% This is LaTeX's plain TeX format. Changes are noted as %%LaTeX % 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 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..127, 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 % \lambda \mathcode`\^^H="0115 % \pi \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`\\="20430F % 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, 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 % 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 insert allocation % 20 the most recently allocated number % 21 constant -1 % New counters are allocated starting with 22, 23, 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 19 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 recommends 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=21 % allocates \count registers 22, 23, ... \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=255 % allocates insertions 254, 253, ... \countdef\insc@unt=19 % the insertion counter \countdef\allocationnumber=20 % the most recent allocation \countdef\m@ne=21 \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} \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, \newswitch{foo} creates \footrue, \foofalse, and \iffoo. \outer\def\newswitch#1{\expandafter\let\csname if#1\endcsname\relax \toks@{\iftrue}% \expandafter\edef\csname#1true\endcsname {\let\csname if#1\endcsname=\the\toks@}% \toks@{\iffalse}% \expandafter\edef\csname#1false\endcsname {\let\csname if#1\endcsname=\the\toks@}% \csname#1false\endcsname} % the switch starts out false % 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 % \tracingonline=0 % \tracingmacros=0 % \tracingstats=0 % \tracingparagraphs=0 % \tracingpages=0 % \tracingoutput=0 \tracinglostchars=1 % \tracingcommands=0 % \tracingrestores=0 \uchyph=1 % \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 \hfuzz=0.1pt \vfuzz=0.1pt \overfullrule=5pt \hsize=6.5in \vsize=8.9in \maxdepth=2pt \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 \input lfonts % this has gotta be here. %%\def\magstephalf{1095 } %%\def\magstep#1{\ifcase#1 \@m\or 1200\or 1440\or 1728\or 2074\or 2488\fi\relax} %%LaTeX: This page commented out for LaTeX % Note: At present, "am" fonts are loaded instead of "cm" ones. % The "almost computer modern" typefaces will be replaced by % better fonts in the future; meanwhile we must use these. % 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=amr10 % roman text %%\font\preloaded=amr9 %%\font\preloaded=amr8 %%\font\sevenrm=amr7 %%\font\preloaded=amr6 %%\font\fiverm=amr5 %%\font\teni=ami10 % math italic %%\font\preloaded=ami9 %%\font\preloaded=ami8 %%\font\seveni=ami7 %%\font\preloaded=ami6 %%\font\fivei=ami5 %%\font\tensy=amsy10 % math symbols %%\font\preloaded=amsy9 %%\font\preloaded=amsy8 %%\font\sevensy=amsy7 %%\font\preloaded=amsy6 %%\font\fivesy=amsy5 %%\font\tenex=amex10 % math extension %%\font\preloaded=amss10 % sans serif %%\font\preloaded=amssq8 %%\font\preloaded=amssi10 % sans serif italic %%\font\preloaded=amssqi8 %%\font\tenbf=ambx10 % boldface extended %%\font\preloaded=ambx9 %%\font\preloaded=ambx8 %%\font\sevenbf=ambx7 %%\font\preloaded=ambx6 %%\font\fivebf=ambx5 %%\font\tentt=amtt10 % typewriter %%\font\preloaded=amtt9 %%\font\preloaded=amtt8 %%\font\preloaded=amsltt10 % slanted typewriter %%\font\tensl=amsl10 % slanted roman %%\font\preloaded=amsl9 %%\font\preloaded=amsl8 %%\font\tenit=amti10 % text italic %%\font\preloaded=amti9 %%\font\preloaded=amti8 %%\font\preloaded=amti7 %%\message{more fonts,} %%\font\preloaded=amu10 % unslanted text italic %%\font\preloaded=ambi10 % bold math italic %%\font\preloaded=ambsy10 % bold math symbols %%\font\preloaded=amcsc10 % caps and small caps %%\font\preloaded=amssbx10 % sans serif bold extended %%\font\preloaded=amdunh10 % Dunhill style %%\font\preloaded=amr7 scaled \magstep4 % for titles %%\font\preloaded=amtt10 scaled \magstep2 %%\font\preloaded=amssbx10 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 = control \def\^^I{\ } % same for \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\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{\tabskip\z@skip\halign} % initialized \halign \newcount\mscount \def\multispan#1{\omit \mscount#1 \loop\ifnum\mscount>\@ne \sp@n\repeat} \def\sp@n{\span\omit\advance\mscount\m@ne} \newswitch{us@} \newswitch{@cr} \newbox\tabs \newbox\tabsyet \newbox\tabsdone \def\cleartabs{\global\setbox\tabsyet\null \setbox\tabs\null} \outer\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\+\let\next\relax \def\next{\afterassignment\s@tt@b\let\next}% \else\let\next\s@tcols\fi\next} \def\s@tt@b{\let\next\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{\filbreak\bigskip \message{#1}\leftline{\bf#1}\nobreak\smallskip\vskip-\parskip \noindent} \outer\def\proclaim #1. #2\par{\medbreak\vskip-\parskip \noindent{\bf#1.\enspace}{\sl#2}\par \ifdim\lastskip<\medskipamount \removelastskip\penalty55\medskip\fi} \def\raggedright{\rightskip\z@ plus2em \spaceskip.3333em \xspaceskip.5em } \def\ttraggedright{\tt\rightskip\z@ plus2em } % 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{h}\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\oalign#1{\leavevmode\vtop{\baselineskip\z@skip \lineskip.25ex% \ialign{##\crcr#1\crcr}}} % put characters over each other \def\ooalign{\lineskiplimit-\maxdimen \oalign} \def\d#1{\oalign{#1\crcr\hidewidth.\hidewidth}} \def\b#1{\oalign{#1\crcr\hidewidth \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}} \def\c#1{\setbox\z@\hbox{#1}\ifdim\ht\z@=1ex\accent24 #1% \else{\ooalign{\hidewidth\char24\hidewidth\crcr\unhbox\z@}}\fi} \def\copyright{{\ooalign{\hfil\raise.07ex\hbox{c}\hfil\crcr\mathhexbox20D}}} \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{$\m@th\mathord-\mkern-6mu% \cleaders\hbox{$\mkern-2mu\mathord-\mkern-2mu$}\hfill \mkern-6mu\mathord\rightarrow$} \def\leftarrowfill{$\m@th\mathord\leftarrow\mkern-6mu% \cleaders\hbox{$\mkern-2mu\mathord-\mkern-2mu$}\hfill \mkern-6mu\mathord-$} \mathchardef\braceld="37A \mathchardef\bracerd="37B \mathchardef\bracelu="37C \mathchardef\braceru="37D \def\downbracefill{$\m@th\braceld\leaders\vrule\hfill\braceru \bracelu\leaders\vrule\hfill\bracerd$} \def\upbracefill{$\m@th\bracelu\leaders\vrule\hfill\bracerd \braceld\leaders\vrule\hfill\braceru$} \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\edef\next{\the\textfont2}\next\char2}{}{}} {\catcode`\'=\active \gdef'{^\bgroup\prim@s}} \def\prim@s{\prime\futurelet\next\pr@m@s} \def\pr@m@s{\ifx'\next \let\next\pr@@@s \else\let\next\egroup\fi \next} \def\pr@@@s#1{\prim@s} {\catcode`\^^Z=\active \gdef^^Z{\not=}} % ^^Z is like \ne in math {\catcode`\_=\active \let_=\_} % _ is like \_ if not used for subscripts \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\mskip-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{$\m@th\scriptstyle##$\cr\not\mathrel{\mkern14mu}\cr \noalign{\nointerlineskip} \mkern2.5mu\leaders\hrule height.34pt\hfill\mkern2.5mu\cr}}}} \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\lefttophalfarrow="3128 \mathchardef\leftbothalfarrow="3129 \mathchardef\righttophalfarrow="312A \mathchardef\rightbothalfarrow="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="602E % 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{\baselineskip 4\p@\kern6\p@\hbox{.}\hbox{.}\hbox{.}}} \def\ddots{\mathinner{\mskip1mu\raise7\p@\vbox{\kern7\p@\hbox{.}}\mskip2mu \raise4\p@\hbox{.}\mskip2mu\raise\p@\hbox{.}\mskip1mu}} \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"717E } \def\dot{\mathaccent"705F } \def\widetilde{\mathaccent"0365 } \def\widehat{\mathaccent"0362 } \def\overrightarrow#1{\vbox{\ialign{##\crcr \rightarrowfill\crcr\noalign{\kern-\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} \def\overleftarrow#1{\vbox{\ialign{##\crcr \leftarrowfill\crcr\noalign{\kern-\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} \def\overbrace#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@} \downbracefill\crcr\noalign{\kern3\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}} \def\underbrace#1{\mathop{\vtop{\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip} \upbracefill\crcr\noalign{\kern3\p@}}}}} \def\skew#1#2#3{{#2{#3\mkern#1mu}\mkern-#1mu}{}} \def\lmoustache{\delimiter"4000340 } % top from (, bottom from ) \def\rmoustache{\delimiter"5000341 } % top from ), bottom from ( \def\lgroup{\delimiter"400033A } % extensible ( with sharper tips \def\rgroup{\delimiter"500033B } % extensible ) with sharper tips \def\arrowvert{\delimiter"033C } % arrow without arrowheads \def\Arrowvert{\delimiter"033D } % double arrow without arrowheads \def\bracevert{\delimiter"033E } % the vertical bar that extends braces \def\Vert{\delimiter"026B30D } \let\|=\Vert \def\vert{\delimiter"026A30C } \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"026E30F } % 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@ \mskip5mu\raise.6\dimen@\copy\rootbox \mskip-10mu \box\z@} \newswitch{v@} \newswitch{h@} \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{\vbox to\z@{\kern-\ht\z@\box\z@\vss}} \def\cong{\mathrel{\mathpalette\@vereq\sim}} % congruence sign \def\@vereq#1#2{\lower.5\p@\vbox{\baselineskip\z@skip\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{\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} \def\rightlefthalfarrows{\mathrel{\mathpalette\rlh@{}}} \def\rlh@#1{\vcenter{\hbox{\ooalign{\raise2pt \hbox{$#1\righttophalfarrow$}\crcr $#1\leftbothalfarrow$}}}} \def\buildrel#1\over#2{\mathrel{\mathop{#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{\mskip-\medmuskip\mskip5mu \mathbin{\rm mod}\penalty900\mskip5mu\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{\,\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{$\kern\wd\@ne\kern-\p@renwd\left(\kern-\wd\@ne \global\setbox\@ne\vbox{\box\@ne\kern2\p@}% \vcenter{\kern-\ht\@ne\unvbox\z@\kern-\baselineskip}\,\right)$}% \;\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{\,\vcenter{\openup\jot\m@th \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil \crcr#1\crcr}}\,} \newswitch{dt@p} \def\displ@y{\global\dt@ptrue\openup\jot\m@th \everycr{\noalign{\ifdt@p \global\dt@pfalse \vskip-\lineskiplimit \vskip\normallineskiplimit \else \penalty\interdisplaylinepenalty \fi}}} \def\displaylines#1{\displ@y \halign{\hbox to\displaywidth{$\hfil\displaystyle##\hfil$}\crcr #1\crcr}} \def\eqalignno#1{\displ@y \tabskip\centering \halign to\displaywidth{\hfil$\displaystyle{##}$\tabskip\z@skip &$\displaystyle{{}##}$\hfil\tabskip\centering &\llap{$##$}\tabskip\z@skip\crcr #1\crcr}} \def\leqalignno#1{\displ@y \tabskip\centering \halign to\displaywidth{\hfil$\displaystyle{##}$\tabskip\z@skip &$\displaystyle{{}##}$\hfil\tabskip\centering &\kern-\displaywidth\rlap{$##$}\tabskip\displaywidth\crcr #1\crcr}} % Definitions related to output %%LaTeX: This page commented out for LaTeX %%\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 %%\newswitch{r@ggedbottom} %%\def\raggedbottom{\topskip 10\p@ plus60\p@ \r@ggedbottomtrue} %%\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 %% \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 %% \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 %%\newswitch{p@ge} \newswitch{@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 %% \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@\line{\the\footline}} %%\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over %% \vbox to-\topskip{\line{}\vss}\vfill\supereject\fi} %%\def\pagecontents{\ifvoid\topins\else\unvbox\topins\fi %% \unvbox\@cclv % open up \box255 %% \ifvoid\footins\else % footnote info is present %% \vskip\skip\footins %% \footnoterule %% \unvbox\footins\fi %% \ifr@ggedbottom\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} \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\@ne\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 don't select roman font!!! \nonfrenchspacing % punctuation affects the spacing \catcode`@=12 % at signs are no longer letters \def\fmtname{lplain}\def\fmtversion{0.9999} % identifies the current format %%\input lfonts %% moved to where fonts are preloaded in PLAIN %%\input latex %% temporarily commented out for testing.