative but can grow +\newskip\centering \centering=0pt plus 1000pt minus 1000pt +\newdimen\p@ \p@=1pt % this saves macro space and time +\newdimen\z@ \z@=0pt % can be used both for 0pt and 0 +\newskip\z@skip \z@skip=0pt plus0pt minus0pt +\newbox\voidb@x % permanently void box register + +% And here's a different sort of allocation: +% For example, \newif\iffoo creates \footrue, \foofalse to go with \iffoo. +\outer\def\newif#1{\count@\escapechar \escapechar\m@ne + \expandafter\expandafter\expandafter + \def\@if#1{true}{\let#1=\iftrue}% + \expandafter\expandafter\expandafter + \def\@if#1{false}{\let#1=\iffalse}% + \@if#1{false}\escapechar\count@} % the condition starts out false +\def\@if#1#2{\csname\expandafter\if@\string#1#2\endcsname} +{\uccode`1=`i \uccode`2=`f \uppercase{\gdef\if@12{}}} % `if' is required + +% Assign initial values to TeX's parameters + +\message{parameters,} + +% All of TeX's numeric parameters are listed here, +% but the code is commented out if no special value needs to be set. +% INITEX makes all parameters zero except where noted. + +\pretolerance=100 +\tolerance=200 % INITEX sets this to 10000 +\hbadness=1000 +\vbadness=1000 +\linepenalty=10 +\hyphenpenalty=50 +\exhyphenpenalty=50 +\binoppenalty=700 +\relpenalty=500 +\clubpenalty=150 +\widowpenalty=150 +\displaywidowpenalty=50 +\brokenpenalty=100 +\predisplaypenalty=10000 +% \postdisplaypenalty=0 +% \interlinepenalty=0 +% \floatingpenalty=0, set during \insert +% \outputpenalty=0, set before TeX enters \output +\doublehyphendemerits=10000 +\finalhyphendemerits=5000 +\adjdemerits=10000 +% \looseness=0, cleared by TeX after each paragraph +% \pausing=0 +% \holdinginserts=0 +% \tracingonline=0 +% \tracingmacros=0 +% \tracingstats=0 +% \tracingparagraphs=0 +% \tracingpages=0 +% \tracingoutput=0 +\tracinglostchars=1 +% \tracingcommands=0 +% \tracingrestores=0 +% \language=0 +\uchyph=1 +% \lefthyphenmin=2 \righthyphenmin=3 set below +% \globaldefs=0 +% \maxdeadcycles=25 % INITEX does this +% \hangafter=1 % INITEX does this, also TeX after each paragraph +% \fam=0 +% \mag=1000 % INITEX does this +% \escapechar=`\\ % INITEX does this +\defaulthyphenchar=`\- +\defaultskewchar=-1 +% \endlinechar=`\^^M % INITEX does this +\newlinechar=-1 +\delimiterfactor=901 +% \time=now % TeX does this at beginning of job +% \day=now % TeX does this at beginning of job +% \month=now % TeX does this at beginning of job +% \year=now % TeX does this at beginning of job +\showboxbreadth=5 +\showboxdepth=3 +\errorcontextlines=5 + +\hfuzz=0.1pt +\vfuzz=0.1pt +\overfullrule=5pt +\hsize=6.5in +\vsize=8.9in +\maxdepth=4pt +\splitmaxdepth=\maxdimen +\boxmaxdepth=\maxdimen +% \lineskiplimit=0pt, changed by \normalbaselines +\delimitershortfall=5pt +\nulldelimiterspace=1.2pt +\scriptspace=0.5pt +% \mathsurround=0pt +% \predisplaysize=0pt, set before TeX enters $$ +% \displaywidth=0pt, set before TeX enters $$ +% \displayindent=0pt, set before TeX enters $$ +\parindent=20pt +% \hangindent=0pt, zeroed by TeX after each paragraph +% \hoffset=0pt +% \voffset=0pt + +% \baselineskip=0pt, changed by \normalbaselines +% \lineskip=0pt, changed by \normalbaselines +\parskip=0pt plus 1pt +\abovedisplayskip=12pt plus 3pt minus 9pt +\abovedisplayshortskip=0pt plus 3pt +\belowdisplayskip=12pt plus 3pt minus 9pt +\belowdisplayshortskip=7pt plus 3pt minus 4pt +% \leftskip=0pt +% \rightskip=0pt +\topskip=10pt +\splittopskip=10pt +% \tabskip=0pt +% \spaceskip=0pt +% \xspaceskip=0pt +\parfillskip=0pt plus 1fil + +\thinmuskip=3mu +\medmuskip=4mu plus 2mu minus 4mu +\thickmuskip=5mu plus 5mu + +% We also define special registers that function like parameters: +\newskip\smallskipamount \smallskipamount=3pt plus 1pt minus 1pt +\newskip\medskipamount \medskipamount=6pt plus 2pt minus 2pt +\newskip\bigskipamount \bigskipamount=12pt plus 4pt minus 4pt +\newskip\normalbaselineskip \normalbaselineskip=12pt +\newskip\normallineskip \normallineskip=1pt +\newdimen\normallineskiplimit \normallineskiplimit=0pt +\newdimen\jot \jot=3pt +\newcount\interdisplaylinepenalty \interdisplaylinepenalty=100 +\newcount\interfootnotelinepenalty \interfootnotelinepenalty=100 + +% Definitions for preloaded fonts + +\def\magstephalf{1095 } +\def\magstep#1{\ifcase#1 \@m\or 1200\or 1440\or 1728\or 2074\or 2488\fi\relax} + +% Fonts assigned to \preloaded are not part of "plain TeX", +% but they are preloaded so that other format packages can use them. +% For example, if another set of macros says "\font\ninerm=cmr9", +% TeX will not have to reload the font metric information for cmr9. + +\message{fonts,} + +\font\tenrm=cmr10 % roman text +\font\preloaded=cmr9 +\font\preloaded=cmr8 +\font\sevenrm=cmr7 +\font\preloaded=cmr6 +\font\fiverm=cmr5 + +\font\teni=cmmi10 % math italic +\font\preloaded=cmmi9 +\font\preloaded=cmmi8 +\font\seveni=cmmi7 +\font\preloaded=cmmi6 +\font\fivei=cmmi5 + +\font\tensy=cmsy10 % math symbols +\font\preloaded=cmsy9 +\font\preloaded=cmsy8 +\font\sevensy=cmsy7 +\font\preloaded=cmsy6 +\font\fivesy=cmsy5 + +\font\tenex=cmex10 % math extension + +\font\preloaded=cmss10 % sans serif +\font\preloaded=cmssq8 + +\font\preloaded=cmssi10 % sans serif italic +\font\preloaded=cmssqi8 + +\font\tenbf=cmbx10 % boldface extended +\font\preloaded=cmbx9 +\font\preloaded=cmbx8 +\font\sevenbf=cmbx7 +\font\preloaded=cmbx6 +\font\fivebf=cmbx5 + +\font\tentt=cmtt10 % typewriter +\font\preloaded=cmtt9 +\font\preloaded=cmtt8 + +\font\preloaded=cmsltt10 % slanted typewriter + +\font\tensl=cmsl10 % slanted roman +\font\preloaded=cmsl9 +\font\preloaded=cmsl8 + +\font\tenit=cmti10 % text italic +\font\preloaded=cmti9 +\font\preloaded=cmti8 +\font\preloaded=cmti7 + +\message{more fonts,} +\font\preloaded=cmu10 % unslanted text italic + +\font\preloaded=cmmib10 % bold math italic +\font\preloaded=cmbsy10 % bold math symbols + +\font\preloaded=cmcsc10 % caps and small caps + +\font\preloaded=cmssbx10 % sans serif bold extended + +\font\preloaded=cmdunh10 % Dunhill style + +\font\preloaded=cmr7 scaled \magstep4 % for titles +\font\preloaded=cmtt10 scaled \magstep2 +\font\preloaded=cmssbx10 scaled \magstep2 + +\font\preloaded=manfnt % METAFONT logo and dragon curve and special symbols + +% Additional \preloaded fonts can be specified here. +% (And those that were \preloaded above can be eliminated.) + +\let\preloaded=\undefined % preloaded fonts must be declared anew later. + +\skewchar\teni='177 \skewchar\seveni='177 \skewchar\fivei='177 +\skewchar\tensy='60 \skewchar\sevensy='60 \skewchar\fivesy='60 + +\textfont0=\tenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm +\def\rm{\fam\z@\tenrm} +\textfont1=\teni \scriptfont1=\seveni \scriptscriptfont1=\fivei +\def\mit{\fam\@ne} \def\oldstyle{\fam\@ne\teni} +\textfont2=\tensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy +\def\cal{\fam\tw@} +\textfont3=\tenex \scriptfont3=\tenex \scriptscriptfont3=\tenex +\newfam\itfam \def\it{\fam\itfam\tenit} % \it is family 4 +\textfont\itfam=\tenit +\newfam\slfam \def\sl{\fam\slfam\tensl} % \sl is family 5 +\textfont\slfam=\tensl +\newfam\bffam \def\bf{\fam\bffam\tenbf} % \bf is family 6 +\textfont\bffam=\tenbf \scriptfont\bffam=\sevenbf +\scriptscriptfont\bffam=\fivebf +\newfam\ttfam \def\tt{\fam\ttfam\tentt} % \tt is family 7 +\textfont\ttfam=\tentt + +% Macros for setting ordinary text +\message{macros,} + +\def\frenchspacing{\sfcode`\.\@m \sfcode`\?\@m \sfcode`\!\@m + \sfcode`\:\@m \sfcode`\;\@m \sfcode`\,\@m} +\def\nonfrenchspacing{\sfcode`\.3000\sfcode`\?3000\sfcode`\!3000% + \sfcode`\:2000\sfcode`\;1500\sfcode`\,1250 } + +\def\normalbaselines{\lineskip\normallineskip + \baselineskip\normalbaselineskip \lineskiplimit\normallineskiplimit} + +\def\^^M{\ } % control <return> = control <space> +\def\^^I{\ } % same for <tab> + +\def\lq{`} \def\rq{'} +\def\lbrack{[} \def\rbrack{]} + +\let\endgraf=\par \let\endline=\cr + +\def\space{ } +\def\empty{} +\def\null{\hbox{}} + +\let\bgroup={ \let\egroup=} + +% In \obeylines, we say `\let^^M=\par' instead of `\def^^M{\par}' +% since this allows, for example, `\let\par=\cr \obeylines \halign{...' +{\catcode`\^^M=\active % these lines must end with % + \gdef\obeylines{\catcode`\^^M\active \let^^M\par}% + \global\let^^M\par} % this is in case ^^M appears in a \write +\def\obeyspaces{\catcode`\ \active} +{\obeyspaces\global\let =\space} + +\def\loop#1\repeat{\def\body{#1}\iterate} +\def\iterate{\body \let\next\iterate \else\let\next\relax\fi \next} +\let\repeat=\fi % this makes \loop...\if...\repeat skippable + +\def\thinspace{\kern .16667em } +\def\negthinspace{\kern-.16667em } +\def\enspace{\kern.5em } + +\def\enskip{\hskip.5em\relax} +\def\quad{\hskip1em\relax} +\def\qquad{\hskip2em\relax} + +\def\smallskip{\vskip\smallskipamount} +\def\medskip{\vskip\medskipamount} +\def\bigskip{\vskip\bigskipamount} + +\def\nointerlineskip{\prevdepth-1000\p@} +\def\offinterlineskip{\baselineskip-1000\p@ + \lineskip\z@ \lineskiplimit\maxdimen} + +\def\topglue{\nointerlineskip\vglue-\topskip\vglue} % for top of page +\def\vglue{\afterassignment\vgl@\skip@=} +\def\vgl@{\par \dimen@\prevdepth \hrule height\z@ + \nobreak\vskip\skip@ \prevdepth\dimen@} +\def\hglue{\afterassignment\hgl@\skip@=} +\def\hgl@{\leavevmode \count@\spacefactor \vrule width\z@ + \nobreak\hskip\skip@ \spacefactor\count@} + +\def~{\penalty\@M \ } % tie +\def\slash{/\penalty\exhyphenpenalty} % a `/' that acts like a `-' + +\def\break{\penalty-\@M} +\def\nobreak{\penalty \@M} +\def\allowbreak{\penalty \z@} + +\def\filbreak{\par\vfil\penalty-200\vfilneg} +\def\goodbreak{\par\penalty-500 } +\def\eject{\par\break} +\def\supereject{\par\penalty-\@MM} + +\def\removelastskip{\ifdim\lastskip=\z@\else\vskip-\lastskip\fi} +\def\smallbreak{\par\ifdim\lastskip<\smallskipamount + \removelastskip\penalty-50\smallskip\fi} +\def\medbreak{\par\ifdim\lastskip<\medskipamount + \removelastskip\penalty-100\medskip\fi} +\def\bigbreak{\par\ifdim\lastskip<\bigskipamount + \removelastskip\penalty-200\bigskip\fi} + +\def\line{\hbox to\hsize} +\def\leftline#1{\line{#1\hss}} +\def\rightline#1{\line{\hss#1}} +\def\centerline#1{\line{\hss#1\hss}} + +\def\rlap#1{\hbox to\z@{#1\hss}} +\def\llap#1{\hbox to\z@{\hss#1}} + +\def\m@th{\mathsurround\z@} +\def\underbar#1{$\setbox\z@\hbox{#1}\dp\z@\z@ + \m@th \underline{\box\z@}$} + +\newbox\strutbox +\setbox\strutbox=\hbox{\vrule height8.5pt depth3.5pt width\z@} +\def\strut{\relax\ifmmode\copy\strutbox\else\unhcopy\strutbox\fi} + +\def\hidewidth{\hskip\hideskip} % for alignment entries that can stick out +\def\ialign{\everycr{}\tabskip\z@skip\halign} % initialized \halign +\newcount\mscount +\def\multispan#1{\omit \mscount#1\relax + \loop\ifnum\mscount>\@ne \sp@n\repeat} +\def\sp@n{\span\omit\advance\mscount\m@ne} + +\newif\ifus@ \newif\if@cr +\newbox\tabs \newbox\tabsyet \newbox\tabsdone + +\def\cleartabs{\global\setbox\tabsyet\null \setbox\tabs\null} +\def\settabs{\setbox\tabs\null \futurelet\next\sett@b} +\let\+=\relax % in case this file is being read in twice +\def\sett@b{\ifx\next\+\def\nxt{\afterassignment\s@tt@b\let\nxt}% + \else\let\nxt\s@tcols\fi \let\next\relax \nxt} +\def\s@tt@b{\let\nxt\relax \us@false\m@ketabbox} +\def\tabalign{\us@true\m@ketabbox} % non-\outer version of \+ +\outer\def\+{\tabalign} +\def\s@tcols#1\columns{\count@#1\dimen@\hsize + \loop\ifnum\count@>\z@ \@nother \repeat} +\def\@nother{\dimen@ii\dimen@ \divide\dimen@ii\count@ + \setbox\tabs\hbox{\hbox to\dimen@ii{}\unhbox\tabs}% + \advance\dimen@-\dimen@ii \advance\count@\m@ne} + +\def\m@ketabbox{\begingroup + \global\setbox\tabsyet\copy\tabs + \global\setbox\tabsdone\null + \def\cr{\@crtrue\crcr\egroup\egroup + \ifus@\unvbox\z@\lastbox\fi\endgroup + \setbox\tabs\hbox{\unhbox\tabsyet\unhbox\tabsdone}}% + \setbox\z@\vbox\bgroup\@crfalse + \ialign\bgroup&\t@bbox##\t@bb@x\crcr} + +\def\t@bbox{\setbox\z@\hbox\bgroup} +\def\t@bb@x{\if@cr\egroup % now \box\z@ holds the column + \else\hss\egroup \global\setbox\tabsyet\hbox{\unhbox\tabsyet + \global\setbox\@ne\lastbox}% now \box\@ne holds its size + \ifvoid\@ne\global\setbox\@ne\hbox to\wd\z@{}% + \else\setbox\z@\hbox to\wd\@ne{\unhbox\z@}\fi + \global\setbox\tabsdone\hbox{\box\@ne\unhbox\tabsdone}\fi + \box\z@} + +\def\hang{\hangindent\parindent} +\def\textindent#1{\indent\llap{#1\enspace}\ignorespaces} +\def\item{\par\hang\textindent} +\def\itemitem{\par\indent \hangindent2\parindent \textindent} +\def\narrower{\advance\leftskip\parindent + \advance\rightskip\parindent} + +\outer\def\beginsection#1\par{\vskip\z@ plus.3\vsize\penalty-250 + \vskip\z@ plus-.3\vsize\bigskip\vskip\parskip + \message{#1}\leftline{\bf#1}\nobreak\smallskip\noindent} +\outer\def\proclaim #1. #2\par{\medbreak + \noindent{\bf#1.\enspace}{\sl#2\par}% + \ifdim\lastskip<\medskipamount \removelastskip\penalty55\medskip\fi} + +\def\raggedright{\rightskip\z@ plus2em \spaceskip.3333em \xspaceskip.5em\relax} +\def\ttraggedright{\tt\rightskip\z@ plus2em\relax} % for use with \tt only + +\chardef\%=`\% +\chardef\&=`\& +\chardef\#=`\# +\chardef\$=`\$ +\chardef\ss="19 +\chardef\ae="1A +\chardef\oe="1B +\chardef\o="1C +\chardef\AE="1D +\chardef\OE="1E +\chardef\O="1F +\chardef\i="10 \chardef\j="11 % dotless letters +\def\aa{\accent23a} +\def\l{\char32l} +\def\L{\leavevmode\setbox0\hbox{L}\hbox to\wd0{\hss\char32L}} + +\def\leavevmode{\unhbox\voidb@x} % begins a paragraph, if necessary +\def\_{\leavevmode \kern.06em \vbox{\hrule width.3em}} +\def\AA{\leavevmode\setbox0\hbox{!}\dimen@\ht0\advance\dimen@-1ex% + \rlap{\raise.67\dimen@\hbox{\char'27}}A} + +\def\mathhexbox#1#2#3{\leavevmode + \hbox{$\m@th \mathchar"#1#2#3$}} +\def\dag{\mathhexbox279} +\def\ddag{\mathhexbox27A} +\def\S{\mathhexbox278} +\def\P{\mathhexbox27B} +\def\Orb{\mathhexbox20D} + +\def\oalign#1{\leavevmode\vtop{\baselineskip\z@skip \lineskip.25ex% + \ialign{##\crcr#1\crcr}}} \def\o@lign{\lineskiplimit\z@ \oalign} +\def\ooalign{\lineskiplimit-\maxdimen \oalign} % chars over each other +{\catcode`p=12 \catcode`t=12 \gdef\\#1pt{#1}} \let\getf@ctor=\\ +\def\sh@ft#1{\dimen@#1\kern\expandafter\getf@ctor\the\fontdimen1\font + \dimen@} % kern by #1 times the current slant +\def\d#1{{\o@lign{\relax#1\crcr\hidewidth\sh@ft{-1ex}.\hidewidth}}} +\def\b#1{{\o@lign{\relax#1\crcr\hidewidth\sh@ft{-3ex}% + \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}} +\def\c#1{{\setbox\z@\hbox{#1}\ifdim\ht\z@=1ex\accent24 #1% + \else\ooalign{\unhbox\z@\crcr\hidewidth\char24\hidewidth}\fi}} +\def\copyright{{\ooalign{\hfil\raise.07ex\hbox{c}\hfil\crcr\Orb}}} + +\def\dots{\relax\ifmmode\ldots\else$\m@th\ldots\,$\fi} +\def\TeX{T\kern-.1667em\lower.5ex\hbox{E}\kern-.125emX} + +\def\`#1{{\accent18 #1}} +\def\'#1{{\accent19 #1}} +\def\v#1{{\accent20 #1}} \let\^^_=\v +\def\u#1{{\accent21 #1}} \let\^^S=\u +\def\=#1{{\accent22 #1}} +\def\^#1{{\accent94 #1}} \let\^^D=\^ +\def\.#1{{\accent95 #1}} +\def\H#1{{\accent"7D #1}} +\def\~#1{{\accent"7E #1}} +\def\"#1{{\accent"7F #1}} +\def\t#1{{\edef\next{\the\font}\the\textfont1\accent"7F\next#1}} + +\def\hrulefill{\leaders\hrule\hfill} +\def\dotfill{\cleaders\hbox{$\m@th \mkern1.5mu.\mkern1.5mu$}\hfill} +\def\rightarrowfill{$\m@th\smash-\mkern-7mu% + \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill + \mkern-7mu\mathord\rightarrow$} +\def\leftarrowfill{$\m@th\mathord\leftarrow\mkern-7mu% + \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill + \mkern-7mu\smash-$} +\mathchardef\braceld="37A \mathchardef\bracerd="37B +\mathchardef\bracelu="37C \mathchardef\braceru="37D +\def\downbracefill{$\m@th \setbox\z@\hbox{$\braceld$}% + \braceld\leaders\vrule height\ht\z@ depth\z@\hfill\braceru + \bracelu\leaders\vrule height\ht\z@ depth\z@\hfill\bracerd$} +\def\upbracefill{$\m@th \setbox\z@\hbox{$\braceld$}% + \bracelu\leaders\vrule height\ht\z@ depth\z@\hfill\bracerd + \braceld\leaders\vrule height\ht\z@ depth\z@\hfill\braceru$} + +\outer\def\bye{\par\vfill\supereject\end} + +% Macros for math setting +\message{math definitions,} + +\let\sp=^ \let\sb=_ +\def\,{\mskip\thinmuskip} +\def\>{\mskip\medmuskip} +\def\;{\mskip\thickmuskip} +\def\!{\mskip-\thinmuskip} +\def\*{\discretionary{\thinspace\the\textfont2\char2}{}{}} +{\catcode`\'=\active \gdef'{^\bgroup\prim@s}} +\def\prim@s{\prime\futurelet\next\pr@m@s} +\def\pr@m@s{\ifx'\next\let\nxt\pr@@@s \else\ifx^\next\let\nxt\pr@@@t + \else\let\nxt\egroup\fi\fi \nxt} +\def\pr@@@s#1{\prim@s} \def\pr@@@t#1#2{#2\egroup} +{\catcode`\^^Z=\active \gdef^^Z{\not=}} % ^^Z is like \ne in math + +{\catcode`\_=\active \global\let_=\_} % _ in math is either subscript or \_ + +\mathchardef\alpha="010B +\mathchardef\beta="010C +\mathchardef\gamma="010D +\mathchardef\delta="010E +\mathchardef\epsilon="010F +\mathchardef\zeta="0110 +\mathchardef\eta="0111 +\mathchardef\theta="0112 +\mathchardef\iota="0113 +\mathchardef\kappa="0114 +\mathchardef\lambda="0115 +\mathchardef\mu="0116 +\mathchardef\nu="0117 +\mathchardef\xi="0118 +\mathchardef\pi="0119 +\mathchardef\rho="011A +\mathchardef\sigma="011B +\mathchardef\tau="011C +\mathchardef\upsilon="011D +\mathchardef\phi="011E +\mathchardef\chi="011F +\mathchardef\psi="0120 +\mathchardef\omega="0121 +\mathchardef\varepsilon="0122 +\mathchardef\vartheta="0123 +\mathchardef\varpi="0124 +\mathchardef\varrho="0125 +\mathchardef\varsigma="0126 +\mathchardef\varphi="0127 +\mathchardef\Gamma="7000 +\mathchardef\Delta="7001 +\mathchardef\Theta="7002 +\mathchardef\Lambda="7003 +\mathchardef\Xi="7004 +\mathchardef\Pi="7005 +\mathchardef\Sigma="7006 +\mathchardef\Upsilon="7007 +\mathchardef\Phi="7008 +\mathchardef\Psi="7009 +\mathchardef\Omega="700A + +\mathchardef\aleph="0240 +\def\hbar{{\mathchar'26\mkern-9muh}} +\mathchardef\imath="017B +\mathchardef\jmath="017C +\mathchardef\ell="0160 +\mathchardef\wp="017D +\mathchardef\Re="023C +\mathchardef\Im="023D +\mathchardef\partial="0140 +\mathchardef\infty="0231 +\mathchardef\prime="0230 +\mathchardef\emptyset="023B +\mathchardef\nabla="0272 +\def\surd{{\mathchar"1270}} +\mathchardef\top="023E +\mathchardef\bot="023F +\def\angle{{\vbox{\ialign{$\m@th\scriptstyle##$\crcr + \not\mathrel{\mkern14mu}\crcr + \noalign{\nointerlineskip} + \mkern2.5mu\leaders\hrule height.34pt\hfill\mkern2.5mu\crcr}}}} +\mathchardef\triangle="0234 +\mathchardef\forall="0238 +\mathchardef\exists="0239 +\mathchardef\neg="023A \let\lnot=\neg +\mathchardef\flat="015B +\mathchardef\natural="015C +\mathchardef\sharp="015D +\mathchardef\clubsuit="027C +\mathchardef\diamondsuit="027D +\mathchardef\heartsuit="027E +\mathchardef\spadesuit="027F + +\mathchardef\coprod="1360 +\mathchardef\bigvee="1357 +\mathchardef\bigwedge="1356 +\mathchardef\biguplus="1355 +\mathchardef\bigcap="1354 +\mathchardef\bigcup="1353 +\mathchardef\intop="1352 \def\int{\intop\nolimits} +\mathchardef\prod="1351 +\mathchardef\sum="1350 +\mathchardef\bigotimes="134E +\mathchardef\bigoplus="134C +\mathchardef\bigodot="134A +\mathchardef\ointop="1348 \def\oint{\ointop\nolimits} +\mathchardef\bigsqcup="1346 +\mathchardef\smallint="1273 + +\mathchardef\triangleleft="212F +\mathchardef\triangleright="212E +\mathchardef\bigtriangleup="2234 +\mathchardef\bigtriangledown="2235 +\mathchardef\wedge="225E \let\land=\wedge +\mathchardef\vee="225F \let\lor=\vee +\mathchardef\cap="225C +\mathchardef\cup="225B +\mathchardef\ddagger="227A +\mathchardef\dagger="2279 +\mathchardef\sqcap="2275 +\mathchardef\sqcup="2274 +\mathchardef\uplus="225D +\mathchardef\amalg="2271 +\mathchardef\diamond="2205 +\mathchardef\bullet="220F +\mathchardef\wr="226F +\mathchardef\div="2204 +\mathchardef\odot="220C +\mathchardef\oslash="220B +\mathchardef\otimes="220A +\mathchardef\ominus="2209 +\mathchardef\oplus="2208 +\mathchardef\mp="2207 +\mathchardef\pm="2206 +\mathchardef\circ="220E +\mathchardef\bigcirc="220D +\mathchardef\setminus="226E % for set difference A\setminus B +\mathchardef\cdot="2201 +\mathchardef\ast="2203 +\mathchardef\times="2202 +\mathchardef\star="213F + +\mathchardef\propto="322F +\mathchardef\sqsubseteq="3276 +\mathchardef\sqsupseteq="3277 +\mathchardef\parallel="326B +\mathchardef\mid="326A +\mathchardef\dashv="3261 +\mathchardef\vdash="3260 +\mathchardef\nearrow="3225 +\mathchardef\searrow="3226 +\mathchardef\nwarrow="322D +\mathchardef\swarrow="322E +\mathchardef\Leftrightarrow="322C +\mathchardef\Leftarrow="3228 +\mathchardef\Rightarrow="3229 +\def\neq{\not=} \let\ne=\neq +\mathchardef\leq="3214 \let\le=\leq +\mathchardef\geq="3215 \let\ge=\geq +\mathchardef\succ="321F +\mathchardef\prec="321E +\mathchardef\approx="3219 +\mathchardef\succeq="3217 +\mathchardef\preceq="3216 +\mathchardef\supset="321B +\mathchardef\subset="321A +\mathchardef\supseteq="3213 +\mathchardef\subseteq="3212 +\mathchardef\in="3232 +\mathchardef\ni="3233 \let\owns=\ni +\mathchardef\gg="321D +\mathchardef\ll="321C +\mathchardef\not="3236 +\mathchardef\leftrightarrow="3224 +\mathchardef\leftarrow="3220 \let\gets=\leftarrow +\mathchardef\rightarrow="3221 \let\to=\rightarrow +\mathchardef\mapstochar="3237 \def\mapsto{\mapstochar\rightarrow} +\mathchardef\sim="3218 +\mathchardef\simeq="3227 +\mathchardef\perp="323F +\mathchardef\equiv="3211 +\mathchardef\asymp="3210 +\mathchardef\smile="315E +\mathchardef\frown="315F +\mathchardef\leftharpoonup="3128 +\mathchardef\leftharpoondown="3129 +\mathchardef\rightharpoonup="312A +\mathchardef\rightharpoondown="312B + +\def\joinrel{\mathrel{\mkern-3mu}} +\def\relbar{\mathrel{\smash-}} % \smash, because - has the same height as + +\def\Relbar{\mathrel=} +\mathchardef\lhook="312C \def\hookrightarrow{\lhook\joinrel\rightarrow} +\mathchardef\rhook="312D \def\hookleftarrow{\leftarrow\joinrel\rhook} +\def\bowtie{\mathrel\triangleright\joinrel\mathrel\triangleleft} +\def\models{\mathrel|\joinrel=} +\def\Longrightarrow{\Relbar\joinrel\Rightarrow} +\def\longrightarrow{\relbar\joinrel\rightarrow} +\def\longleftarrow{\leftarrow\joinrel\relbar} +\def\Longleftarrow{\Leftarrow\joinrel\Relbar} +\def\longmapsto{\mapstochar\longrightarrow} +\def\longleftrightarrow{\leftarrow\joinrel\rightarrow} +\def\Longleftrightarrow{\Leftarrow\joinrel\Rightarrow} +\def\iff{\;\Longleftrightarrow\;} + +\mathchardef\ldotp="613A % ldot as a punctuation mark +\mathchardef\cdotp="6201 % cdot as a punctuation mark +\mathchardef\colon="603A % colon as a punctuation mark +\def\ldots{\mathinner{\ldotp\ldotp\ldotp}} +\def\cdots{\mathinner{\cdotp\cdotp\cdotp}} +\def\vdots{\vbox{\baselineskip4\p@ \lineskiplimit\z@ + \kern6\p@\hbox{.}\hbox{.}\hbox{.}}} +\def\ddots{\mathinner{\mkern1mu\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu + \raise4\p@\hbox{.}\mkern2mu\raise\p@\hbox{.}\mkern1mu}} + +\def\acute{\mathaccent"7013 } +\def\grave{\mathaccent"7012 } +\def\ddot{\mathaccent"707F } +\def\tilde{\mathaccent"707E } +\def\bar{\mathaccent"7016 } +\def\breve{\mathaccent"7015 } +\def\check{\mathaccent"7014 } +\def\hat{\mathaccent"705E } +\def\vec{\mathaccent"017E } +\def\dot{\mathaccent"705F } +\def\widetilde{\mathaccent"0365 } +\def\widehat{\mathaccent"0362 } +\def\overrightarrow#1{\vbox{\m@th\ialign{##\crcr + \rightarrowfill\crcr\noalign{\kern-\p@\nointerlineskip} + $\hfil\displaystyle{#1}\hfil$\crcr}}} +\def\overleftarrow#1{\vbox{\m@th\ialign{##\crcr + \leftarrowfill\crcr\noalign{\kern-\p@\nointerlineskip} + $\hfil\displaystyle{#1}\hfil$\crcr}}} +\def\overbrace#1{\mathop{\vbox{\m@th\ialign{##\crcr\noalign{\kern3\p@} + \downbracefill\crcr\noalign{\kern3\p@\nointerlineskip} + $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} +\def\underbrace#1{\mathop{\vtop{\m@th\ialign{##\crcr + $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip} + \upbracefill\crcr\noalign{\kern3\p@}}}}\limits} +\def\skew#1#2#3{{\muskip\z@#1mu\divide\muskip\z@\tw@ \mkern\muskip\z@ + #2{\mkern-\muskip\z@{#3}\mkern\muskip\z@}\mkern-\muskip\z@}{}} + +\def\lmoustache{\delimiter"437A340 } % top from (, bottom from ) +\def\rmoustache{\delimiter"537B341 } % top from ), bottom from ( +\def\lgroup{\delimiter"462833A } % extensible ( with sharper tips +\def\rgroup{\delimiter"562933B } % extensible ) with sharper tips +\def\arrowvert{\delimiter"26A33C } % arrow without arrowheads +\def\Arrowvert{\delimiter"26B33D } % double arrow without arrowheads +\def\bracevert{\delimiter"77C33E } % the vertical bar that extends braces +\def\Vert{\delimiter"26B30D } \let\|=\Vert +\def\vert{\delimiter"26A30C } +\def\uparrow{\delimiter"3222378 } +\def\downarrow{\delimiter"3223379 } +\def\updownarrow{\delimiter"326C33F } +\def\Uparrow{\delimiter"322A37E } +\def\Downarrow{\delimiter"322B37F } +\def\Updownarrow{\delimiter"326D377 } +\def\backslash{\delimiter"26E30F } % for double coset G\backslash H +\def\rangle{\delimiter"526930B } +\def\langle{\delimiter"426830A } +\def\rbrace{\delimiter"5267309 } \let\}=\rbrace +\def\lbrace{\delimiter"4266308 } \let\{=\lbrace +\def\rceil{\delimiter"5265307 } +\def\lceil{\delimiter"4264306 } +\def\rfloor{\delimiter"5263305 } +\def\lfloor{\delimiter"4262304 } + +\def\bigl{\mathopen\big} +\def\bigm{\mathrel\big} +\def\bigr{\mathclose\big} +\def\Bigl{\mathopen\Big} +\def\Bigm{\mathrel\Big} +\def\Bigr{\mathclose\Big} +\def\biggl{\mathopen\bigg} +\def\biggm{\mathrel\bigg} +\def\biggr{\mathclose\bigg} +\def\Biggl{\mathopen\Bigg} +\def\Biggm{\mathrel\Bigg} +\def\Biggr{\mathclose\Bigg} +\def\big#1{{\hbox{$\left#1\vbox to8.5\p@{}\right.\n@space$}}} +\def\Big#1{{\hbox{$\left#1\vbox to11.5\p@{}\right.\n@space$}}} +\def\bigg#1{{\hbox{$\left#1\vbox to14.5\p@{}\right.\n@space$}}} +\def\Bigg#1{{\hbox{$\left#1\vbox to17.5\p@{}\right.\n@space$}}} +\def\n@space{\nulldelimiterspace\z@ \m@th} + +\def\choose{\atopwithdelims()} +\def\brack{\atopwithdelims[]} +\def\brace{\atopwithdelims\{\}} + +\def\sqrt{\radical"270370 } + +\def\mathpalette#1#2{\mathchoice{#1\displaystyle{#2}}% + {#1\textstyle{#2}}{#1\scriptstyle{#2}}{#1\scriptscriptstyle{#2}}} +\newbox\rootbox +\def\root#1\of{\setbox\rootbox + \hbox{$\m@th\scriptscriptstyle{#1}$}\mathpalette\r@@t} +\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\sqrt{#2}$}\dimen@\ht\z@ + \advance\dimen@-\dp\z@ + \mkern5mu\raise.6\dimen@\copy\rootbox \mkern-10mu\box\z@} +\newif\ifv@ \newif\ifh@ +\def\vphantom{\v@true\h@false\ph@nt} +\def\hphantom{\v@false\h@true\ph@nt} +\def\phantom{\v@true\h@true\ph@nt} +\def\ph@nt{\ifmmode\def\next{\mathpalette\mathph@nt}% + \else\let\next\makeph@nt\fi\next} +\def\makeph@nt#1{\setbox\z@\hbox{#1}\finph@nt} +\def\mathph@nt#1#2{\setbox\z@\hbox{$\m@th#1{#2}$}\finph@nt} +\def\finph@nt{\setbox\tw@\null + \ifv@ \ht\tw@\ht\z@ \dp\tw@\dp\z@\fi + \ifh@ \wd\tw@\wd\z@\fi \box\tw@} +\def\mathstrut{\vphantom(} +\def\smash{\relax % \relax, in case this comes first in \halign + \ifmmode\def\next{\mathpalette\mathsm@sh}\else\let\next\makesm@sh + \fi\next} +\def\makesm@sh#1{\setbox\z@\hbox{#1}\finsm@sh} +\def\mathsm@sh#1#2{\setbox\z@\hbox{$\m@th#1{#2}$}\finsm@sh} +\def\finsm@sh{\ht\z@\z@ \dp\z@\z@ \box\z@} + +\def\cong{\mathrel{\mathpalette\@vereq\sim}} % congruence sign +\def\@vereq#1#2{\lower.5\p@\vbox{\lineskiplimit\maxdimen\lineskip-.5\p@ + \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}} +\def\notin{\mathrel{\mathpalette\c@ncel\in}} +\def\c@ncel#1#2{\m@th\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} +\def\rightleftharpoons{\mathrel{\mathpalette\rlh@{}}} +\def\rlh@#1{\vcenter{\m@th\hbox{\ooalign{\raise2pt + \hbox{$#1\rightharpoonup$}\crcr + $#1\leftharpoondown$}}}} +\def\buildrel#1\over#2{\mathrel{\mathop{\kern\z@#2}\limits^{#1}}} +\def\doteq{\buildrel\textstyle.\over=} + +\def\log{\mathop{\rm log}\nolimits} +\def\lg{\mathop{\rm lg}\nolimits} +\def\ln{\mathop{\rm ln}\nolimits} +\def\lim{\mathop{\rm lim}} +\def\limsup{\mathop{\rm lim\,sup}} +\def\liminf{\mathop{\rm lim\,inf}} +\def\sin{\mathop{\rm sin}\nolimits} +\def\arcsin{\mathop{\rm arcsin}\nolimits} +\def\sinh{\mathop{\rm sinh}\nolimits} +\def\cos{\mathop{\rm cos}\nolimits} +\def\arccos{\mathop{\rm arccos}\nolimits} +\def\cosh{\mathop{\rm cosh}\nolimits} +\def\tan{\mathop{\rm tan}\nolimits} +\def\arctan{\mathop{\rm arctan}\nolimits} +\def\tanh{\mathop{\rm tanh}\nolimits} +\def\cot{\mathop{\rm cot}\nolimits} +\def\coth{\mathop{\rm coth}\nolimits} +\def\sec{\mathop{\rm sec}\nolimits} +\def\csc{\mathop{\rm csc}\nolimits} +\def\max{\mathop{\rm max}} +\def\min{\mathop{\rm min}} +\def\sup{\mathop{\rm sup}} +\def\inf{\mathop{\rm inf}} +\def\arg{\mathop{\rm arg}\nolimits} +\def\ker{\mathop{\rm ker}\nolimits} +\def\dim{\mathop{\rm dim}\nolimits} +\def\hom{\mathop{\rm hom}\nolimits} +\def\det{\mathop{\rm det}} +\def\exp{\mathop{\rm exp}\nolimits} +\def\Pr{\mathop{\rm Pr}} +\def\gcd{\mathop{\rm gcd}} +\def\deg{\mathop{\rm deg}\nolimits} + +\def\bmod{\nonscript\mskip-\medmuskip\mkern5mu + \mathbin{\rm mod}\penalty900\mkern5mu\nonscript\mskip-\medmuskip} +\def\pmod#1{\allowbreak\mkern18mu({\rm mod}\,\,#1)} + +\def\cases#1{\left\{\,\vcenter{\normalbaselines\m@th + \ialign{$##\hfil$&\quad##\hfil\crcr#1\crcr}}\right.} +\def\matrix#1{\null\,\vcenter{\normalbaselines\m@th + \ialign{\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr + \mathstrut\crcr\noalign{\kern-\baselineskip} + #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,} +\def\pmatrix#1{\left(\matrix{#1}\right)} +\newdimen\p@renwd +\setbox0=\hbox{\tenex B} \p@renwd=\wd0 % width of the big left ( +\def\bordermatrix#1{\begingroup \m@th + \setbox\z@\vbox{\def\cr{\crcr\noalign{\kern2\p@\global\let\cr\endline}}% + \ialign{$##$\hfil\kern2\p@\kern\p@renwd&\thinspace\hfil$##$\hfil + &&\quad\hfil$##$\hfil\crcr + \omit\strut\hfil\crcr\noalign{\kern-\baselineskip}% + #1\crcr\omit\strut\cr}}% + \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{$\kern\wd\@ne\kern-\p@renwd\left(\kern-\wd\@ne + \global\setbox\@ne\vbox{\box\@ne\kern2\p@}% + \vcenter{\kern-\ht\@ne\unvbox\z@\kern-\baselineskip}\,\right)$}% + \null\;\vbox{\kern\ht\@ne\box\tw@}\endgroup} + +\def\openup{\afterassignment\@penup\dimen@=} +\def\@penup{\advance\lineskip\dimen@ + \advance\baselineskip\dimen@ + \advance\lineskiplimit\dimen@} +\def\eqalign#1{\null\,\vcenter{\openup\jot\m@th + \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil + \crcr#1\crcr}}\,} +\newif\ifdt@p +\def\displ@y{\global\dt@ptrue\openup\jot\m@th + \everycr{\noalign{\ifdt@p \global\dt@pfalse \ifdim\prevdepth>-1000\p@ + \vskip-\lineskiplimit \vskip\normallineskiplimit \fi + \else \penalty\interdisplaylinepenalty \fi}}} +\def\@lign{\tabskip\z@skip\everycr{}} % restore inside \displ@y +\def\displaylines#1{\displ@y \tabskip\z@skip + \halign{\hbox to\displaywidth{$\@lign\hfil\displaystyle##\hfil$}\crcr + #1\crcr}} +\def\eqalignno#1{\displ@y \tabskip\centering + \halign to\displaywidth{\hfil$\@lign\displaystyle{##}$\tabskip\z@skip + &$\@lign\displaystyle{{}##}$\hfil\tabskip\centering + &\llap{$\@lign##$}\tabskip\z@skip\crcr + #1\crcr}} +\def\leqalignno#1{\displ@y \tabskip\centering + \halign to\displaywidth{\hfil$\@lign\displaystyle{##}$\tabskip\z@skip + &$\@lign\displaystyle{{}##}$\hfil\tabskip\centering + &\kern-\displaywidth\rlap{$\@lign##$}\tabskip\displaywidth\crcr + #1\crcr}} + +% Definitions related to output + +\message{output routines,} + +\countdef\pageno=0 \pageno=1 % first page is number 1 +\newtoks\headline \headline={\hfil} % headline is normally blank +\newtoks\footline \footline={\hss\tenrm\folio\hss} + % footline is normally a centered page number in font \tenrm +\newif\ifr@ggedbottom +\def\raggedbottom{\topskip 10\p@ plus60\p@ \r@ggedbottomtrue} +\def\normalbottom{\topskip 10\p@ \r@ggedbottomfalse} % undoes \raggedbottom +\def\folio{\ifnum\pageno<\z@ \romannumeral-\pageno \else\number\pageno \fi} +\def\nopagenumbers{\footline{\hfil}} % blank out the footline +\def\advancepageno{\ifnum\pageno<\z@ \global\advance\pageno\m@ne + \else\global\advance\pageno\@ne \fi} % increase |pageno| + +\newinsert\footins +\def\footnote#1{\let\@sf\empty % parameter #2 (the text) is read later + \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi + #1\@sf\vfootnote{#1}} +\def\vfootnote#1{\insert\footins\bgroup + \interlinepenalty\interfootnotelinepenalty + \splittopskip\ht\strutbox % top baseline for broken footnotes + \splitmaxdepth\dp\strutbox \floatingpenalty\@MM + \leftskip\z@skip \rightskip\z@skip \spaceskip\z@skip \xspaceskip\z@skip + \textindent{#1}\footstrut\futurelet\next\fo@t} +\def\fo@t{\ifcat\bgroup\noexpand\next \let\next\f@@t + \else\let\next\f@t\fi \next} +\def\f@@t{\bgroup\aftergroup\@foot\let\next} +\def\f@t#1{#1\@foot} +\def\@foot{\strut\egroup} +\def\footstrut{\vbox to\splittopskip{}} +\skip\footins=\bigskipamount % space added when footnote is present +\count\footins=1000 % footnote magnification factor (1 to 1) +\dimen\footins=8in % maximum footnotes per page + +\newinsert\topins +\newif\ifp@ge \newif\if@mid +\def\topinsert{\@midfalse\p@gefalse\@ins} +\def\midinsert{\@midtrue\@ins} +\def\pageinsert{\@midfalse\p@getrue\@ins} +\skip\topins=\z@skip % no space added when a topinsert is present +\count\topins=1000 % magnification factor (1 to 1) +\dimen\topins=\maxdimen % no limit per page +\def\@ins{\par\begingroup\setbox\z@\vbox\bgroup} % start a \vbox +\def\endinsert{\egroup % finish the \vbox + \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@ \advance\dimen@12\p@ + \advance\dimen@\pagetotal \advance\dimen@-\pageshrink + \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi + \if@mid \bigskip\box\z@\bigbreak + \else\insert\topins{\penalty100 % floating insertion + \splittopskip\z@skip + \splitmaxdepth\maxdimen \floatingpenalty\z@ + \ifp@ge \dimen@\dp\z@ + \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero + \else \box\z@\nobreak\bigskip\fi}\fi\endgroup} + +\output{\plainoutput} +\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% + \advancepageno + \ifnum\outputpenalty>-\@MM \else\dosupereject\fi} +\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} +\def\makeheadline{\vbox to\z@{\vskip-22.5\p@ + \line{\vbox to8.5\p@{}\the\headline}\vss}\nointerlineskip} +\def\makefootline{\baselineskip24\p@\lineskiplimit\z@\line{\the\footline}} +\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over + \line{}\kern-\topskip\nobreak\vfill\supereject\fi} + +\def\pagecontents{\ifvoid\topins\else\unvbox\topins\fi + \dimen@=\dp\@cclv \unvbox\@cclv % open up \box255 + \ifvoid\footins\else % footnote info is present + \vskip\skip\footins + \footnoterule + \unvbox\footins\fi + \ifr@ggedbottom \kern-\dimen@ \vfil \fi} +\def\footnoterule{\kern-3\p@ + \hrule width 2truein \kern 2.6\p@} % the \hrule is .4pt high + +% Hyphenation, miscellaneous macros, and initial values for standard layout +\message{hyphenation} + +\lefthyphenmin=2 \righthyphenmin=3 % disallow x- or -xx breaks +\input hyphen + +\def\magnification{\afterassignment\m@g\count@} +\def\m@g{\mag\count@ + \hsize6.5truein\vsize8.9truein\dimen\footins8truein} + +\def\loggingall{\tracingcommands\tw@\tracingstats\tw@ + \tracingpages\@ne\tracingoutput\@ne\tracinglostchars\@ne + \tracingmacros\tw@\tracingparagraphs\@ne\tracingrestores\@ne + \showboxbreadth\maxdimen\showboxdepth\maxdimen} +\def\tracingall{\tracingonline\@ne\loggingall} + +\def\showhyphens#1{\setbox0\vbox{\parfillskip\z@skip\hsize\maxdimen\tenrm + \pretolerance\m@ne\tolerance\m@ne\hbadness0\showboxdepth0\ #1}} + +\normalbaselines\rm % select roman font +\nonfrenchspacing % punctuation affects the spacing +\catcode`@=12 % at signs are no longer letters + +\def\fmtname{plain}\def\fmtversion{3.141592653} % identifies the current format |