% 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 under any circumstances. \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 formfeed 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 \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{\ } % \ = \ \def\^^I{\ } % \ = \ \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 \ } \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 % dotless i \chardef\j="11 % dotless j \def\aa{\accent23a} %^accent \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% %^accent \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}} %^accent \def\'#1{{\accent19 #1}} %^accent \def\v#1{{\accent20 #1}} %^accent \let\^^_=\v \def\u#1{{\accent21 #1}} %^accent \let\^^S=\u \def\=#1{{\accent22 #1}} %^accent \def\^#1{{\accent94 #1}} %^accent \let\^^D=\^ \def\.#1{{\accent95 #1}} %^accent \def\H#1{{\accent"7D #1}} %^accent \def\~#1{{\accent"7E #1}} %^accent \def\"#1{{\accent"7F #1}} %^accent \def\t#1{{\edef\next{\the\font}\the\textfont1\accent"7F\next#1}} %^accent \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="037A \mathchardef\bracerd="037B \mathchardef\bracelu="037C \mathchardef\braceru="037D \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 } %^math_accent \def\grave{\mathaccent"7012 } %^math_accent \def\ddot{\mathaccent"707F } %^math_accent \def\tilde{\mathaccent"707E } %^math_accent \def\bar{\mathaccent"7016 } %^math_accent \def\breve{\mathaccent"7015 } %^math_accent \def\check{\mathaccent"7014 } %^math_accent \def\hat{\mathaccent"705E } %^math_accent \def\vec{\mathaccent"017E } %^math_accent \def\dot{\mathaccent"705F } %^math_accent \def\widetilde{\mathaccent"0365 } %^math_accent \def\widehat{\mathaccent"0362 } %^math_accent \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 % Box to hold radicand for nth root commands. \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\tracingall{\tracingonline\@ne\tracingcommands\tw@\tracingstats\tw@ \tracingpages\@ne\tracingoutput\@ne\tracinglostchars\@ne \tracingmacros\tw@\tracingparagraphs\@ne\tracingrestores\@ne \showboxbreadth\maxdimen\showboxdepth\maxdimen\errorstopmode} \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{3.1415926} % identifies the current format