DOS/V Power Report 1996 December/VPR9612A.ISO/WINTEX/AMS/AMSTEX/DOC/AMSPPT.DOC

Text File | 1993-02-25 | 131KB | 3,009 lines

%% @texfile{
%%     filename="amsppt.sty",
\def\filename{amsppt.sty}
%      filename="amsppt.doc",
%%     version="2.1c",
\def\fileversion{2.1c}
%%     date="11-Dec-1992",
\def\filedate{11-Dec-1992}
%%     filetype="AMS-TeX: documentstyle",
%%     copyright="Copyright (C) American Mathematical Society,
%%            all rights reserved.  Copying of this file is
%%            authorized only if either:
%%            (1) you make absolutely no changes to your copy
%%                including name; OR
%%            (2) if you do make changes, you first rename it to some
%%                other name.",
%%     author="American Mathematical Society",
%%     address="American Mathematical Society,
%%            Technical Support Department,
%%            P. O. Box 6248,
%%            Providence, RI 02940,
%%            USA",
%%     telephone="401-455-4080 or (in the USA) 800-321-4AMS",
%%     email="Internet: [e-mail]",
%%     codetable="ISO/ASCII",
%%     checksum = "33694 3008 15390 127718",
%%     keywords="amstex, ams-tex, tex",
%%     abstract="This file is a documentstyle for use with
%%       AMS-TeX 2.1. It exists in two forms: amsppt.doc, which
%%       is the full form containing all technical documentation,
%%       and amsppt.sty, which is identical except that all lines
%%       beginning with a single percent sign are removed, to
%%       make the file more rapid-loading when processed by
%%       TeX."
%%     }
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       -0- CONTENTS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       -0- Contents
%       -1- Preliminary
%       -2- Utility definitions
%       -3- Fonts
%       -4- Page dimensions and other global settings
%       -5- Top matter definitions
%       -6- Section headings
%       -7- Theorem environments and similar structures
%       -8- Rosters
%       -9- Footnotes
%      -10- Tables
%      -11- Figure spaces and captions
%      -12- Miscellaneous formatting macros
%      -13- References/Bibliography
%      -14- End of document
%      -15- Output routine
%      -16- Hyphenation exceptions
%      -17- Notes
%      -18- Appendix: Notes on version 2.1
%      -19- Appendix: Notes on version 2.1a
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       -1- PRELIMINARY
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%      AMSPPT.DOC contains all the code for AMSPPT.STY, with
%      additional comments. AMSPPT.STY is produced by removing from
%      AMSPPT.DOC all blank lines and lines beginning with a percent
%      sign.  This is done to allow it to be loaded faster by TeX.
%
%      For the most part the internals of AMSPPT.STY aren't closely
%      related to AMSTEX.TEX: AMSTEX.TEX handles mathematics,
%      AMSPPT.STY handles visual design and overall structure of
%      documents.  But some parts of AMSTEX.DOC are relevant, e.g.,
%      the standard abbreviations \DN@, \RIfM@, etc., the description
%      of "compressed format", the remarks about the "K-method", and
%      the allocation of scratch registers and variables such as
%      \toks@@.
%
%      The style produced by AMSPPT.STY is based on the style of the
%      Journal of the American Mathematical Society (as of December
%      1990), but is not intended to reproduce it exactly.  For one
%      thing, most users of AMSPPT.STY will probably have Computer
%      Modern fonts, while the Journal of the AMS uses Times Roman
%      fonts licensed from Autologic, Inc.  This means that line
%      breaks and page breaks are sure to change when a paper is
%      submitted to the AMS.  For another thing, preprints naturally
%      differ in some respects from articles in final published form:
%      published articles generally have the journal name, volume and
%      year of publication somewhere on the first page, a ``received
%      by the editors'' date, subject classification numbers, perhaps
%      key words and phrases, and an abstract, none of which are
%      necessary in a preprint (though the last few are sometimes
%      present).  In addition, the Journal of the AMS has a few
%      idiosyncrasies such as placement of the abstract at the end of
%      an article rather than at the beginning, and a non-zero value
%      of \mathsurround, which were deemed inappropriate for inclusion
%      in the preprint style (in particular, a non-zero \mathsurround
%      would require the user to do extra work in certain situations
%      to cancel unwanted side effects).  Since we are not matching
%      the style of the Journal of the AMS exactly, we sometimes have
%      rounded off measurements in AMSPPT.STY to convenient amounts
%      such as \bigskipamount and \medskipamount or the nearest whole
%      or half pica.  For example \belowheadskip is 7pt in the Journal
%      of the AMS, but AMSPPT.STY uses 6pt (half a pica).
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%     Bug in amsppt.sty version 2.1 left \amsppt.sty = \endinput
%     after the file was loaded. This will fix it if amsppt.sty
%     was put in the format file.
%
\expandafter\ifx\csname amsppt.sty\endcsname\endinput
  \expandafter\def\csname amsppt.sty\endcsname{2.1 (1-JUL-1991)}\fi
%
%    Check to see if this file was previously loaded and, if so,
%    if the version numbers agree.
%
\xdef\fileversiontest{\fileversion\space(\filedate)}
\expandafter\ifx\csname\filename\endcsname\fileversiontest
%    Then file is already loaded, and versions agree. Quit here.
%    \endinput and \fi MUST be on the same line:
  \message{[already loaded]}\endinput\fi
%
%    If the file versions disagree, we generate an error message,
%    but we don't do an \endinput: maybe the user will want to
%    continue, inputting the new version, and see what happens.
%
\expandafter\ifx\csname\filename\endcsname\relax % file not yet loaded
  \else\errmessage{Discrepancy in `\filename' file versions:
     version \csname\filename\endcsname\space already loaded, trying
     now to load version \fileversiontest}\fi
%
%    Since we are about to change the catcode of @, we define
%    \csname\filename\endcsname to set the catcode back to its previous
%    value. Furthermore, it then redefines itself to record the file
%    version number for future reference (e.g., the test above).
%
\expandafter\xdef\csname\filename\endcsname{%
  \catcode`\noexpand\@=\the\catcode`\@
  \expandafter\gdef\csname\filename\endcsname{%
     \fileversion\space(\filedate)}}
%
%    Enable the use of @ as letter in `private' control sequence names.
%    Cf. TeXbook, p. 344 (above the \mathcode table).
%
\catcode`\@=11
%
%    Besides putting the file version on screen, this message also
%    records it in the transcript/log file (which is useful for
%    troubleshooting). The file name was already given on screen and in
%    the transcript file by TeX, as part of the automatic processing
%    surrounding file input.
%
\message{version \fileversion\space(\filedate):}
%
%    If another documentstyle inputs amsppt.sty, it should define
%    \styname and \styversion appropriately. We use an `ifundefined'
%    test to avoid overriding the definitions, in that case.
\expandafter\ifx\csname styname\endcsname\relax
  \def\styname{AMSPPT}\def\styversion{2.1a}
\fi
%
%      In AMSPPT.STY we follow the convention in amstex.tex of
%      appending @ signs at the end of control sequences, rather than
%      substituting @ signs for vowels as is frequently done in
%      plain.tex.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -2- UTILITY DEFINITIONS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{Loading utility definitions,}
%
%      For several macros, e.g., \title, we want to allow the user the
%      following two options:
%
%      \title xxx\endtitle
%      \title\nofrills xxx\endtitle
%
%      In the first case, we want the text of the title to be stored
%      in a box for later use.  In the second case, we want certain
%      parts of the typesetting to be omitted when constructing the
%      box.  Internally this is done by prefixing them with \frills@,
%      which in the normal cases is simply an identity function
%      (\let\frills@\identity@), whereas in the nofrills case it
%      gobbles its argument (\let\frills@\eat@).
%
%      In order to test for \nofrills we have to use \futurelet
%      (because if \nofrills is absent, we don't want to do anything
%      that might affect the actual text of the title, such as
%      stripping braces or adding an unwanted extra pair around the
%      first token or group).
%
\def\identity@#1{#1}
%
\def\nofrills@@#1{%
%      This extra step in defining \next@ is a precaution in case #1
%      might be more than one token.
 \DN@{#1}%
 \ifx\next\nofrills \let\frills@\eat@
   \expandafter\expandafter\expandafter\next@\expandafter\eat@
  \else \let\frills@\identity@\expandafter\next@\fi}
%
\def\nofrillscheck#1{\def\nofrills@{\nofrills@@{#1}}%
  \futurelet\next\nofrills@}
%
%      Typical use: if we want to execute a macro called \title, but
%      check to see if \nofrills is coming up next, we do this:
%
%      ... \nofrillscheck\title
%
%      If indeed the next thing is \nofrills, then we will execute
%      \nofrills@@ before calling \title again.  This involves some
%      shuffling around in order for us to get back the ``real''
%      definition of \title afterwards and yet still be able to use a
%      control sequence named \title to read the argument. This is
%      important in giving the user a useful error message if they
%      accidentally omit or misspell the matching \endtitle or
%      whatever. We could use instead the trick used with \align of
%      adding a space onto the \csname with which we read the
%      argument, but that would increase the use of hash size.
%
%      We define \usualspace to give a warning message if used in
%      a place where it's not intended to be used:
%
\Invalid@\usualspace
%
%      Facility for adding to a token list, providing it was named
%      with the particular naming convention that we require: an
%      additional @ sign at the end of the control sequence name.
%      Usage: \addto\tenpoint{...}
%
\def\addto#1#2{\csname \expandafter\eat@\string#1@\endcsname
  \expandafter{\the\csname \expandafter\eat@\string#1@\endcsname#2}}
%
%      Fix Plain's \big, \Big, etc. macros so that they can scale with
%      size changes.  The relations in \tenpoint are:
%
%             total    height above
%             height   baseline
%      --------------------------------------------------------------
%      \big:   12pt    8.5   (12/2 = 6, + 2.5 (height of math axis))
%      \Big:   18pt    11.5  (18/2 = 9, + 2.5 (height of math axis))
%      \bigg:  24pt    14.5  (24/2 = 12, + 2.5 (height of math axis))
%      \Bigg:  30pt    17.5  (30/2 = 15, + 2.5 (height of math axis))
%
%      In \tenpoint \bigsize@ will be set to 12pt, the height of an
%      ordinary parenthesis in the roman font, x 1.2
\newdimen\bigsize@
%
%      Using \vcenter automatically factors the height of the math
%      axis into our sizing.  We set \nulldelimiterspace to zero,
%      since we only want the delimiterspace from the \left delimiter.
%
\def\big@#1#2{{\hbox{$\left#2\vcenter to#1\bigsize@{}%
  \right.\nulldelimiterspace\z@\m@th$}}}
\def\big{\big@\@ne}
\def\Big{\big@{1.5}}
\def\bigg{\big@\tw@}
\def\Bigg{\big@{2.5}}
%
%      Definition almost verbatim from TeXbook p. 317.  This is used
%      in several places, currently (28-DEC-1989) including \head,
%      \title, \author, \dedicatory, \affil, and \topcaption.
%
\def\raggedcenter@{\leftskip\z@ plus.4\hsize \rightskip\leftskip
 \parfillskip\z@ \parindent\z@ \spaceskip.3333em \xspaceskip.5em
 \pretolerance9999\tolerance9999 \exhyphenpenalty\@M
 \hyphenpenalty\@M \let\\\linebreak}
%
%      We now define a version of \uppercase that sidesteps any math,
%      to prevent uppercasing math variables.  In order to be handled
%      properly the $..$ must be on the outer level (not enclosed in
%      braces) but this is the usual case in our applications of
%      \uppercasetext@. Also we increase inter-word space in the
%      uppercase text. Footnotes are not handled by
%      \uppercasetext@---a footnote within a \title would have to be
%      done by using \footnotemark within the title and \footnotetext
%      after. In most cases footnotes within a title are something for
%      which the author should use \thanks or \affil or \address
%      instead.
%
%      One other little problem: uppercasing of a few special
%      characters like the German "ss" and the undotted i and j (\i
%      and \j), used sometimes with accents.  We do some reassignments
%      here to handle these.  We don't worry about restoring the
%      lowercase special characters within math embedded in the text
%      being uppercased---it's conceivable that someone might want to
%      use them there, but too unlikely to need providing for.
%      (Undotted i and j in math would be typed as \imath and \jmath,
%      not as \i and \j.)
%
%      This is what plain.tex has for the special characters:
%
% \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\AA{\leavevmode\setbox0\hbox{h}\dimen@\ht0\advance\dimen@-1ex%
%   \rlap{\raise.67\dimen@\hbox{\char'27}}A}
% \def\l{\char32l}
% \def\L{\leavevmode\setbox0\hbox{L}\hbox to\wd0{\hss\char32L}}
%
\def\uppercasetext@#1{%
   {\spaceskip1.3\fontdimen2\the\font plus1.3\fontdimen3\the\font
    \def\ss{SS}\let\i=I\let\j=J\let\ae\AE\let\oe\OE
    \let\o\O\let\aa\AA\let\l\L
    \skipmath@#1$\skipmath@$}}
%
\def\skipmath@#1$#2${\uppercase{#1}%
  \ifx\skipmath@#2\else$#2$\expandafter\skipmath@\fi}
%
%      Macro to check for missing \endsomething.
\def\add@missing#1{\expandafter\ifx\envir@end#1%
  \Err@{You seem to have a missing or misspelled
  \expandafter\string\envir@end ...}%
%      It is useful to supply the necessary missing piece, especially
%      in the case of \endref.
  \envir@end
\fi}
%
%      \revert@ and \envir@stack are for use by any environments that
%      don't enclose their text in a group, e.g., \proclaim,
%      \definition, \roster.
%
\newtoks\revert@
%
\def\envir@stack#1{\toks@\expandafter{\envir@end}%
  \edef\next@{\def\noexpand\envir@end{\the\toks@}%
    \revert@{\the\revert@}}%
  \revert@\expandafter{\next@}%
  \def\envir@end{#1}}
%
%      Some special trickery is necessary to get around the outerness
%      of \enddocument
\begingroup
\catcode`\ =11
\gdef\revert@envir#1{\expandafter\ifx\envir@end#1%
%      restore previous \envir@end:
\the\revert@%
%      The space after \enddocument is significant:
\else\ifx\envir@end\enddocument \Err@{Extra \string#1}%
\else\expandafter\add@missing\envir@end\revert@envir#1%
\fi\fi}
%      This definition can be made here because \enddocument  has not
%      yet been declared \outer.
%      The space at the end of \enddocument is necessary:
\xdef\enddocument {\string\enddocument}%
%      The space at the end of \enddocument is necessary here also:
\global\let\envir@end\enddocument %%%%%% don't remove the final space!
\endgroup\relax
%
\def\first@#1#2\end{#1}
\def\true@{TT}
\def\false@{TF}
\def\empty@{}
%
%      Test to see whether a given argument is empty or not.  If the
%      argument = a single space, it will test the same as empty,
%      which is in fact what we want.
%
\begingroup  \catcode`\-=3
\long\gdef\notempty#1{%
%      \empty@ is needed if we want the case #1 = {} to work properly:
  \expandafter\ifx\first@#1-\end-\empty@ \false@\else \true@\fi}
\endgroup
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -3- FONTS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{more fonts,}
%      Load some fonts that are not loaded in plain.tex, or only
%      preloaded (which means that the font information is in TeX's
%      memory but a control sequence name for the font still needs to
%      be assigned). plain.tex only loads cmex10, because originally
%      that was the only size available.  So we load cmex7 and later
%      cmex8, but we don't load any smaller sizes, in order to
%      conserve font memory; a need for the extension font in sizes
%      smaller than 7-point is most unusual.  For subscript sums or
%      other extension symbols in eightpoint text we will use cmex7
%      rather than cmex6, to allow us to get away without loading
%      cmex6.
%
%      We use \font@, not simply \font, so that these fonts will be
%      handled properly by AMS-TeX's syntax check.
%
%      Postscript versions by Blue Sky Research of the math fonts from
%      the AMSFonts package come only in sizes 10, 7 and 5, i.e. sizes
%      8 and 6 are not included. Therefore we include a switch that
%      can be set to determine which tfm files are used when loading
%      the 8 and 6-point size fonts.
%
%%\def\PSAMSFonts{TT}%  Blue Sky PS AMS fonts: True
\def\PSAMSFonts{TF}% Blue Sky PS AMS fonts: False
%
\font@\tensmc=cmcsc10 \relax
\if\PSAMSFonts
  \font@\sevenex=cmex10 at 7pt
\else
  \font@\sevenex=cmex7 \relax
\fi
%
%      We need cmti7 in case \italic is used in a subscript or
%      superscript. Once again we will conserve font space by not
%      loading cmti6 or cmti5, and declare the \scriptfont in
%      \eightpoint to be cmti7 rather than cmti6.  At least until we
%      know that users actually are using \italic in sub-subscript
%      size.
%
\font@\sevenit=cmti7 \relax
%
%      We have to load a lot of other fonts for eight-point text
%      (footnotes, abstracts, bibliography).  Note that cmti and cmsl
%      in sizes 5, 6 don't get loaded, since they may not exist (cmti7
%      is one of the standard 75 Computer Modern fonts, but cmti5 and
%      cmti6 aren't, nor are any of cmsl5, cmsl6, cmsl7).  AMSPPT
%      provides for ten-point and eight-point font sets;
%
\font@\eightrm=cmr8 \relax % preloaded in plain.tex
\font@\sixrm=cmr6 \relax % preloaded in plain.tex
\font@\eighti=cmmi8 \relax     \skewchar\eighti='177 % preloaded
\font@\sixi=cmmi6 \relax       \skewchar\sixi='177   % preloaded
\font@\eightsy=cmsy8 \relax    \skewchar\eightsy='60 % preloaded
\font@\sixsy=cmsy6 \relax      \skewchar\sixsy='60   % preloaded
\if\PSAMSFonts
  \font@\eightex=cmex10 at 8pt
\else
  \font@\eightex=cmex8 \relax
\fi
\font@\eightbf=cmbx8 \relax % preloaded in plain.tex
\font@\sixbf=cmbx6 \relax   % preloaded in plain.tex
\font@\eightit=cmti8 \relax % preloaded in plain.tex
\font@\eightsl=cmsl8 \relax % preloaded in plain.tex
\if\PSAMSFonts
  \font@\eightsmc=cmcsc10 at 8pt
\else
  \font@\eightsmc=cmcsc8 \relax
\fi
\font@\eighttt=cmtt8 \relax % preloaded in plain.tex
%
%      NOTE THE DOUBLE PERCENT SIGNS:
%% Nine-point fonts are not needed but are included here, commented
%% out, to make it easier for a user to add them if they are needed.
%
%%\font@\ninerm=cmr9 \relax
%%\font@\ninei=cmmi9 \relax   \skewchar\ninei='177
%%\font@\ninesy=cmsy9 \relax  \skewchar\ninesy='60
%%\if\PSAMSFONTS
%%  \font@\nineex=cmex10 at9pt % non-AMSfonts substitute
%%\else
%%  \font@\nineex=cmex9 \relax
%%\fi
%%\font@\ninebf=cmbx9 \relax
%%\font@\nineit=cmti9 \relax
%%\font@\ninesl=cmsl9 \relax
%%\font@\ninesmc=cmcsc9 \relax
%%
%%\font@\ninemsa=msam9 \relax
%%\font@\ninemsb=msbm9 \relax
%%\font@\nineeufm=eufm9 \relax
%
%      \UseAMSsymbols calls \loadmsam and \loadmsbm, then inputs the
%      file amssym.tex, which defines all the symbol names of the extra
%      math symbols in msam and msbm, as well as defining \frak and
%      \goth for eufm. Exception: if version 2.1 or later of amsppt.sty
%      is used together with amstex 2.0, \UseAMSsymbols doesn't
%      automatically load the MSAM and MSBM fonts. Therefore we
%      call \loadmsam and \loadmsbm in any case, since in version 2.1
%      the redundant calls inside \UseAMSsymbols are harmless (note
%      that in version 2.0 redundant calls of \loadxxx macros
%      wastefully advanced the \newfam allocation counter).
%
%      If memory space is tight for control sequence names, the first
%      thing to do is comment out the line containing "\UseAMSsymbols",
%      and load special symbols only as needed, with \newsymbol.
%
%%     To use amsppt.sty without AMSFonts, comment out the following
%%     two lines (and refer to the lines above that begin with double
%%     percent signs); to load extra math symbols only on demand (with
%%     \newsymbol) comment out the second line.
\loadeufm \loadmsam \loadmsbm
\message{symbol names}\UseAMSsymbols\message{,}
%
%      Now we define \tenpoint and \eightpoint for regular text and
%      footnotes, similarly to the TeXbook, p. 414.  We not only
%      change the \baselineskip, but also change the glue above and
%      below displayed formulas, in case an abstract or footnote
%      happens to have them.  We also need to set not only \strutbox,
%      but also \strutbox@. The height of \strutbox@ is the height of
%      \strutbox, minus the value of \normallineskiplimit.  And we
%      will set \ex@ in each case (for \tenpoint it is supposed to be
%      equivalent to 1pt, while for \eightpoint it will then
%      presumably be equivalent to .8pt).
%
%      When \ifsyntax@ is true, so that we are checking syntax, then
%      we won't bother specifying fonts (since we would only change
%      them all to \dummyft@ anyway), and we simply let \big and its
%      variants gobble up things with the proper syntax, instead of
%      worrying about getting the right sizes.
%
%      \tenpoint@ is a hook where new material can be added.
%      \topmatter makes use of this.  Note that to change the
%      baselineskip to say 14pt, one should say
%
%      \addto\tenpoint{\normalbaselineskip14pt\normalbaselines}
%
%      rather than just \addto\tenpoint{\baselineskip14pt}
%
\newtoks\tenpoint@
%
\def\tenpoint{\normalbaselineskip12\p@
 \abovedisplayskip12\p@ plus3\p@ minus9\p@
 \belowdisplayskip\abovedisplayskip
 \abovedisplayshortskip\z@ plus3\p@
 \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
 \textonlyfont@\rm\tenrm \textonlyfont@\it\tenit
 \textonlyfont@\sl\tensl \textonlyfont@\bf\tenbf
 \textonlyfont@\smc\tensmc \textonlyfont@\tt\tentt
 \ifsyntax@ \def\big##1{{\hbox{$\left##1\right.$}}}%
  \let\Big\big \let\bigg\big \let\Bigg\big
 \else
   \textfont\z@\tenrm  \scriptfont\z@\sevenrm
       \scriptscriptfont\z@\fiverm
   \textfont\@ne\teni  \scriptfont\@ne\seveni
       \scriptscriptfont\@ne\fivei
   \textfont\tw@\tensy \scriptfont\tw@\sevensy
       \scriptscriptfont\tw@\fivesy
   \textfont\thr@@\tenex \scriptfont\thr@@\sevenex
        \scriptscriptfont\thr@@\sevenex
   \textfont\itfam\tenit \scriptfont\itfam\sevenit
        \scriptscriptfont\itfam\sevenit
   \textfont\bffam\tenbf \scriptfont\bffam\sevenbf
        \scriptscriptfont\bffam\fivebf
   \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
%      The height of \strutbox@ is supposed to be the height of
%      \strutbox minus \normallineskip.  We take half from the top and
%      half from the bottom.
   \setbox\strutbox@\hbox{\lower.5\normallineskiplimit\vbox{%
        \kern-\normallineskiplimit\copy\strutbox}}%
%      We set \bigsize@ to the height of a parenthesis, times 1.2.
%      \bigsize@ controls the height of \big, \Big, \bigg and \Bigg
%      delimiters.
   \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
  \fi
%      \ex@ is supposed to come out to 1pt; multiplication factor may
%      need to be changed if Computer Modern is not being used. \jot,
%      a dimen register usually used for extra spacing between lines
%      of a multi-line displayed equation or similar structure, is
%      reset to 3\ex@ (in plain.tex it is always 3pt, but in AMSPPT it
%      may be reduced by \eightpoint).
  \normalbaselines\rm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
  \the\tenpoint@}
%
%      Like \tenpoint@, \eightpoint@ is a hook where extra material
%      can be added to the definition of \eightpoint.
%
\newtoks\eightpoint@
%
\def\eightpoint{\normalbaselineskip10\p@
 \abovedisplayskip10\p@ plus2.4\p@ minus7.2\p@
 \belowdisplayskip\abovedisplayskip
 \abovedisplayshortskip\z@ plus2.4\p@
 \belowdisplayshortskip5.6\p@ plus2.4\p@ minus3.2\p@
 \textonlyfont@\rm\eightrm \textonlyfont@\it\eightit
 \textonlyfont@\sl\eightsl \textonlyfont@\bf\eightbf
 \textonlyfont@\smc\eightsmc \textonlyfont@\tt\eighttt
 \ifsyntax@\def\big##1{{\hbox{$\left##1\right.$}}}%
  \let\Big\big \let\bigg\big \let\Bigg\big
 \else
  \textfont\z@\eightrm \scriptfont\z@\sixrm
       \scriptscriptfont\z@\fiverm
  \textfont\@ne\eighti \scriptfont\@ne\sixi
       \scriptscriptfont\@ne\fivei
  \textfont\tw@\eightsy \scriptfont\tw@\sixsy
       \scriptscriptfont\tw@\fivesy
%      The smallest size of the extension font currently available is
%      7-point.
  \textfont\thr@@\eightex \scriptfont\thr@@\sevenex
   \scriptscriptfont\thr@@\sevenex
  \textfont\itfam\eightit \scriptfont\itfam\sevenit
   \scriptscriptfont\itfam\sevenit
  \textfont\bffam\eightbf \scriptfont\bffam\sixbf
   \scriptscriptfont\bffam\fivebf
 \setbox\strutbox\hbox{\vrule height7\p@ depth3\p@ width\z@}%
%      The height of \strutbox@ is supposed to be the height of
%      \strutbox minus \normallineskip.  We take half from the top and
%      half from the bottom.
 \setbox\strutbox@\hbox{\raise.5\normallineskiplimit\vbox{%
   \kern-\normallineskiplimit\copy\strutbox}}%
%      We set \bigsize@ to the height of a parenthesis, times 1.2.
%      \bigsize@ controls the height of \big, \Big, \bigg and \Bigg
%      delimiters.
 \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
 \fi
%      \ex@ is supposed to come out to .8pt; multiplication factor may
%      need to be changed if Computer Modern is not being used. \jot,
%      a dimen register usually used for extra spacing between lines
%      of a multi-line displayed equation or similar structure, is
%      reset to 3\ex@ (in plain.tex it is 3pt).
 \normalbaselines\eightrm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
 \the\eightpoint@}
%
%      \linespacing command to introduce a factor by which
%      \normalbaselineskip will be multiplied. Multiplying by the
%      factor will cause any stretch or shrink to be lost; normally
%      that's not a problem.
\def\linespacing#1{%
  \addto\tenpoint{\normalbaselineskip=#1\normalbaselineskip
    \normalbaselines
%      Reset the strut boxes.
    \setbox\strutbox=\hbox{\vrule height.7\normalbaselineskip
      depth.3\normalbaselineskip}%
    \setbox\strutbox@\hbox{\raise.5\normallineskiplimit
      \vbox{\kern-\normallineskiplimit\copy\strutbox}}%
  }%
  \addto\eightpoint{\normalbaselineskip=#1\normalbaselineskip
    \normalbaselines
%      Reset the strut boxes.
    \setbox\strutbox=\hbox{\vrule height.7\normalbaselineskip
      depth.3\normalbaselineskip}%
    \setbox\strutbox@\hbox{\raise.5\normallineskiplimit
      \vbox{\kern-\normallineskiplimit\copy\strutbox}}%
  }%
}
%
\if\PSAMSFonts
  \def\extrafont@#1#2#3{%
    \font#1=#2%
%    Concatenate the proper size spec to the preceding letters
      \ifnum#3=9 10 at9pt%
      \else\ifnum#3=8 10 at8pt%
      \else\ifnum#3=6 7 at6pt%
%      Sizes other than 9, 8 or 6 are not expected, so this branch might
%      generate an error:
              \else #3\fi\fi\fi\relax}
\else
  \def\extrafont@#1#2#3{\font#1=#2#3\relax}
\fi
%
%      If the user has specified \loadeufb, \loadbold, \loadeusm,
%      \loadeusm, \loadeurm, \loadeurb, we need to add eightpoint
%      fonts.  We do this in \topmatter, and the user documentation
%      instructs the user to include any \load... command between
%      \documentstyle and \topmatter.
%
\def\loadextrasizes@#1#2#3#4#5#6#7{%
 \ifx\undefined#1%
 \else \extrafont@{#4}{#2}{8}\extrafont@{#6}{#2}{6}%
   \ifsyntax@
   \else
     \addto\tenpoint{\textfont#1#3\scriptfont#1#5%
       \scriptscriptfont#1#7}%
    \addto\eightpoint{\textfont#1#4\scriptfont#1#6%
       \scriptscriptfont#1#7}%
   \fi
 \fi
}
%
\def\loadextrafonts@{%
  \loadextrasizes@\msafam{msam}%
    \tenmsa\eightmsa\sevenmsa\sixmsa\fivemsa
  \loadextrasizes@\msbfam{msbm}%
    \tenmsb\eightmsb\sevenmsb\sixmsb\fivemsb
  \loadextrasizes@\eufmfam{eufm}%
    \teneufm\eighteufm\seveneufm\sixeufm\fiveeufm
  \loadextrasizes@\eufbfam{eufb}%
    \teneufb\eighteufb\seveneufb\sixeufb\fiveeufb
  \loadextrasizes@\eusmfam{eusm}%
    \teneusm\eighteusm\seveneusm\sixeusm\fiveeusm
  \loadextrasizes@\eusbfam{eusb}%
    \teneusb\eighteusb\seveneusb\sixeusb\fiveeusb
  \loadextrasizes@\eurmfam{eurm}%
    \teneurm\eighteurm\seveneurm\sixeurm\fiveeurm
  \loadextrasizes@\eurbfam{eurb}%
    \teneurb\eighteurb\seveneurb\sixeurb\fiveeurb
  \loadextrasizes@\cmmibfam{cmmib}%
    \tencmmib\eightcmmib\sevencmmib\sixcmmib\fivecmmib
  \loadextrasizes@\cmbsyfam{cmbsy}%
    \tencmbsy\eightcmbsy\sevencmbsy\sixcmbsy\fivecmbsy
  \let\loadextrafonts@\empty@
}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -4- PAGE DIMENSIONS AND OTHER GLOBAL SETTINGS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{page dimension settings,}
%      First we set up some basic parameters, which are different than
%      in plain.  These values are the ones currently in use (November
%      1989) in the Journal of the AMS.
%
\parindent1pc
\newdimen\normalparindent \normalparindent\parindent
\normallineskiplimit\p@
%
%      We use a common indent value for setting left and right margins
%      for abstract, table of contents, figure captions, and block
%      environments. The name is chosen as if we are going to have
%      several levels of indent, called \indenti, \indentii, ...; such
%      names can be constructed using \csname and \romannumeral with a
%      count register, which might be useful some time.
%
\newdimen\indenti \indenti=2pc
%
%      Provide a way to change the page height and width; changing the
%      page width automatically adjusts the caption width as well.
%      \pagewidth is in AMSTEX.TEX but it sets the caption width to a
%      different value than the one we want.
%
\def\pageheight#1{\vsize#1\relax}
\def\pagewidth#1{\hsize#1%
   \captionwidth@\hsize \advance\captionwidth@-2\indenti}
%
%      The height we use here is the height of the ``text block'', not
%      including the running heads, rather than the the height of the
%      ``type block'', the total type area on the page. Thus from the
%      Journal of the AMS type block measurement of 49pc  we subtract
%      22.5pt for the running head  (see the plain.tex definition of
%      \makeheadline)  and round to the nearest pica.
%
\pagewidth{30pc} \pageheight{47pc}
%
%      Change \magnification (from plain.tex) so that it doesn't reset the
%      page dimensions to 6.5 x 9 true inches.
\let\magnification=\mag
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -5- TOP MATTER DEFINITIONS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{top matter,}
%      After it's first called, since
%      we do not need \topmatter any longer, we define it to be empty,
%      to release the memory that the definition takes up.
%
\def\topmatter{\loadextrafonts@ \let\topmatter\relax}
%
%      \chapter is used within \title...\endtitle to produce something
%      such as "CHAPTER II", centered above the main text of the
%      chapter title. We do a little trickery with \afterassignment so
%      that the user can remove not only the word "CHAPTER" but also
%      the uppercasing and romannumeralizing by \nofrills.   Note that
%      we can't use \ignorespaces after \chapter@ in the usual way
%      because it would get in the way of the \count@ assignment.  In
%      fact spaces will be ignored by the assignment operation, the
%      only problem would be when \nofrills is used.
%
\def\chapterno@{\uppercase\expandafter{\romannumeral\chaptercount@}}
%
\newcount\chaptercount@
%
%      In order to avoid interfering with \topskip, we put the
%      \chapter material in the first line of the title, and do some
%      box and glue tricks to get it in position.
%
%      Perhaps need a test to make sure #1 is a number---if the user
%      does \chapter{IV} instead of \chapter{4} they may not
%      understand the error message they get.
%
%      \chaptercount@ assignment needs to be global because we are
%      working from inside the first line of \title.
%
\def\chapter{\let\savedef@\chapter
  \def\chapter##1{\let\chapter\savedef@
  \leavevmode\hskip-\leftskip
%      Put the \chapter stuff in an \rlap so it doesn't affect
%      centering of the title, and in an "uplap" so it is placed above
%      where we want it.
   \rlap{\vbox to\z@{\vss\centerline{\eightpoint
%      We do a baselineskip of 2pc from the base of the "CHAPTER"
%      banner to the base of the first title line.  (The baseline of
%      the \null will coincide with the baseline of the first title
%      line.)
   \frills@{CHAPTER\space\afterassignment\chapterno@
       \global\chaptercount@=}%
   ##1\unskip}\baselineskip2pc\null}}\hskip\leftskip}%
 \nofrillscheck\chapter}
%
%      We store the title in a box using a \setbox.  It could also be
%      done by defining \thetitle@.  One advantage of \setbox is that
%      syntax errors within the title (say for math) are reported
%      immediately instead of during the processing of \endtopmatter.
%      The title box is always put on the page by \endtopmatter, even
%      if it's empty. (With other pieces of the topmatter we check
%      first to see whether there's any text to typeset and skip to
%      the next item if not.) The text of the title is stored up for
%      the running heads, unless \rightheadtoks is nonempty---then
%      presumably the user has already used \rightheadtext to set the
%      right-hand running head, in which case we leave it unchanged.
%
%      The default for titles is uppercasing.  From a design
%      standpoint it might be preferable to do titles in 14-point text
%      with initial caps, but since titles may potentially contain any
%      kind of math, doing this would require a full-fledged
%      \fourteenpoint analogous to \tenpoint.  So to give the title
%      extra prominence we use uppercasing instead.  The uppercasing
%      can be removed by \nofrills.
%
\newbox\titlebox@
%
\def\title{\let\savedef@\title
%      We use a \vtop here because we want to know the height of the
%      first line of the title when we start typesetting the
%      topmatter.  In order to get the correct sinkage from the top of
%      the page.
 \def\title##1\endtitle{\let\title\savedef@
   \global\setbox\titlebox@\vtop{\tenpoint\bf
   \raggedcenter@
%      Increased \baselineskip is because of the uppercasing.  We do
%      it like this instead of putting it inside the \uppercasetext@
%      macro, because it only applies where an entire paragraph is
%      made up of uppercase text.
   \baselineskip1.3\baselineskip
   \frills@\uppercasetext@{##1}\endgraf}%
%      Check to see if right and left hand running heads have been
%      already assigned by the user---if so, don't override.
 \ifmonograph@ \edef\next{\the\leftheadtoks}%
    \ifx\next\empty@
    \leftheadtext{##1}\fi
 \fi
 \edef\next{\the\rightheadtoks}\ifx\next\empty@ \rightheadtext{##1}\fi
 }%
 \nofrillscheck\title}
%
%      Currently \author has no need for a \nofrills option, unlike
%      \title, since uppercasing is not done.
%
\newbox\authorbox@
\def\author#1\endauthor{\global\setbox\authorbox@
 \vbox{\tenpoint\smc\raggedcenter@
 #1\endgraf}\relaxnext@ \edef\next{\the\leftheadtoks}%
 \ifx\next\empty@\leftheadtext{#1}\fi}
%
\newbox\affilbox@
\def\affil#1\endaffil{\global\setbox\affilbox@
 \vbox{\tenpoint\raggedcenter@#1\endgraf}}
%
%      Since \address can be used any number of times, we have to
%      store the different addresses in control sequences that we
%      manufacture as needed. We use \addresscount@ to store the
%      number of times \address is used.
%
\newcount\addresscount@
\addresscount@\z@
\def\address#1\endaddress{\global\advance\addresscount@\@ne
%      The first address is `\address1', the next is `\address2', etc.
  \expandafter\gdef\csname address\number\addresscount@\endcsname
%      The unusually large shrinkability in the vskip before the
%      address is there because we don't want the addresses to fall on
%      a separate page at the end of a paper, and extra shrinkability
%      may help them to fit on the previous page in borderline cases.
  {\nobreak\vskip12\p@ minus6\p@\indent\eightpoint\smc#1\par}}
%
%      \curraddr was added in version 2.1.  It uses the address count
%      without advancing it, to add to the most recent address macro.
%
\def\curraddr{\let\savedef@\curraddr
  \def\curraddr##1\endcurraddr{\let\curraddr\savedef@
  \toks@\expandafter\expandafter\expandafter{%
       \csname address\number\addresscount@\endcsname}%
  \toks@@{##1}%
  \expandafter\xdef\csname address\number\addresscount@\endcsname
  {\the\toks@\endgraf\noexpand\nobreak
    \indent{\noexpand\rm
    \frills@{{\noexpand\it Current address\noexpand\/}:\space}%
    \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}%
  \nofrillscheck\curraddr}
%
%      \email uses the same counter as \address, since they should
%      pair up.
%
\def\email{\let\savedef@\email
  \def\email##1\endemail{\let\email\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\endgraf\indent\eightpoint}%
  \toks@@{##1\par}%
  \expandafter\xdef\csname email\number\addresscount@\endcsname
  {\the\toks@\frills@{{\noexpand\it E-mail address\noexpand\/}:%
     \noexpand\enspace}\the\toks@@}}%
  \nofrillscheck\email}
%
\def\thedate@{}
\def\date#1\enddate{\gdef\thedate@{\tenpoint#1\unskip}}
%
\def\thethanks@{}
\def\thanks#1\endthanks{%
  \ifx\thethanks@\empty@ \gdef\thethanks@{\eightpoint#1}%
  \else
    \expandafter\gdef\expandafter\thethanks@\expandafter{%
     \thethanks@\endgraf#1}%
  \fi}
%
\def\thekeywords@{}
\def\keywords{\let\savedef@\keywords
  \def\keywords##1\endkeywords{\let\keywords\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\eightpoint}%
  \toks@@{##1\unskip.}%
  \edef\thekeywords@{\the\toks@\frills@{{\noexpand\it
    Key words and phrases.\noexpand\enspace}}\the\toks@@}}%
 \nofrillscheck\keywords}
%
%      \subjclass is exactly analogous.
%
\def\thesubjclass@{}
\def\subjclass{\let\savedef@\subjclass
 \def\subjclass##1\endsubjclass{\let\subjclass\savedef@
   \toks@{\def\usualspace{{\rm\enspace}}\eightpoint}%
   \toks@@{##1\unskip.}%
   \edef\thesubjclass@{\the\toks@
     \frills@{{\noexpand\rm1991 {\noexpand\it Mathematics Subject
       Classification}.\noexpand\enspace}}%
     \the\toks@@}}%
  \nofrillscheck\subjclass}
%
%      Put the abstract in a box with margins at each side equal to
%      \indenti, obtained by reducing \hsize within a vbox centered by
%      $$...$$.  Notice that the \noindent is not erased by \nofrills
%      and that's what we want.
%
\newbox\abstractbox@
\def\abstract{\let\savedef@\abstract
 \def\abstract{\let\abstract\savedef@
  \setbox\abstractbox@\vbox\bgroup\noindent$$\vbox\bgroup
  \def\envir@end{\endabstract}\advance\hsize-2\indenti
  \def\usualspace{\enspace}\eightpoint \noindent
  \frills@{{\smc Abstract.\enspace}}}%
 \nofrillscheck\abstract}
%
%      Finish the box.  The \unskip is here in case the abstract ends
%      with something that adds vertical space, such as a \proclaim.
%
\def\endabstract{\par\unskip\egroup$$\egroup}
%
%      \widestnumber used to reset hanging indention in a table of
%      contents or bibliography.  Other applications may also be added
%      later.
%
%      The outerness of the heading macros causes problems. Therefore
%      we process \widestnumber in two stages: first, inside a group,
%      removing the outerness by letting the macros = \relax.  Then,
%      using an \expandafter\endgroup trick, we read the arguments
%      while the macros are still nonouter, but process the arguments
%      after we have exited from the group.
%
\def\widestnumber{\begingroup \let\head\relax\let\subhead\relax
  \let\subsubhead\relax \expandafter\endgroup\setwidest@}
%
\def\setwidest@#1#2{%
   \ifx#1\head\setbox\tocheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\subhead\setbox\tocsubheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\subsubhead\setbox\tocsubheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\key\refstyle A%
       \setboxz@h{\refsfont@\keyformat{#2}}%
       \refindentwd\wd\z@
   \else\ifx#1\no\refstyle C%
       \setboxz@h{\refsfont@\keyformat{#2}}%
       \refindentwd\wd\z@
   \else\ifx#1\page\setbox\z@\hbox{\quad\bf#2}%
       \pagenumwd\wd\z@
%      We assume the default form for \item numbers rather than trying
%      to handle all the variations such as "..."
   \else\ifx#1\item
       \setboxz@h{(#2)}\rosteritemwd\wdz@
   \else\message{\string\widestnumber\space not defined for this
      option (\string#1)}%
\fi\fi\fi\fi\fi\fi\fi}
%
%      \Monograph is capitalized by analogy with \NoRunningHeads and
%      \UseAMSsymbols because of its global scope.  We don't use
%      \global's because if the user puts \Monograph in the preamble
%      area as instructed it will automatically have global effect,
%      and in some special applications (e.g. documentation) it may be
%      nice to be able to localize the effect. \Monograph changes
%      paragraph indention from none to normal for certain structures
%      (subhead, proclaim, definition, ...) via \varindent@; it also
%      changes fonts for \head, \proclaim, \definition, \example,
%      \demo, and \remark.
%
%      The \ifmonograph@ test is used to decide whether to save a \toc
%      in a box or typeset it immediately, as well as whether to
%      typeset \thanks, \subjclass, and \keywords footnotes .
%
\newif\ifmonograph@
%
\def\Monograph{\monograph@true \let\headmark\rightheadtext
  \let\varindent@\indent \def\headfont@{\bf}\def\proclaimheadfont@{\smc}%
  \def\remarkheadfont@{\smc}}
%
\let\varindent@\noindent
%
\newbox\tocheadbox@    \newbox\tocsubheadbox@
\newbox\tocbox@
%
%      Allocate a dimen register for the width of the page number
%      column in table of contents. The true value of \pagenumwd
%    is not assigned until \toc is actually called, to avoid
%    initialization complications.
\newdimen\pagenumwd
%
\def\toc{\toc@{Contents}}
%
%      We make a separate macro that just redefines \title, \chapter,
%      \specialhead, \head, \subhead, \subsubhead, to simplify the
%      code of \toc.  This also makes it a little easier to work
%      around the outerness that most of them have.
%
\def\newtocdefs{%
%      The space after "\def" in these redefinitions is a convenience
%      for someone who wants to look for the main definitions---if
%      they search for "\def\title" the search will pass over "\def
%      \title" and find the main definition further down.
   \def \title##1\endtitle
       {\penaltyandskip@\z@\smallskipamount
        \hangindent\wd\tocheadbox@\noindent{\bf##1}}%
   \def \chapter##1{%
        Chapter \uppercase\expandafter{%
              \romannumeral##1.\unskip}\enspace}%
   \def \specialhead##1\endspecialhead
       {\par\hangindent\wd\tocheadbox@ \noindent##1\par}%
   \def \head##1 ##2\endhead
       {\par\hangindent\wd\tocheadbox@ \noindent
        \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil##1\enspace}\fi
        ##2\par}%
%      Since \subhead and \subsubhead change the \leftskip, we need to
%      do a \par before closing the group that localizes the change.
%      Unlike \head, we do not try to right-align the numbers.
%
   \def \subhead##1 ##2\endsubhead
       {\par\vskip-\parskip {\normalbaselines
        \advance\leftskip\wd\tocheadbox@
        \hangindent\wd\tocsubheadbox@ \noindent
        \if\notempty{##1}%
              \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
         ##2\par}}%
   \def \subsubhead##1 ##2\endsubsubhead
       {\par\vskip-\parskip {\normalbaselines
        \advance\leftskip\wd\tocheadbox@
        \hangindent\wd\tocsubheadbox@ \noindent
        \if\notempty{##1}%
              \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
        ##2\par}}}
%
\def\toc@#1{\relaxnext@
 \DN@{\ifx\next\nofrills\DN@\nofrills{\nextii@}%
      \else\DN@{\nextii@{{#1}}}\fi
      \next@}%
 \DNii@##1{%
%      If we're doing a book table of contents, we avoid setting the
%      whole thing in a box because if it's several pages long we
%      might run out of memory.
\ifmonograph@\bgroup\else\setbox\tocbox@\vbox\bgroup
   \centerline{\headfont@\ignorespaces##1\unskip}\nobreak
   \vskip\belowheadskip \fi
%    Redefine \page (it has another definition normally, for use in
%    references). The \hfilneg at the end is to cancel the
%    \parfillskip; the \penalty is to keep the \hfilneg from being
%    removed (normal processing at the end of a paragraph removes the
%    last skip).
   \def\page####1%
       {\unskip\penalty\z@\null\hfil
        \rlap{\hbox to\pagenumwd{\quad\hfil####1}}%
              \hfilneg\penalty\@M}%
   \setbox\tocheadbox@\hbox{0.\enspace}%
   \setbox\tocsubheadbox@\hbox{0.0.\enspace}%
   \leftskip\indenti \rightskip\leftskip
%      Increase \rightskip to move in the right margin to leave room
%      for page numbers (which will hang over into the "right margin").
%      The \bf is for taking into account page numbers for chapter titles,
%      which are bold.  A little extra width shouldn't hurt for toc's
%      without chapter titles.
   \setboxz@h{\bf\quad000}\pagenumwd\wd\z@
   \advance\rightskip\pagenumwd
%      Redefine all the heading macros to be their table-of-contents
%      versions.
   \newtocdefs
 }%
 \FN@\next@}
%
%      The \egroup closes the \vbox; or if we're in a monograph, just
%      matches the beginning \bgroup.
%
\def\endtoc{\par\egroup}
%
%      \pretitle, ..., \prepaper are entry points between the other
%      parts of the \topmatter so that users can insert things if
%      necessary.  If \pretitle is used to put any kind of box on the
%      page, it will throw off the sinkage of the title and everything
%      will have to be recalculated.
%
\let\pretitle\relax
\let\preauthor\relax
\let\preaffil\relax
\let\predate\relax
\let\preabstract\relax
\let\prepaper\relax
%
%      Now \dedicatory shows how to make use of the \pre... entry
%      points defined above.
%
\def\dedicatory #1\enddedicatory{\def\preabstract{{\medskip
  \eightpoint\it \raggedcenter@#1\endgraf}}}
%
%      A hook is provided for a translator name, for translations.
%      \eightpoint is used instead of just \eightrm, to be on the safe
%      side.  For instance, in transliteration some Russian names have
%      a ``prime'' symbol to represent the Russian ``soft sign''.  If
%      we didn't use \eightpoint we'd get a 10-point prime symbol.
%
\def\thetranslator@{}
\def\translator{%
  \let\savedef@\translator
  \def\translator##1\endtranslator{\let\translator\savedef@
    \edef\thetranslator@{\noexpand\nobreak\noexpand\medskip
      \noexpand\line{\noexpand\eightpoint\hfil
      \frills@{Translated by \uppercase}{##1}\qquad\qquad}%
       \noexpand\nobreak}}%
  \nofrillscheck\translator}
%
%      \endtopmatter now puts all of these things together on the
%      page. We start by checking to see if the left-hand running head
%      has been defined; if not, presumably it's because \author has
%      not been used, and presumably that means we are in a book
%      chapter rather than in an article. So we define it to be the
%      same as the right-hand running head, which will usually be the
%      text of the title.
%
%      When doing chapters in a book, \subjclass, \keywords and
%      \thanks should not print at the bottom of the page.
%
%      The baseline of the title should always fall at a fixed
%      distance from the top of the page, so we do the spacing with
%      \topskip instead of \vskip.
%
%      The spacing between elements of the topmatter in AMSPPT is
%      intended to be the same as in the Journal of the AMS; however
%      the actual spacing currently used in the latter is the rather
%      idiosyncratic result of a couple of years of piecemeal changes,
%      so that rather than follow it blindly we have opted to come as
%      close as possible by choosing whole or half-pica amounts.  The
%      situation is further complicated by the fact that the
%      documentstyle for the Journal of the AMS uses a different
%      method for putting running heads on the page, so that we cannot
%      measure distance from the top of the page in the same way; and
%      the date, affiliation, and abstract are handled differently as
%      well.
%
%      In this diagram the first measurement is from the top of the
%      type block to the baseline of the first line of the title.  In
%      the Journal of the AMS the value is 5.5pc rather than 4pc,
%      because it's measured to the top of the running head (which
%      extends above the text block). The rest of the measurements are
%      approximate visual space, done in \endtopmatter by \vskip's;
%      the effective base-to-base distance is approximately half a
%      pica more than the amount of the \vskip.
%
%      ______________________________ top of type area
%        |                            (according to \pageheight)
%        | 4pc baselineskip
%        |   |----------------------|
%      __|___|_______ TITLE ________|__
%            | WHICH MAY BE SEVERAL |
%            |      LINES LONG      |
%            |----------------------|
%                      2.5pc
%                   |--------|
%                   | AUTHOR |
%                   |--------|
%                       1pc
%                   |--------|
%                   | AFFIL  |
%                   |--------|
%                       1pc
%                    |------|
%                    | DATE |
%                    |------|
%                       1pc
%                 |------------|
%                 | DEDICATORY |
%                 |------------|
%                      1.5pc
%        |------------------------------|
%        |           ABSTRACT           |
%        |------------------------------|
%                      1.5pc
%        |------------------------------|
%        |       TABLE OF CONTENTS      |
%        |------------------------------|
%                       2pc
%      |-----------------------------------|
%      |           START OF TEXT           |
%      |                                   |
%
%
%      Make this \outer to catch missing or misspelled \end... in the
%      topmatter.  It doesn't work with \abstract though because that
%      uses the \setbox\vbox\bgroup ... \egroup mechanism, so we use
%      \add@missing to catch missing \endabstract's.
%
\outer\def\endtopmatter{\add@missing\endabstract
 \edef\next{\the\leftheadtoks}\ifx\next\empty@
  \expandafter\leftheadtext\expandafter{\the\rightheadtoks}\fi
 \ifmonograph@\else
   \ifx\thesubjclass@\empty@\else \makefootnote@{}{\thesubjclass@}\fi
   \ifx\thekeywords@\empty@\else \makefootnote@{}{\thekeywords@}\fi
%      If \thanks given, treat it as a footnote text (with no footnote
%      mark).
   \ifx\thethanks@\empty@\else \makefootnote@{}{\thethanks@}\fi
 \fi
%      We want a sinkage of 4pc from the top of the page (= the top of
%      the text area, not including the running heads) for articles,
%      and 7pc for monograph chapters.
  \pretitle
  \begingroup % to localize variant topskip
  \ifmonograph@ \topskip7pc \else \topskip4pc \fi
%      We don't unvbox the titlebox because we don't expect footnotes
%      to ever appear in the title, so we don't need to worry about
%      allowing them to migrate to the outer level.  (Some journals
%      use footnotes in titles to give acknowledgments of research
%      support; in AMSPPT this is an unnumbered footnote, done with
%      \thanks, outside of the title.)
  \box\titlebox@
  \endgroup
  \preauthor
  \ifvoid\authorbox@\else \vskip2.5pcplus1pc\unvbox\authorbox@\fi
  \preaffil
  \ifvoid\affilbox@\else \vskip1pcplus.5pc\unvbox\affilbox@\fi
  \predate
  \ifx\thedate@\empty@\else
       \vskip1pcplus.5pc\line{\hfil\thedate@\hfil}\fi
  \preabstract
  \ifvoid\abstractbox@\else
       \vskip1.5pcplus.5pc\unvbox\abstractbox@ \fi
  \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi
  \prepaper
  \vskip2pcplus1pc\relax
}
%
\def\document{%
%    We call \loadextrafonts@ here as well as in \topmatter; this is
%    to allow use of the extra sizes of the fonts in e.g. test documents
%    that don't include a full topmatter section. If \topmatter was
%    executed, \loadextrafonts@ will now be a harmless no-op.
  \loadextrafonts@
  \let\fontlist@\relax\let\alloclist@\relax
%      Start out in \tenpoint
  \tenpoint}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -6- SECTION HEADINGS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{section heads,}
%      In accordance with conventional design principles, the space
%      below headings is not given any stretchability or
%      shrinkability.
%
\newskip\aboveheadskip       \aboveheadskip\bigskipamount
\newdimen\belowheadskip      \belowheadskip6\p@
\def\headfont@{\smc}
%
%      Since we often want to do a penalty and vskip, and since there
%      are extra complications involved if there is a preceding vskip
%      from something else, we define a macro to do it.  Normally it
%      is used while we're working on the main vertical list, so we
%      have to use \removelastskip (which does a negative skip) rather
%      than \unskip (which REALLY removes the last skip).  If the last
%      thing on the main vertical list is anything other than a vskip,
%      say a penalty from \pagebreak, the value returned by \lastskip
%      will be 0, but the potential complications are a whole other
%      subject.  This macro handles the straightforward cases.
%
%      In some cases we may not want to put a penalty at all.
%      We refrain from doing any penalty if the first argument of
%      \penaltyandskip@ is 0; the essential effect of an explicit
%      \penalty0 can be gotten by doing a penalty of 1 instead.
%
%      We use \penalty@ instead of \penalty, so that we can redefine
%      \penalty@ in \nobreak, to prevent page breaks between certain
%      pairs such as \head \subhead or \head \proclaim or \nopagebreak
%      \proclaim ---for example, in
%
%      "... which leads to this theorem:
%      \proclaim{Theorem 8.2} ..."
%
%      a page break after the colon would be bad, and a user might
%      want to be able to add a \nopagebreak.
%
%      The sequence
%
%           \subhead Text...\endsubhead
%           \subsubhead Text...\endsubsubhead
%
%      will still have the weakness of allowing a pagebreak between
%      the two headings, because \endsubhead doesn't do a \nobreak
%      (since it's a run-in heading.
%
\def\penaltyandskip@#1#2{\par\skip@#2\relax
  \ifdim\lastskip<\skip@\relax\removelastskip
      \ifnum#1=\z@\else\penalty@#1\relax\fi\vskip\skip@
  \else\ifnum#1=\z@\else\penalty@#1\relax\fi\fi}
%
\def\nobreak{\penalty\@M
%      Change the definition of \penalty@ so that the following number
%      will be gobbled (by assigning it to the scratch register
%      \count@@@).
  \ifvmode\gdef\penalty@{\global\let\penalty@\penalty\count@@@}%
%      If the next piece of the document after \nobreak is something
%      like \subhead or \proclaim that calls \penaltyandskip@, then
%      \penalty@ will reset itself in the way that we want.  But if
%      not, then we still want to reset \penalty@; so we use
%      \everypar.  There are probably some unusual cases that will
%      still have problems, but at the moment this is the best
%      solution we have.
  \everypar{\global\let\penalty@\penalty\everypar{}}\fi}
%
\let\penalty@\penalty
%
%      We equate the old form of the headings to the new form, for
%      backward compatibility.  It's easier to do this now rather than
%      later because \head and \subhead are going to be outer.
%
\def\heading#1\endheading{\head#1\endhead}
\def\subheading{\DN@{\ifx\next\nofrills
    \expandafter\subheading@
  \else \expandafter\subheading@\expandafter\empty@
  \fi}%
  \FN@\next@
}
\def\subheading@#1#2{\subhead#1#2\endsubhead}
%
%      One more heading level, for occasional use.  This is the next
%      level ABOVE \head.  The default style is ragged right;
%      otherwise it's the same as \head.
%
\def\specialheadfont@{\bf}
\outer\def\specialhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  \begingroup\interlinepenalty\@M\rightskip\z@ plus\hsize
  \let\\\linebreak
  \specialheadfont@\noindent}
\def\endspecialhead{\par\endgroup\nobreak\vskip\belowheadskip}
%
%      penalty-200 is the penalty amount used by plain.tex's
%      \bigbreak.
%
\outer\def\head#1\endhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\headfont@\raggedcenter@\interlinepenalty\@M
  #1\endgraf}\headmark{#1}%
  \nobreak
  \vskip\belowheadskip}
%
%      \headmark will be redefined to be \rightheadtext by \Monograph.
%
\let\headmark\eat@
%
%      The purpose of \restoredef@ is to work around problems caused
%      by the outerness of things like \subhead. \relax at the
%      beginning prevents the \savedef@ (which may be \outer) from
%      being read prematurely in certain kinds of expansion.
%
\def\restoredef@#1{\relax\let#1\savedef@\let\savedef@\relax}
%
%      \subhead and \subsubhead are simpler, though they allow
%      \nofrills. (\head, being centered, does not have automatic
%      punctuation put in at the end and so \nofrills doesn't have
%      anything to do.) The syntax of \subhead is changed from
%      \subheading{...} (version 1) to \subhead...\endsubhead (version
%      2). This was done for the following reasons: (1) to be
%      consistent with \head...\endhead (we could have changed \head
%      instead of \subhead, but the \x...\endx syntax is the one
%      currently in  use in AMS production); (2) if someone (perhaps
%      us) ever wants to do something tricky with the headings, having
%      the \end... may help them avoid technical complications.
%
\newskip\subheadskip       \subheadskip\medskipamount
\def\subheadfont@{\bf}
\outer\def\subhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \let\savedef@\subhead \let\subhead\relax
  \def\subhead##1\endsubhead{\restoredef@\subhead
    \penaltyandskip@{-100}\subheadskip
    \varindent@{\def\usualspace{{\subheadfont@\enspace}}%
    \subheadfont@\ignorespaces##1\unskip\frills@{.\enspace}}%
    \ignorespaces}%
  \nofrillscheck\subhead}
%
%      In version 2.0 of amsppt.sty we also add a third level of
%      heading, \subsubhead.
%
\newskip\subsubheadskip       \subsubheadskip\medskipamount
\def\subsubheadfont@{\it}
\outer\def\subsubhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo
  \add@missing\endexample \add@missing\endproclaim
  \let\savedef@\subsubhead \let\subsubhead\relax
  \def\subsubhead##1\endsubsubhead{\restoredef@\subsubhead
    \penaltyandskip@{-50}\subsubheadskip
%      Add italic correction in \usualspace, because \subheadfont@ is
%      italic, in case the substituted punctuation is something tall
%      like a question mark or exclamation point.
      {\def\usualspace{\/{\it\enspace}}%
    \subsubheadfont@##1\unskip\frills@{.\enspace}}}%
  \nofrillscheck\subsubhead}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -7- THEOREM ENVIRONMENTS AND SIMILAR STRUCTURES
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{theorems/proofs/definitions/remarks,}
%
\def\proclaimheadfont@{\bf}
%      Make \proclaimfont a non-private control sequence, so that
%      users can change it back to \sl if desired without
%      complications.
\def\proclaimfont{\it}
%
\outer\def\proclaim{%
  \let\savedef@\proclaim \let\proclaim\relax
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\endproclaim \envir@stack\endproclaim
%      penalty-100 is the penalty amount used by plain.tex's
%      \medbreak.
 \def\proclaim##1{\restoredef@\proclaim
   \penaltyandskip@{-100}\medskipamount\varindent@
   \def\usualspace{{\proclaimheadfont@\enspace}}\proclaimheadfont@
   \ignorespaces##1\unskip\frills@{.\enspace}%
  \proclaimfont\ignorespaces}%
 \nofrillscheck\proclaim}
%
%      \endproclaim ends the paragraph, switches back to \rm and adds
%      spacing. (This means that if, for some strange reason, a whole
%      section of text happens to be in italics, then the user must
%      type \it again after each \endproclaim, but that seems too
%      special a case to need providing for.)  The penalty of 55 is
%      just the plain.tex penalty for \endproclaim, carried over
%      without change. Version 2.1 change: removed \outer prefix, to
%      simplify some programming related to \add@missing and
%      \revert@envir.
%
\def\endproclaim{\revert@envir\endproclaim \par\rm
  \penaltyandskip@{55}\medskipamount}
%
%      In \remark, we take the opportunity again to issue an error
%      message if a previous \proclaim has no matching \endproclaim.
%
\def\remarkheadfont@{\it}
\def\remark{\let\savedef@\remark \let\remark\relax
  \add@missing\endroster \add@missing\endproclaim
  \envir@stack\endremark
  \def\remark##1{\restoredef@\remark
    \penaltyandskip@\z@\medskipamount
  {\def\usualspace{{\remarkheadfont@\enspace}}%
  \varindent@\remarkheadfont@\ignorespaces##1\unskip%
  \frills@{.\enspace}}\rm
  \ignorespaces}\nofrillscheck\remark}
%
%      \endremark is easy.
%
\def\endremark{\par\revert@envir\endremark}
%
\ifx\undefined\square
  \def\square{\vrule width.6em height.5em depth.1em\relax}\fi
\def\qed{\ifhmode\unskip\nobreak\fi\quad
  \ifmmode\square\else$\m@th\square$\fi}
%
%      Proofs are the same as Remarks, except there is an additional
%      \medskip after a Proof.  We don't have a runaway demo or remark
%      check until \enddocument because proofs within proofs (and
%      perhaps remarks within remarks) are possible.
%
\def\demo{\DN@{\ifx\next\nofrills
    \DN@####1####2{\remark####1{####2}\envir@stack\enddemo
      \ignorespaces}%
  \else
    \DN@####1{\remark{####1}\envir@stack\enddemo\ignorespaces}%
  \fi
  \next@}%
\FN@\next@}

\def\enddemo{\par\revert@envir\enddemo \endremark\medskip}
%
%      \definition uses \proclaimheadfont@ because normally the two
%      use the same font for the head font, with \definition using \rm
%      for the text as opposed to the \it used for \proclaim.
%
\def\definition{\let\savedef@\definition \let\definition\relax
  \add@missing\endproclaim \add@missing\endroster
  \add@missing\enddefinition \envir@stack\enddefinition
%      \proclaimheadfont@ comes after the period here because
%      sometimes we want the period to be roman rather than bold, e.g.
%      when the preceding thing is a math formula or a citation, set
%      in roman type.
   \def\definition##1{\restoredef@\definition
     \penaltyandskip@{-100}\medskipamount
        {\def\usualspace{{\proclaimheadfont@\enspace}}%
        \varindent@\proclaimheadfont@\ignorespaces##1\unskip
        \frills@{.\proclaimheadfont@\enspace}}%
        \rm \ignorespaces}%
  \nofrillscheck\definition}
\def\enddefinition{\revert@envir\enddefinition
  \par\medskip}
%
\def\example{\DN@{\ifx\next\nofrills
    \DN@####1####2{\definition####1{####2}\envir@stack\endexample
      \ignorespaces}%
  \else
    \DN@####1{\definition{####1}\envir@stack\endexample\ignorespaces}%
  \fi
  \next@}%
\FN@\next@}
\def\endexample{\revert@envir\endexample \enddefinition }
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -8- ROSTERS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{rosters,}
%      In version 2 of amsppt we provide a more convenient way of
%      changing the indention of roster items.
%
\newdimen\rosteritemwd
\rosteritemwd16pt % approximately the width of (iii) in 10 point text
%
%      \roster uses \rostercount@ to store the \item number. The first
%      item is treated specially, because of the extra space before
%      it, so we need a flag \iffirstitem@ to identify it.
%
\newcount\rostercount@
\newif\iffirstitem@
%
%      Since \item in \roster differs from in \plain, we store plain's
%      \item in \plainitem@, so that we can restore the definition
%      after the \roster is over.
%
\let\plainitem@\item
%
%      In order for our \roster's to work, we will also have to be
%      sure that \everypar is {}.  Just in case \everypar already has
%      a value, as it might in some format, we store those values in
%      the token list \everypartoks@, so that we can restore them at
%      the end.  \par@ does this storing, and sets \everypar{}.
%
\newtoks\everypartoks@
\def\par@{\everypartoks@\expandafter{\the\everypar}\everypar{}}
%
\def\leftskip@{}
%
\def\roster{%
  \envir@stack\endroster
%      We also have to store the \leftskip, since it will be changed.
 \edef\leftskip@{\leftskip\the\leftskip}%
 \relaxnext@
 \rostercount@\z@% Initialize \rostercount@ to 0.
 \def\item{\FN@\rosteritem@}%      \item, now redefined, has
%      to look ahead for [ and ", since we allow optional and literal
%      arguments. \rosteritem@ itself is defined below.  The following
%      \next@ (in \DN@) is the one called at the very end of this
%      \def.
 \DN@{\ifx\next\runinitem\let\next@\nextii@\else
  \let\next@\nextiii@\fi\next@}%
%      First we look to see whether \roster is followed by \runinitem,
%      since this requires different processing.
 \DNii@\runinitem% If \runinitem occurs, \nextii@ must kill it off.
  {\unskip% This unskips any space before the original \roster.
%      Our definition of \nextii@\runinitem itself uses compressed
%      format and a \futurelet\next\next@, because we still have to
%      allow [ or " to come next.
   \DN@{\ifx\next[\let\next@\nextii@\else
    \ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi\fi\next@}%
%      The following \nextii@ is the one created by
%      \nextii@\runinitem; there is no conflict of names, since the
%      first calls the second.
   \DNii@[####1]{\rostercount@####1\relax
    \enspace\therosteritem{\number\rostercount@}~\ignorespaces}%
%      If [...] comes next, we use (...) but we explicitly do this by
%      setting \rostercount@ equal to ... so that succeeding \item's
%      will have the right numbers (use of something other than a
%      number will give an error message).
   \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}%
%      If "..." comes next, we use ... exactly as typed.
   \def\nextiv@{\enspace\therosteritem1\rostercount@\@ne~}%
%      Otherwise just use (1).
   \par@\firstitem@false% Before doing any of this we still change
%      \everypar, if necessary, which is normally done elsewhere, and
%      set \firstitem@false, since this \runinitem counts as the
%      first.
   \FN@\next@}%      End of definition of \nextii@\runinitem.
%      The following \nextiii@ will be used if we didn't have
%      \runinitem.
 \def\nextiii@{\par\par@% End the present paragraph, change \everypar
%      if necessary, prohibit a break, add a small skip, but add
%      something to offset any \parskip, if there is any, which would
%      be contributed when the next paragraph is begun by the next
%      \item.
  \penalty\@m\smallskip\vskip-\parskip
%      And set \firstitem@true for use with \item.
  \firstitem@true}
 \FN@\next@}
%
%      Remember that \rosteritem@ is called by
%      \futurelet\next\rosteritem@.
%
\def\rosteritem@{\iffirstitem@\firstitem@false
  \else\par\vskip-\parskip\fi
%      Except at the first \item, we end the paragraph (consisting of
%      the previous \item), and subtract any space that might be added
%      by the next \item.
 \leftskip\rosteritemwd \advance\leftskip\normalparindent
 \advance\leftskip.5em \noindent
 \DNii@[##1]{\rostercount@##1\relax\itembox@}%
%      If [...] follows \item, we use ... as the number, again by
%      setting \rostercount@, so that succeeding \items will have the
%      right number.
 \def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}%
%      If "..." follows  \item, we use ... exactly as typed.
 \def\nextiv@{\advance\rostercount@\@ne\itembox@}%
%      Otherwise we print the \rostercount@ in parentheses.
 \def\therosteritem@{\therosteritem{\number\rostercount@}}%
 \ifx\next[\let\next@\nextii@\else\ifx\next"\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}
%
\def\itembox@{\llap{\hbox to\rosteritemwd{\hss
  \kern\z@ % kern to thwart \unskip in \rom
  \therosteritem@}\enspace}\ignorespaces}
%
%      \therosteritem is just a convenience for the user.
%
\def\therosteritem#1{\rom{(\ignorespaces#1\unskip)}}
%
%      We want to save \Runinitem for last, but it is relevant even to
%      the definition of \endroster, since we have to worry whether
%      \endroster is followed by another \Runinitem.  We will use a
%      flag \ifnextRunin@ to tell us.
%
\newif\ifnextRunin@
%
\def\endroster{\relaxnext@
 \revert@envir\endroster % restore \envir@end
 \par\leftskip@% End the paragraph, and restore the \leftskip.
 \global\rosteritemwd16\p@ % restore default value
 \penalty-50 \vskip-\parskip\smallskip% Add a good break and
%      subtract any space that will be started by next paragraph, but
%      add a \smallskip.
 \DN@{\ifx\next\Runinitem\let\next@\relax
%      Don't do anything else if \Runinitem comes next.
  \else\nextRunin@false\let\item\plainitem@% Otherwise, set
%      \nextRunin@false, and restore \item to its definition in plain;
   \ifx\next\par% moreover, if \endroster is followed by \par,
    \DN@\par{\everypar\expandafter{\the\everypartoks@}}%
%      delete that instruction (since we've already put in a \par),
%      and restore \everypar,
   \else% but if the \endroster isn't followed by a new paragraph,
    \DN@{\noindent\everypar\expandafter{\the\everypartoks@}}%
%      start the next paragraph unindented, and restore \everypar.
  \fi\fi\next@}%
 \FN@\next@}
%
%      Finally, for \Runinitem ... \roster\runinitem we have the usual
%      junk for worrying about [ or " coming next, and then more
%      interesting things:  We have to find out how many lines of text
%      we had before the \roster; we will store this in
%      \rosterhangafter@.
%
\newcount\rosterhangafter@
\def\Runinitem#1\roster\runinitem{\relaxnext@
  \envir@stack\endroster
%      Initialize \rostercount@ to 0.
 \rostercount@\z@
%      Define \item as before.
 \def\item{\FN@\rosteritem@}%
%      Store everything up to the roster in \runinitem@.
 \def\runinitem@{#1}%
 \DN@{\ifx\next[\let\next\nextii@\else\ifx\next"\let\next\nextiii@
  \else\let\next\nextiv@\fi\fi\next}%
 \DNii@[##1]{\rostercount@##1\relax
%      If [...] follows \runinitem, we proceed as before, except we
%      call this first instance \item@, and we let \nextv@, defined
%      below, take care of everything.
  \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
%      If "..." follows \runinitem, we define \item@ to use it.
 \def\nextiii@"##1"{\def\item@{{\rm##1}}\nextv@}%
 \def\nextiv@{\advance\rostercount@\@ne
%      Otherwise, we use the proper \rostercount@. Now comes \nextv@,
%      which has to properly typeset things.
  \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
%      First store things in \box0 .
 \def\nextv@{\setbox\z@\vbox
%      Start unindented if we have \ifnextRunin@true.  This will
%      happen only if we had \Runinitem...\endroster right before.
  {\ifnextRunin@\noindent\fi
%      Add the stored things in \runinitem@, and then \item@.
  \runinitem@\unskip\enspace\item@~\par
%      This sets \rosterhangafter@ to the number of lines in \box0 ,
%      i.e., of the material so far; see the TeXbook, p. 103. We need
%      to say \global since this is set  within \box0. Now we're done
%      with \box0 !
  \global\rosterhangafter@\prevgraf}%
  \firstitem@false% Set \firstitem@false for future \item's.
%      End previous paragraph unless we had \Runinitem ...\endroster
%      right before. Now comes the good part: we
%      \hangindent3\parindent, as before, but we do it for
%      \rosterhangafter@ lines, the number that already appeared in
%      the material we set in \box0 .
  \ifnextRunin@\else\par\fi
  \hangafter\rosterhangafter@\hangindent3\normalparindent
%      Start unindented if we had a \Runinitem ... \endroster right
%      before.
  \ifnextRunin@\noindent\fi
  \runinitem@\unskip\enspace%  Put in all the stored stuff
  \item@~\ifnextRunin@\else\par@\fi% and the \item@, and
%      end the paragraph, unless we had a \Runinitem ... \endroster
%      before.
  \nextRunin@true\ignorespaces}%% Here's where we set \nextRunin@true.
 \FN@\next@}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -9- FOOTNOTES
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{footnotes,}
%      \footmarkform@ tells how to treat a general type of footnote
%      marker.  And \thefootnotemark is for the user, analogous to
%      \thetag in AMSTEX.TEX.
%
\def\footmarkform@#1{$\m@th^{#1}$}
\let\thefootnotemark\footmarkform@
%
%      \makefootnote@ takes care of the general problem of creating a
%      footnote whose marker is #1 and whose text is #2, so that we
%      can concentrate separately on the problem of how the marker is
%      determined.  It is essentially \vfootnote from the TeXbook, p.
%      363, except that we don't do fancy things to worry about
%      category code changes, and instead of adding a \strut at the
%      end, we will just add the lower part of the strut.
%
\def\makefootnote@#1#2{\insert\footins
 {\interlinepenalty\interfootnotelinepenalty
 \eightpoint\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox
 \floatingpenalty\@MM\leftskip\z@skip\rightskip\z@skip
 \spaceskip\z@skip\xspaceskip\z@skip
 \leavevmode{#1}\footstrut\ignorespaces#2\unskip\lower\dp\strutbox
 \vbox to\dp\strutbox{}}}
%
%      Before version 2.0 \footmarkcount@ was declared in amstex.tex.
%
\newcount\footmarkcount@
\footmarkcount@\z@
%
%      \footnotemark basically just advances \footmarkcount@ by 1 and
%      then uses \footmarkform@{\number\footmarkcount@}---we still
%      have to worry about the space factor as in the definition of
%      \footnote in the TeXbook, p. 363.  However, we are allowing
%      both an `optional' argument [#1], where we instead use
%      \footmarkform@{#1}, and a `literal' argument "#1", where we
%      instead use #1 exactly as typed, so we need to use a \futurelet
%      to look at the next symbol. Compressed format is used.
%
\def\footnotemark{\let\@sf\empty@\relaxnext@
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]{\footmarkform@{##1}\@sf}%
 \def\nextiii@"##1"{{##1}\@sf}%
 \def\nextiv@{\iffirstchoice@\global\advance\footmarkcount@\@ne\fi
  \footmarkform@{\number\footmarkcount@}\@sf}%
 \FN@\next@}
%
%      \footnotetext essentially applies \makefootnote@ to the next
%      group, using \footmarkcount@ for the marker that goes before
%      the footnote text. However, we once again allow optional and
%      literal arguments.  Compressed format is used.
%
\def\footnotetext{\relaxnext@
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}%
 \def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}%
 \def\nextiv@##1{\makefootnote@{\footmarkform@%
  {\number\footmarkcount@}}{##1}}%
 \FN@\next@}
%
%      Finally, \footnote is basically \footnotemark\footnote, but we
%      can't write it directly that way because it, too, can take
%      optional and literal arguments.  Compressed format again.
%
\def\footnote{\let\@sf\empty@\relaxnext@
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}%
 \def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}%
 \def\nextiv@##1{\footnotemark\footnotetext{##1}}%
 \FN@\next@}
%
%      \adjustfootnotemark just allows the user to change
%      \footmarkcount@.
%
\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax}
%
%      We use the definition of \footnoterule provided by plain, but
%      change its width from 2 truein to 5pc.
%
\def\footnoterule{\kern-3\p@
  \hrule width5pc\kern 2.6\p@}%      the \hrule is .4pt high
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -10- TABLES
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%      At the present time no table macros are provided.  Captions can
%      be gotten using \topcaption or \botcaption.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -11- FIGURE SPACES AND CAPTIONS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{figures and captions,}
\def\captionfont@{\smc}
%
%      These captions are designed for use within \topinsert's and
%      \midinsert's.  \nofrills is not currently an option, though
%      probably it should be added eventually.
%
\def\topcaption#1#2\endcaption{%
%      The captionwidth may have been changed by the user so we don't
%      make the assumption that it is equal to \hsize - 2\indenti.
  {\dimen@\hsize \advance\dimen@-\captionwidth@
%      \raggedcenter@ uses the em so we set the font before calling
%      it. \leftskip and \rightskip are changed by \raggedcenter so
%      the modifications of \leftskip and \rightskip must come after.
   \rm\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip
  {\captionfont@#1}%
  \if\notempty{#2}.\enspace\ignorespaces#2\fi
  \endgraf}\nobreak\bigskip}
%
%      For whatever reason, the style in current AMS production has
%      figure captions (= \botcaption) set in a block while table
%      captions are set ragged center style.
%
\def\botcaption#1#2\endcaption{%
%      The previous vskip may be blank space for a figure, so we can't
%      use \penaltyandskip@ here, otherwise the \bigskip would not be
%      added (assuming the preceding vskip is greater than
%      \bigskipamount):
  \nobreak\bigskip
%      Measure how wide the caption is.  Maybe it's only "Figure 1",
%      or maybe it's "Figure 1. Blah blah blah ... for 10 lines."  In
%      the first case center it, in the second case put it in
%      paragraph form.
  \setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\rm#2\fi}%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \leftskip.5\dimen@ \rightskip\leftskip
%      long caption---set it in a paragraph
   \noindent \ifdim\wdz@>\captionwidth@
%      short caption---add \hfil to balance with \parfillskip.
   \else\hfil\fi
  {\captionfont@#1}%
  \if\notempty{#2}.\enspace\rm#2\fi\endgraf}}
%
%      Redefine plain TeX \@ins to add definition of \vspace (locally)
%      for use with caption macros.  Also \captionwidth.
%
\def\@ins{\par\begingroup\def\vspace##1{\vskip##1\relax}%
  \def\captionwidth##1{\captionwidth@##1\relax}%
  \setbox\z@\vbox\bgroup} % start a \vbox
%
%      CASE 1: \topcaption plus a table typed by the author.
%
%      \topinsert
%      \topcaption{Table 1}This is a table caption.\endcaption
%      \halign{ ...
%       ...
%      }
%      \endinsert
%
%      CASE 2: \topcaption plus some blank space.
%
%      \midinsert
%      \topcaption{Table 2}This is another table caption.\endcaption
%      \vspace{13pc}
%      \endinsert
%
%      CASE 3: \botcaption plus some blank space.
%
%      \topinsert
%      \vspace{7pc}
%      \botcaption{Figure 1}\endcaption
%      \endinsert
%
%      Use of \captionwidth:
%
%      \topinsert
%      \captionwidth{14pc}
%      \topcaption{Table 1}Text ...
%      \endcaption
%      \endinsert
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -12- MISCELLANEOUS FORMATTING MACROS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{miscellaneous,}
%    \block is intended for typing long quotes in a block, indented on
%    both margins. It is set up so that it can be used in either of two
%    ways:
%
%         $$\block...\endblock\tag1.1$$
%
%    or
%
%         Normal text.
%         \block ...  \endblock
%         Continue with more text.
%
%    In the latter case, we use a TeX display to provide spacing above
%    and below the block. If we're in vertical mode when \block is
%    called, we use \noindent to avoid getting an extra blank line
%    before the display. But then we will get the short display skips
%    instead of the full display skips, so we set \predisplaysize
%    explicitly to ensure the full display skips.
%
\def\block{\RIfMIfI@\nondmatherr@\block\fi
       \else\ifvmode\noindent$$\predisplaysize\hsize
         \else$$\fi
  \def\endblock{\par\egroup$$}\fi
  \vbox\bgroup\advance\hsize-2\indenti\noindent}
\def\endblock{\par\egroup}
%
%      In version 1 of amsppt \cite did some parsing to locate a comma
%      in its argument and if one was found the font was switched from
%      \citefont to \rm.  In version 2 we no longer do this because if
%      a \cite deviates too much from the expected form we run into
%      problems:  The expected form was either \cite{13}, or \cite{13,
%      Theorem 2.2}.  But if for example the user wants to cite two
%      references together, \cite{13,15}, we don't want to switch off
%      \citefont after the comma.  And since authors tend to invent
%      even more imaginative variations than this, we just did away
%      with the parsing altogether.
%
%      \m@th is in case the author uses subscripts in his citation
%      codes.
%
\def\cite#1{\rom{[{\citefont@\m@th#1}]}}
%
%      In version 1 of amsppt \citefont was \bf.
%
\def\citefont@{\rm}
%
%      \rom provides a way for getting roman punctuation and numerals
%      in italic text. It takes pains to handle italic corrections
%      reasonably nicely.
%
\def\rom#1{\leavevmode
  \edef\prevskip@{\ifdim\lastskip=\z@ \else\hskip\the\lastskip\relax\fi}%
  \unskip
  \edef\prevpenalty@{\ifnum\lastpenalty=\z@ \else
    \penalty\the\lastpenalty\relax\fi}%
  \unpenalty \/\prevpenalty@ \prevskip@ {\rm #1}}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -13- BIBLIOGRAPHY
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{references,}
%
\def\refsfont@{\eightpoint}
%
%      \refindentwd controls the indention from the left margin of the
%      ref item numbers or key labels.  The initial setting is to 2
%      decimal digits; numbers up to 99 will be aligned on the right
%      within a box the width of \refindentwd.  \key labels will be
%      aligned on the LEFT within a box of the same width; but when
%      \key's are being used, the indention may need to be increased
%      if it's required that the labels remain clear from the text.
%      The \widestnumber macro can be used to do this:
%      \widestnumber\key{MNOPQ} will increase \refindentwd to the
%      width of a box containing "[MNOPQ]\enspace". \widestnumber can
%      also be used with \no: \widestnumber\no{000} for 3-digit
%      numbers, \widestnumber\no{0} for 1-digit numbers, and so on.
%
\newdimen\refindentwd
\setboxz@h{\refsfont@ 00.\enspace}
\refindentwd\wdz@
%
\outer\def\Refs{\add@missing\endroster \add@missing\endproclaim
 \let\savedef@\Refs \let\Refs\relax % because of \outer-ness
 \def\Refs##1{\restoredef@\Refs
%      For a monograph where the title of the References section is
%      done using \title, we want to omit the normal "References"
%      heading and the vertical skips above and below.  This can be
%      accomplished using \Refs\nofrills{}.  As long as the vskip at
%      the end of \endtopmatter is not less than \aboveheadskip and
%      \belowheadskip, this will be accomplished by the fact that
%      \penaltyandskip@ doesn't add to a previous larger vskip, and
%      the ragged center part will simply vanish if #1 is empty.
   \if\notempty{##1}\penaltyandskip@{-200}\aboveheadskip
     \begingroup \raggedcenter@\headfont@
       \ignorespaces##1\endgraf\endgroup
     \penaltyandskip@\@M\belowheadskip
   \fi
   \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m
   }%
%      This line here is a little tricky. If a \nofrills is found when
%      we look ahead, then \frills@ will become equal to \eat@ and it
%      will eat "References" before \Refs is allowed to read its
%      argument.  Also we have to use a \csname trick to get around
%      the outerness of \Refs.  MJD
 \nofrillscheck{\csname Refs\expandafter\endcsname
  \frills@{{References}}}}
%
\def\endRefs{\par % This will check for a missing \endref, also
  \endgroup}
%
%      These two conditionals are used for handling the logic of
%      typesetting book versus journal article versus proceedings
%      article references.
\newif\ifbook@ \newif\ifprocpaper@
%
%      The \else clause here is to handle the case when \nofrills is
%      used outside of the References section in an unexpected place
%      (i.e., not immediately after \proclaim, \definition, \head, or
%      the other things that have a \nofrills option).
%
\def\nofrills{%
%      Are we inside a \ref...\endref pair?  If so, OK to continue.
  \expandafter\ifx\envir@end\endref
    \let\do\relax
    \xdef\nofrills@list{\nofrills@list\do\curbox}%
  \else\errmessage{\Invalid@@ \string\nofrills}%
  \fi}%
%
\def\defaultreftexts{\gdef\edtext{ed.}\gdef\pagestext{pp.}%
  \gdef\voltext{vol.}\gdef\issuetext{no.}}
\defaultreftexts
%
\def\ref{\par
  \begingroup \def\envir@end{\endref}%
%      Start the reference.
  \noindent\hangindent\refindentwd
%      Change \par so that it will supply a (presumably) missing
%      \endref, with an error message.
  \def\par{\add@missing\endref}%
%      \nofrills@list should always be assigned globally, to conserve
%      save stack.
  \global\let\nofrills@list\empty@
%
%      Change \linebreak and \mathbreak to work properly in the
%      special ref environment.
  \refbreaks
  \procpaper@false \book@false \moreref@false
%      Start an initial box, to match up properly with the first
%      upcoming \makerefbox; this will be discarded.
  \def\curbox{\z@}\setbox\z@\vbox\bgroup
}
%
%      \keyhook@ is used for switching  the style of reference labels
%      automatically behind the scenes. This is for phasing in,
%      without loss of backward compatibilty, a \refstyle command to
%      implement the various reference styles currently used in AMS
%      production.  [19-MAR-1991] See the definition of \refstyle.
%
\let\keyhook@\empty@
%
\def\endref{%
%      To wind up the preceding box it is convenient to call
%      \makerefbox again; it will also open a new box, however, so we
%      give it arguments \thr@@ and \endgraf\egroup that will cause
%      the new box to be closed immediately and discarded. But we must
%      first make sure box 3 is void or we'll trigger an error
%      message.  This is done by dumping the current contents of
%      (global register) box 3 into (local register) box 2; the \box
%      command always makes its argument globally void.  (Because box
%      0 is used heavily in \makerefbox, it's easier to just use box 2
%      here, rather than try to verify that using box 0 would be safe
%      in all cases.)
  \setbox\tw@\box\thr@@
  \makerefbox?\thr@@{\endgraf\egroup}%
%      Then we call \endref@ to take all the saved material and
%      combine it into a paragraph, adding punctuation to separate
%      pieces.
  \endref@
%      The \endgraf is done here rather than in \endref@ because in
%      \moreref or \transl cases \endref@ shouldn't do the \endgraf.
  \endgraf
%      Finally, we need to close the group that was started by \ref.
%      This has the effect of killing the current definition of
%      \envir@end, among other things.
  \endgroup
  \keyhook@
  \global\let\keyhook@\empty@ % \global to conserve save stack
}
%
\def\key{\gdef\key{\makerefbox\key\keybox@\empty@}\key} \newbox\keybox@
\def\no{\gdef\no{\makerefbox\no\keybox@\empty@}%
  \gdef\keyhook@{\refstyle C}\no}
\def\by{\makerefbox\by\bybox@\empty@} \newbox\bybox@
\let\manyby\by % for backward compatibility
\def\bysame{\by\hbox to3em{\hrulefill}\thinspace\kern\z@}
\def\paper{\makerefbox\paper\paperbox@\it} \newbox\paperbox@
\def\paperinfo{\makerefbox\paperinfo\paperinfobox@\empty@}%
  \newbox\paperinfobox@
\def\jour{\makerefbox\jour\jourbox@
  {\aftergroup\book@false \aftergroup\procpaper@false}} \newbox\jourbox@
\def\issue{\makerefbox\issue\issuebox@\empty@} \newbox\issuebox@
\def\yr{\makerefbox\yr\yrbox@\empty@} \newbox\yrbox@
\def\pages{\makerefbox\pages\pagesbox@\empty@} \newbox\pagesbox@
\def\page{\gdef\pagestext{p.}\makerefbox\page\pagesbox@\empty@}
\def\ed{\makerefbox\ed\edbox@\empty@} \newbox\edbox@
\def\eds{\gdef\edtext{eds.}\makerefbox\eds\edbox@\empty@}
%      The \aftergroup\book@true here sets the \ifbook@ switch so that
%      later (in \endref@) we will know whether we are typesetting a
%      book, a journal article, or a proceedings article. Could use
%      \global instead of \aftergroup but avoiding \global is usually
%      safer when possible.
\def\book{\makerefbox\book\bookbox@
  {\it\aftergroup\book@true \aftergroup\procpaper@false}}
  \newbox\bookbox@
\def\bookinfo{\makerefbox\bookinfo\bookinfobox@\empty@}%
  \newbox\bookinfobox@
\def\publ{\makerefbox\publ\publbox@\empty@} \newbox\publbox@
\def\publaddr{\makerefbox\publaddr\publaddrbox@\empty@}%
  \newbox\publaddrbox@
%      See the above comment for \book about the \aftergroup
\def\inbook{\makerefbox\inbook\bookbox@
  {\aftergroup\procpaper@true \aftergroup\book@false}}
\def\procinfo{\makerefbox\procinfo\procinfobox@\empty@}%
  \newbox\procinfobox@
\def\finalinfo{\makerefbox\finalinfo\finalinfobox@\empty@}%
  \newbox\finalinfobox@
\def\miscnote{\makerefbox\miscnote\miscnotebox@\empty@}%
  \newbox\miscnotebox@
\def\toappear{\miscnote to appear}
\def\lang{\makerefbox\lang\langbox@\empty@} \newbox\langbox@
\newbox\morerefbox@
%
%      \vol is special because in AMS style it takes a different font
%      depending on whether it's a journal volume or a book volume.
%
\def\vol{\makerefbox\vol\volbox@{\ifbook@ \else
  \ifprocpaper@\else\bf\fi\fi}}
\newbox\volbox@
%
\newbox\holdoverbox
%
%      \makerefbox takes three arguments: the first is the name of
%      the calling macro, for use in error messages; argument 2
%      is the box used for storing data (note: some boxes are shared
%      by more than one calling macro); argument 3 is additional
%      material (optional---may be empty) that may be used to
%      affect the contents of the box.
%
\def\makerefbox#1#2#3{\endgraf
%      Set box 0 to the just-completed line of text.
  \setbox\z@\lastbox
%      Although \holdoverbox will usually be void it still doesn't
%      hurt to \unhbox it here in every case, which simplifies the
%      programming.
  \global\setbox\@ne\hbox{\unhbox\holdoverbox
%      \ifvoid test is necessary here to prevent a \linebreak at the
%      end of a field from being removed by the \unpenalty.
    \ifvoid\z@\else\unhbox\z@\unskip\unskip\unpenalty\fi}%
  \egroup
%      If box 1 is empty (width <= 0pt) then set the current box to
%      void (it might still have a baselineskip glue or something in
%      it at this point, for one thing).  Otherwise set it to box 1.
  \setbox\curbox\box\ifdim\wd\@ne>\z@ \@ne \else\voidb@x\fi
%    That finishes the previous box.  Now let's start a new one
%    using the box given as arg 1 of \makerefbox. But first check
%    to see if it's void and if not give an error message.
  \ifvoid#2\else\Err@{Redundant \string#1; duplicate use, or
     mutually exclusive information already given}\fi
  \def\curbox{#2}\setbox\curbox\vbox\bgroup \hsize\maxdimen \noindent
  #3}
%
\def\refbreaks{%
  \def\refconcat##1{\setbox\z@\lastbox \setbox\holdoverbox\hbox{%
       \unhbox\holdoverbox \unhbox\z@\unskip\unskip\unpenalty##1}}%
  \def\holdover##1{%
    \RIfM@
%    Break the current line, adding \null to ensure proper spacing for
%    a preceding mathrel or mathbin. The blank line containing the
%    \null will be discarded by later processing.
      \penalty-\@M\null
%      Put a temporary ending of the current math formula on the next
%      line, by itself.
      \hfil$\clubpenalty\z@\widowpenalty\z@\interlinepenalty\z@
      \offinterlineskip\endgraf
%      Now remove that unwanted extra line and the preceding \lineskip
%      (of 0pt) and any  penalty.  There shouldn't be any penalty,
%      actually, because the relevant penalties were set to 0 above;
%      but the \unpenalty is harmless and perhaps there is an
%      overlooked eventuality that it will catch.
      \setbox\z@\lastbox\unskip \unpenalty
      \refconcat{##1}%
      \noindent
%      Since we did a temporary end of the current math formula there
%      remains some more math coming up; therefore we need to shift
%      into math mode again.  By breaking immediately after the
%      beginning of the math formula we leave the unwanted extra
%      \mathon item in a line by itself; this will be ignored because
%      in the unpacking process we will only take the last line out of
%      the current \vbox.
      $\hfil\penalty-\@M
%      No \null here because we don't need to do anything extra to
%      affect the math spacing of the following item. (Line breaks
%      in math formulas always occur after a \mathbin or \mathrel,
%      not before, according to AMS style.)
    \else
      \endgraf\refconcat{##1}\noindent
    \fi}%
  \def\break{\holdover{\penalty-\@M}}%
  \let\vadjust@\vadjust
  \def\vadjust##1{\holdover{\vadjust@{##1}}}%
%      It seems unlikely that \newpage will be needed inside of a
%      \ref...\endref construction (more likely it will occur between
%      references, if at all).  So we provide only a very simple
%      alternate version using \vadjust.
  \def\newpage{\vadjust{\vfill\break}}%
}
%
\def\refstyle#1{\uppercase{%
  \if#1A\relax \def\keyformat##1{[##1]\enspace\hfil}%
  \else\if#1B\relax
    \def\keyformat##1{\aftergroup\kern
              \aftergroup-\aftergroup\refindentwd}%
    \refindentwd\parindent
 \else\if#1C\relax
   \def\keyformat##1{\hfil##1.\enspace}%
 \fi\fi\fi}% end of \uppercase
}
%
%      Make letters the default for ref labels. This is chosen over
%      refstyle C with a view to eventually phasing out \no in favor
%      of always using \key, with the formatting being determined by
%      the refstyle setting.
\refstyle{A}
%
%      You might think that \refbreak@ shouldn't be necessary here (it
%      executes a line break if the user specified \linebreak in the
%      last field of the reference), but: sometimes there will be a
%      language after the final period, and conceivably someone might
%      need to break the line after the period and before the
%      language.
\def\finalpunct{\ifnum\lastkern=\m@ne\unkern\else.\fi
       \refquotes@\refbreak@}%
\def\continuepunct#1#2#3#4{}%
%
%      \endref@ is shared by \endref, \moreref, and \transl, therefore
%      some of the code needs to be circumspect.
\def\endref@{%
%      Change the format of the reference label, if necessary:
  \keyhook@
%      This variant definition of \nofrillscheck is embedded in
%      \endref@ despite the slight cost in extra execution time, in
%      order to allow, e.g., subheadings within a bibliography section
%      to have normal \nofrills action.
  \def\nofrillscheck##1{%
    \def\do####1{\ifx##1####1\let\frills@\eat@\fi}%
    \let\frills@\identity@ \nofrills@list}%
%      If no author name was given, but editor name was given, then
%      transfer it to the author name box so that it will print at the
%      beginning of the reference.  This  would normally happen only
%      in the case of a proceedings volume or other such collection,
%      cited as a whole.
  \ifvoid\bybox@
    \ifvoid\edbox@
    \else\setbox\bybox@\hbox{\unhbox\edbox@\breakcheck
      \nofrillscheck\edbox@\frills@{\space(\edtext)}\refbreak@}\fi
  \fi
%      \noindent \hangindent\refindentwd was done earlier by \ref, so
%      at this point we just need to put the reference label on the
%      page.
%
%      Using this \ifvoid test is partly to prevent accessing \keybox@
%      in the \moreref and \transl cases:
  \ifvoid\keybox@\else\hbox to\refindentwd{%
       \keyformat{\unhbox\keybox@}}\fi
  \ifmoreref@
%      Even though this reads ``\commaunbox@,'' a semicolon will be
%      substituted for the comma by the action of \punct@ if
%      \morerefbox@ is in fact not void.  (And note that both \transl
%      and \moreref share \morerefbox@.)
    \commaunbox@\morerefbox@
  \else
%      Put in some special kerns to flag the beginning of a reference,
%      to avoid adding unwanted punctuation and space if \by is omitted.
    \kern-\tw@ sp\kern\m@ne sp
  \fi
  \ppunbox@\empty@\empty@\bybox@\empty@
  \ifbook@ % Case 1: \book etc.
    \commaunbox@\bookbox@ \commaunbox@\bookinfobox@
    \ppunbox@\empty@{ (}\procinfobox@)%
    \ppunbox@,{ vol.~}\volbox@\empty@
    \ppunbox@\empty@{ (}\edbox@{, \edtext)}%
    \commaunbox@\publbox@ \commaunbox@\publaddrbox@
    \commaunbox@\yrbox@
    \ppunbox@,{ \pagestext~}\pagesbox@\empty@
  \else
    \commaunbox@\paperbox@ \commaunbox@\paperinfobox@
    \ifprocpaper@ % Case 2: \paper ... \inbook
      \commaunbox@\bookbox@
      \ppunbox@\empty@{ (}\procinfobox@)%
      \ppunbox@\empty@{ (}\edbox@{, \edtext)}%
      \commaunbox@\bookinfobox@
      \ppunbox@,{ \voltext~}\volbox@\empty@
      \commaunbox@\publbox@ \commaunbox@\publaddrbox@
      \commaunbox@\yrbox@
      \ppunbox@,{ \pagestext~}\pagesbox@\empty@
    \else % Case 3: \paper ... \jour
      \commaunbox@\jourbox@
      \ppunbox@\empty@{ }\volbox@\empty@
      \ppunbox@\empty@{ (}\yrbox@)%
      \ppunbox@,{ \issuetext~}\issuebox@\empty@
%      Although \publ and \publaddr will rarely be used with a journal
%      article, it doesn't really hurt to print them if provided, and
%      certain rare cases may benefit.  E.g.:
%
%      \paper \"Uber maximale Monotonie von Operatoren des Typs
%      $L^\ast \Phi\circ L$ \paperinfo Report 78-24 \publ Math. Inst.,
%      Univ. K\"oln \yr 1978 \moreref\jour  published as Manuscripta
%      Math. \vol28 \yr1979\pages 305--316
%
      \commaunbox@\publbox@ \commaunbox@\publaddrbox@
      \commaunbox@\pagesbox@
    \fi
  \fi
  \commaunbox@\finalinfobox@
  \ppunbox@\empty@{ (}\miscnotebox@)%
%      The final punctuation (usually a period) here is not part of a
%      \ppunbox@ clause because it is always inserted even if
%      \langbox@ is void.
  \finalpunct\ppunbox@\empty@{ (}\langbox@)%
%      Restore defaults "ed.", "pp.", etc. in case they were changed.
  \defaultreftexts
}
%
%      \punct@ is the same as \identity@, but we define it rather than
%      using \let, just in case the contents of amsppt.sty ever get
%      shuffled around in such a way that \identity@ is later in the
%      file.
\def\punct@#1{#1}
%      \ppunbox@ takes 4 arguments.  #1 is punctuation that should
%      precede ending quotes and/or a line breaking penalty, from the
%      previous item.  #2 is material (usually a word space) that
%      should come after ending quotes or a penalty.  #3 is the box
%      containing the next part of the current reference.  #4 is other
%      material to follow box #3 (e.g., a closing parenthesis, in some
%      cases).
%
\def\ppunbox@#1#2#3#4{\ifvoid#3\else
  \let\prespace@\relax
%      If nofrills was specified for the previous item, then it will
%      have been ended with a kern of -1sp.  If we find such a kern,
%      we remove it and omit the normal punctuation (arg #1).
  \ifnum\lastkern=\m@ne \unkern\let\punct@\eat@
%      A kern of -2sp here means we are at the very beginning of the
%      reference, after the key or number. In that case we need to
%      omit not only the punctuation, but also any following space.
    \ifnum\lastkern=-\tw@ \unkern\let\prespace@\ignorespaces \fi
  \fi
  \nofrillscheck#3%
  \punct@{#1}\refquotes@\refbreak@
%      Restore normal definition of \punct@:
  \let\punct@\identity@
  \prespace@
%      If \nofrills is not in effect, the \space will be eaten;
%      otherwise it will be substituted for the normal pre-item
%      frills.
  \frills@{#2\eat@}\space
%      \refquotes@ and \refbreak@ will be emptied by \breakcheck
%      (unless of course there is a new line breaking penalty present
%      for next time around).
  \unhbox#3\breakcheck
  \frills@{#4\eat@}{\kern\m@ne sp}\fi}
%
\def\commaunbox@#1{\ppunbox@,\space{#1}\empty@}
%
%      By putting the \ifnum here inside the \edef we get automatic
%      initialization of \refbreak@ for the next time around, instead
%      of needing an extra \let\refbreak@\empty@ step after \refbreak@
%      is used.
\def\breakcheck{\edef\refbreak@{\ifnum\lastpenalty=\z@\else
  \penalty\the\lastpenalty\relax\fi}\unpenalty}
%
%      For quotes, the complication is that the ending quotes must
%      fall after a comma or other such punctuation that might come
%      next (we don't know yet what punctuation will be used, if any).
%      And in addition we have the usual possibility of a line break
%      to worry about at the same time.  Therefore the special control
%      sequence \endquotes is provided, to be used like this, if let's
%      say you want book titles to appear in quotes:
%
%      \ppunbox@,{ ``}\bookbox@\endquotes
%      \commaunbox@\bookinfobox@
%
%      \endquotes defines the control sequence \refquotes@ to add the
%      ending quotes later, after we find out whether a comma, period,
%      or no punctuation at all will be added (not to mention maybe a
%      line breaking penalty that would need to be shuffled around).
%
\def\endquotes{\def\refquotes@{''\let\refquotes@\empty@}}
\let\refquotes@\empty@
\let\refbreak@\empty@
%
%    We need a switch to handle certain complications with the moreref
%    case.
%
\newif\ifmoreref@
%
%    \moreref ends the previous setbox operation, does \endref@ to
%    typeset any information gathered so far, and then prepares to
%    start the equivalent of a new \ref.
%
\def\moreref{%
%    To wind up the preceding box it is convenient to call
%    \makerefbox again; it will also open a new box, however, so we
%    give it arguments \thr@@ and \endgraf\egroup that will cause the
%    new box to be closed immediately and discarded. But we must first
%    make sure box 3 is void or we'll trigger an error message.  This
%    is done by dumping the current contents of (global register) box
%    3 into (local register) box 2; the \box command always makes its
%    argument globally void.  (Because box 0 is used heavily in
%    \makerefbox, it's easier to just use box 2 here, rather than try
%    to verify that using box 0 would be safe in all cases.)
  \setbox\tw@\box\thr@@
  \makerefbox?\thr@@{\endgraf\egroup}%
%    This saved definition will be lost if something else in \endref@
%    uses \savedef@.  Currently (14-MAR-1991) that is not the case,
%    however, so doing it this way allows us to save a bit of memory.
  \let\savedef@\finalpunct  \let\finalpunct\empty@
  \endref@
%    The next time \punct@ is called by \ppunbox, it will change
%    ",\refquotes@" into "\refquotes@;" or similarly for
%    \empty@\refquotes@.  Then \punct@ will be restored to its original
%    definition.  Note that this definition does not need to be
%    global; it is local inside the \begingroup ...\endgroup of the
%    current \ref.
  \def\punct@##1##2{##2;}%
  \global\let\nofrills@list\empty@ % global, to conserve save stack
%      Now restore the normal definition of \finalpunct :
  \let\finalpunct\savedef@
  \moreref@true
%    Set any initial text between \moreref and the following
%    control sequence in \morerefbox@. This is typically used with
%    \transl to add a note such as "English transl."
  \def\curbox{\morerefbox@}%
  \setbox\morerefbox@\vbox\bgroup \hsize\maxdimen \noindent
}
%    And \transl, for setting translation information,
%    doesn't need to be any different than \moreref:
%
\def\transl{\moreref}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -14- END OF DOCUMENT
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{end of document,}
%
\outer\def\enddocument{\par% \par will do a runaway check for \endref
  \add@missing\endRefs
%      Repeat these in case an article (or book chapter!) doesn't have
%      a references section:
  \add@missing\endroster \add@missing\endproclaim
  \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endremark \add@missing\endexample
%      In a monograph we expect the translator name and author
%      addresses to be handled in the front matter rather than at the
%      end of the individual chapters:
 \ifmonograph@ % do nothing
 \else
%      No break between the References and the final matter.
 \nobreak
%      The \address's get printed at the end of the paper.  Also the
%      translator name, if any.  We don't need to do an
%      \ifx\thetranslator@\empty@, as we did with \thesubjclass@ and
%      other items in \endtopmatter, because we're not constructing a
%      footnote, just slapping the material on the page.
 \thetranslator@
%      Print all the \address's, including e-mail addresses if
%      present. If any of the \email's are undefined the \csname will
%      just evaluate to \relax.
 \count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne
 \csname address\number\count@\endcsname
 \csname email\number\count@\endcsname
 \repeat
\fi
 \vfill\supereject\end}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -15- OUTPUT ROUTINE
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{output routine,}
%      Extra braces are added in \folio to localize \foliofont@; this
%      is merely a precaution, since in our basic style it will be
%      localized anyway by being put in an \llap or \rlap.  We provide
%      a \foliofont@ separate from \headlinefont@ because it is not
%      uncommon for documentstyles to have the folios in a different
%      font, although in our basic style this is not the case.
%      \foliofont@ is \eightrm instead of \eightpoint merely for
%      efficiency; we don't expect to need for example math family
%      assignments in order to typeset the folio.  On the other hand
%      we need full math capability for \headlinefont@ since running
%      heads may contain math (from a title or a section head).  From
%      a design standpoint it might be preferable to have seven-point
%      running heads (compare a small caps \head that falls at the top
%      of a page with the running head above it) but it is more
%      convenient to use the already available \eightpoint macro, and
%      this saves a bit of overhead.
%
\def\folio{{\foliofont@\ifnum\pageno<\z@ \romannumeral-\pageno
 \else\number\pageno \fi}}
\def\foliofont@{\eightrm}
\def\headlinefont@{\eightpoint}
%
%      \leftheadline and \rightheadline use the method described in
%      the TeXbook, p. 260 for selecting different pieces of the
%      topmark or botmark.  The necessary \else is inserted by
%      \leftheadtext and \rightheadtext.
%
\def\leftheadline{\rlap{\folio}\hfill \iftrue\topmark\fi \hfill}
\def\rightheadline{\hfill \expandafter\iffalse\botmark\fi
  \hfill \llap{\folio}}
%
\newtoks\leftheadtoks
\newtoks\rightheadtoks
%
%      \leftheadtext and \rightheadtext have a \nofrills option to
%      turn off uppercasing.  They also set their argument in a box,
%      during a syntax check, because otherwise syntax errors in the
%      argument would not be caught (because the output routine, and
%      hence \headline, is never called during a syntax check).
%
\def\leftheadtext{\let\savedef@\leftheadtext
  \def\leftheadtext##1{\let\leftheadtext\savedef@
    \leftheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1}\fi}%
  \nofrillscheck\leftheadtext}
%
\def\rightheadtext{\let\savedef@\rightheadtext
  \def\rightheadtext##1{\let\rightheadtext\savedef@
    \rightheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}%
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1}\fi}%
  \nofrillscheck\rightheadtext}
%
%      In the running heads, we redefine \chapter so that it only does
%      a roman numeral (via \chapterno@) rather than "CHAPTER " +
%      roman numeral. In the \nofrills case, however, e.g. for
%      something like "Appendix A", the given text is printed without
%      modification.  And we redefine \\ because if the running head
%      is taken from a title or section head it might possibly contain
%      a \\ from the line-breaking done in the original text.
%
\headline={\def\\{\unskip\space\ignorespaces}\headlinefont@
  \def\chapter{%
    \def\chapter##1{%
      \frills@{\afterassignment\chapterno@ \chaptercount@=}##1.\space}%
    \nofrillscheck\chapter}%
  \ifodd\pageno \rightheadline \else \leftheadline\fi}
%
%      Capitalization is used to indicate global scope of
%      \NoRunningHeads and \NoPageNumbers, as is done by amstex.tex
%      for \TagsOnLeft, etc.
%
\def\NoRunningHeads{\global\runheads@false\global\let\headmark\eat@}
\def\NoPageNumbers{\gdef\folio{}}
%
\def\logo@{\baselineskip2pc \hbox to\hsize{\hfil\eightpoint Typeset by
 \AmSTeX}}
%
%      In response to the popular demand, reinstate the
%      \nologo command removed in version 2.0.
%
\def\nologo{\def\logo@{}}
%
%      Finally, we are ready for the \output routine. It is based on
%      the \plainoutput routine, but the first page normally has the
%      `Typeset by AmS-TeX' logo attached, and we add a switch for
%      running heads.  The default for running heads is "true".
%
\newif\iffirstpage@     \firstpage@true
\newif\ifrunheads@      \runheads@true
%
\output={\output@}
\def\output@{\shipout\vbox{%
 \iffirstpage@ \global\firstpage@false
  \pagebody \logo@ \makefootline%
 \else \ifrunheads@ \makeheadline \pagebody
       \else \pagebody \makefootline \fi
 \fi}%
 \advancepageno \ifnum\outputpenalty>-\@MM\else\dosupereject\fi}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -16- HYPHENATION EXCEPTIONS
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\message{hyphenation exceptions (U.S. English)}
%      Add some common hyphenation exceptions, from TUGboat files,
%      20-NOV-1989. For more details see TUGboat vol 10, no 3,
%      November 1989, pp. 336--341. Many words from the TUGboat list
%      that seemed less likely to occur in mathematical text have been
%      omitted because hyphenation exceptions use up memory (most
%      versions of TeX currently have a limit of 307 on hyphenation
%      exceptions; each added hyphenation exception uses up something
%      like 2 extra words of main memory as well).  The list of
%      hyphenations for proper names could be expanded forever if room
%      permitted; we restrict ourselves to a rather short, extremely
%      arbitrary list.
%
%      Note: The hyphenation rules of British English differ in some
%      particulars from the U.S. rules.
%
\hyphenation{acad-e-my acad-e-mies af-ter-thought anom-aly anom-alies
an-ti-deriv-a-tive an-tin-o-my an-tin-o-mies apoth-e-o-ses
apoth-e-o-sis ap-pen-dix ar-che-typ-al as-sign-a-ble as-sist-ant-ship
as-ymp-tot-ic asyn-chro-nous at-trib-uted at-trib-ut-able bank-rupt
bank-rupt-cy bi-dif-fer-en-tial blue-print busier busiest
cat-a-stroph-ic cat-a-stroph-i-cally con-gress cross-hatched data-base
de-fin-i-tive de-riv-a-tive dis-trib-ute dri-ver dri-vers eco-nom-ics
econ-o-mist elit-ist equi-vari-ant ex-quis-ite ex-tra-or-di-nary
flow-chart for-mi-da-ble forth-right friv-o-lous ge-o-des-ic
ge-o-det-ic geo-met-ric griev-ance griev-ous griev-ous-ly
hexa-dec-i-mal ho-lo-no-my ho-mo-thetic ideals idio-syn-crasy
in-fin-ite-ly in-fin-i-tes-i-mal ir-rev-o-ca-ble key-stroke
lam-en-ta-ble light-weight mal-a-prop-ism man-u-script mar-gin-al
meta-bol-ic me-tab-o-lism meta-lan-guage me-trop-o-lis
met-ro-pol-i-tan mi-nut-est mol-e-cule mono-chrome mono-pole
mo-nop-oly mono-spline mo-not-o-nous mul-ti-fac-eted mul-ti-plic-able
non-euclid-ean non-iso-mor-phic non-smooth par-a-digm par-a-bol-ic
pa-rab-o-loid pa-ram-e-trize para-mount pen-ta-gon phe-nom-e-non
post-script pre-am-ble pro-ce-dur-al pro-hib-i-tive pro-hib-i-tive-ly
pseu-do-dif-fer-en-tial pseu-do-fi-nite pseu-do-nym qua-drat-ic
quad-ra-ture qua-si-smooth qua-si-sta-tion-ary qua-si-tri-an-gu-lar
quin-tes-sence quin-tes-sen-tial re-arrange-ment rec-tan-gle
ret-ri-bu-tion retro-fit retro-fit-ted right-eous right-eous-ness
ro-bot ro-bot-ics sched-ul-ing se-mes-ter semi-def-i-nite
semi-ho-mo-thet-ic set-up se-vere-ly side-step sov-er-eign spe-cious
spher-oid spher-oid-al star-tling star-tling-ly sta-tis-tics
sto-chas-tic straight-est strange-ness strat-a-gem strong-hold
sum-ma-ble symp-to-matic syn-chro-nous topo-graph-i-cal tra-vers-a-ble
tra-ver-sal tra-ver-sals treach-ery turn-around un-at-tached
un-err-ing-ly white-space wide-spread wing-spread wretch-ed
wretch-ed-ly Brown-ian Eng-lish Euler-ian Feb-ru-ary Gauss-ian
Grothen-dieck Hamil-ton-ian Her-mit-ian Jan-u-ary Japan-ese Kor-te-weg
Le-gendre Lip-schitz Lip-schitz-ian Mar-kov-ian Noe-ther-ian
No-vem-ber Rie-mann-ian Schwarz-schild Sep-tem-ber}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%      We begin with ten-point type.
%
\tenpoint
%
%      Write an empty line on screen to tidy up:
\W@{}
%
%    Now we restore the catcode for @ that was in effect before this
%    file. Note that we do not use \filename here, even though we did
%    at the beginning of this file, because in the absence of a proper
%    filename stack mechanism, we cannot be sure (taking into account
%    possible future changes in the contents of amsppt.sty) that an
%    intervening input file did not change \filename to another value.
%
\csname amsppt.sty\endcsname
%
%      And that's it.
\endinput
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -17- NOTES
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 Abbreviations used in this file:

 From plain.tex:

 \p@             1pt, dimen register
 \z@             0pt, dimen register, can be used also as a number
 \m@ne           -1, count register

 Chardefs and mathchardefs (these control sequences can be used as
 numbers):

 \@ne            1
 \tw@            2
 \thr@@          3
 \active         13
 \sixt@@n        16
 \@cclv          255
 \@cclvi         256
 \@m             1000
 \@M             10000
 \@MM            20000

 Scratch registers:

 \countdef\count@=255
 \dimendef\dimen@=0
 \dimendef\dimen@i=1  global only
 \dimendef\dimen@ii=2
 \skipdef\skip@=0
 \toksdef\toks@=0

 Other:

 \m@th           sets \mathsurround=0pt
 \z@skip         0pt plus 0pt minus 0pt, skip register
 \hideskip       -1000pt plus 1fill, skip register
 \centering      0pt plus 1000pt minus 1000pt, skip register
 \voidb@x        permanently void box register
 \endgraf        same as \par, but will be accepted in arguments where
                   \par would cause an error.

 \space          a macro whose expansion is a space token
 \empty@          a defined macro with a null expansion
 \null           an \hbox with null contents

 From amstex.tex:

 \W@             \immediate\write16
 \eat@           gobbles next token or group in braces
 \strip@         gets rid of trailing space from given argument
 \hashtoks@      token register, containing #
 \centering@     skip register, 0pt plus 1000pt
 \rightappend@ ... \to ...       Append to a token list.
 \space@         a space token (\let equal, not a macro like \space)
 \relaxnext@     \let\next=\relax
 \ex@            dimen, related to x-height, roughly equal to 1pt
 \hexnumber@     convert hex digit from decimal form to hex equivalent
 \font@          font assignment, like \font but modified to make
                   syntax check work
 \macro@@        used for stripping off the first part of the result
                   of a \meaning command.

 \def\FN@{\futurelet\next}
 \def\DN@{\def\next@}
 \def\DNii@{\def\nextii@}
 \def\RIfM@{\relax\ifmmode}
 \def\RIfMIfI@{\relax\ifmmode\ifinner}
 \def\setboxz@h{\setbox\z@\hbox}
 \def\wdz@{\wd\z@}
 \def\boxz@{\box\z@}
 \def\setbox@ne{\setbox\@ne}
 \def\wd@ne{\wd\@ne}

 More scratch registers:

 \toks@@
 \count@@
 \count@@@
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -18- APPENDIX: NOTES ON VERSION 2.1
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

---\curraddr was added, for giving the current address of an author,
if different from the address given in \address.

---\rom was added, for preventing unwanted italicization of certain
things such as parentheses or numbers, in theorems and other italic
passages.  \rom automatically inserts italic corrections.

---The implementation of \nofrills was completely changed, to provide
better error messages for a missing or misspelled \endkeywords or
similar end command, when reading a delimited argument. The error
message is now one of

  ! Forbidden control sequence found while scanning use of \keywords.
  ! Paragraph ended before \keywords was complete.

Previously the message would have had the same form, but would have
referred to a mysterious control sequence ``\next@'' instead of
\keywords.

This change also eliminates a longstanding, very minor bug
(\usualspace@ didn't work if it was stored in something such as
\keywords@ for later use, because of its dependence on the
\ifnofrills@ switch).

---Multiple \thanks commands in the top matter will now produce
multiple acknowledgment footnotes instead of discarding all but the
last one. A period is no longer added automatically at the end of a
\thanks.

---\subjclass was updated to use the date (1991) of the current
Mathematics Subject Classification scheme.

---\widestnumber\item now works as claimed in the User's Guide.

---The missing \par in \penaltyandskip@ was added.

---Additional checks were added for runaway \proclaim, \definition,
\ref, \roster, etc.  The internal macro \runaway@ was changed to make
its usage more consistent and robust; in the process its name was
changed to \add@missing (and as the name suggests, it now tries to
recover by adding the  missing \end... command).

---The bibliography macros were substantially modified to correct
another longstanding bug: line breaks after explicit hyphens,
mathbins, and mathrels were inhibited. This also involved changing the
\ref-specific version of \nofrills.  Backward compatibility (with
version 2.0) is not complete with respect to \nofrills in the
bibliography macros.  This seems best, however, not only to avoid
extra implementation difficulties, but also because the user syntax in
version 2.0 was inferior. \nofrills now should always follow
immediately after the name of the field to which it applies, e.g.,
\transl\nofrills, or \paper\nofrills. Note that this is more
consistent with the usage of \nofrills outside of the references
section. \nofrills will cause all the "frills" such as the parentheses
around years in journal article citations, or words like "eds." or
"vol." that are supplied automatically, to be omitted for the given
field.  In addition, it will suppress the automatic punctuation at the
end of the field, if any.

The macro \refdef@ is gone; instead, to define a new reference
element, you need a definition of the form

  \newbox\jourbox@
  \def\jour{\makerefbox\jour\jourbox@{\it}}

where \makerefbox is a macro with three arguments: #1 is the name of
the calling macro (for use in error messages, if need be), #2 is the
box in which the contents of the \jour field should be stored, and #3
is formatting information (primarily font changes) to be inserted at
the beginning of the box. However, as before, punctuation and words
such as "pp.", "eds.", or "vol." that are to be inserted automatically
are handled by \endref@.

Therefore, to change such frills, or the ordering of the parts of a
reference, you need to modify \endref@.  The macros \ppunbox@ and
\commaunbox@ should normally be used to unpack a box, because they
automatically take care of complications like \nofrills, closing
quotes, or line breaks. \ppunbox@ takes four arguments:

       #1: punctuation that should come before a line break or
           closing quotes of a previous field
       #2: other material such as "(" or "vol." that should be added
           at the beginning of the current field
       #3: the name of the box to be unpacked
       #4: other material such as ")" that should be added
           at the end of the current field

For example, the command to unpack the \yr field is:

       \ppunbox@\empty@{ (}\yrbox@)%

Note the use of \empty@ to specify no preceding comma or other
punctuation.

\commaunbox@ is merely an abbreviation for

       \ppunbox@,\space\xxxbox@\empty@

The switches \ifpaperquotes@ and \ifbookquotes@ are gone.  If quotes
are to be added around a particular part of a reference, it should be
done in \endref@ using \ppunbox@ and \endquotes as follows:

       \ppunbox@,{ ``}\xxxbox@\endquotes

\endquotes does not typeset the ending quotes immediately (because we
don't know yet whether to insert a comma or other punctuation before
the ending quotes).  Instead, it sets a flag to be used in subsequent
processing.

---A \refstyle command was added to allow users to specify one of the
three different reference styles most commonly used in AMS
publications: letter labels in square brackets; unnumbered; and
numbered (denoted A, B, and C, respectively). The syntax is
"\refstyle{A}". Style C, numbered with arabic numerals, is the default
selected by amsppt.sty. Eventually, phasing in the \refstyle command
will allow the formatting for cites in the main text to be
automatically  linked with the corresponding references in the
bibliography. (Since the bibliography style could also affect the
style of cites, the \refstyle command should be placed in the preamble
of a document.) Also, eventually \key could be used for all reference
labels, and the \no command will be unnecessary, because its current
use is merely to indicate different formatting for the reference
number.

---\miscnote was added, and used in the implementation of \toappear,
so that \toappear and \finalinfo would not be mutually exclusive.
\miscnote might also be used for things like "preprint" or
"submitted".  Unlike \finalinfo, \miscnote automatically adds
parentheses.

---\procinfo was added, to give place and date where the meeting
took place, for proceedings volumes.

---\eds or \ed information will now be used in place of an author's
name, if \by is absent.  This would be for collections or proceedings
volumes that are cited as a whole, instead of citing a single paper
within the volume.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      -19- APPENDIX: NOTES ON VERSIONS 2.1a, 2.1b, ...
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Users that have amsppt.sty built into their amstex format file will
need to rebuild their format file if they get a newer version of
amsppt.sty.

Version 2.1a:

---Added a test so that amsppt.sty will give an error message if it's
about to be loaded and a different version of amsppt.sty was preloaded
in the format file.

---Added code to compensate for a bug in version 2.1 that left
\amsppt.sty = \endinput. Probably not necessary---unless the error
message described above is changed in the future to just a warning
message.

---Added \loadmsam and \loadmsbm before the call to \UseAMSsymbols,
so that amsppt.sty 2.1 will work even with an AMSTeX 2.0 format file.

---Changed the definition of \magnification (from plain.tex) so that
it won't reset the page dimensions to 6.5 by 9 true inches if
it is used but will behave in a way that's more appropriate
for the amsppt page dimensions.

---Switched to using box 0 instead of \keybox@ for measuring a \key
given with the \widestnumber command. This prevents a misnumbering
problem that occurred in rare cases (e.g., an unnumbered reference
following numbered references).

---Changed erroneous \proclaimfont@ to \proclaimheadfont@ and
\demofont@ to \remarkheadfont@ in the definition of \Monograph.  Note:
This means that fonts used for \remark, \demo, \proclaim \definition,
\example, were wrong for any document that used \Monograph with amsppt
2.1; switching to amsppt version 2.1a will make the fonts correct
according to AMS standard monograph style, but with a slight chance of
changing line breaks.

---Added \pagenumwd and put the table-of-contents definition of
\page inside the \toc group so that it will not conflict with
the normal definition of \page if a single document contains
both \toc (with \widestnumber\page used) and \Refs.

---Added default definition for \leftskip@ to handle rare cases.
Added \envir@stack\endroster in \Runinitem to prevent spurious
"missing \endroster" error every time it's used.

---Change handling of \key and \no to better handle the complications
related to \refstyle and the need to maintain backward compatibility.
(I.e., \refstyle should automatically be reset to C if \no is used.)

---Added \procpaper@false and \book@false where appropriate in \book,
\jour, \inbook to handle (rare?) \moreref cases where the additional
ref is not the same type as the first ref. Switched around \moreref
and \transl, a cosmetic change but makes the code easier to
understand. (It seems reasonable for \transl to be based on \moreref,
but rather odd for \moreref to be based on \transl, as in version
2.1.)

---Added \ifvoid test in \makerefbox to give an error message
if the same tag is used twice or mutually exclusive tags (e.g.,
\book and \inbook) are used.

---Added some code to print out editors and pages information
if given even when according to AMS style it should normally
be omitted.

Version 2.1b:

---Restored the old \nologo command by popular demand.

---Added \linespacing command to facilitate changing line spacing
globally: \linespacing{2.0} increases line spacing by a factor of 2,
similarly \linespacing{1.5} or \linespacing{2.3} for arbitrary
factors.

---Italic font is now used instead of slanted throughout (for e.g.
\proclaim).

---Omitting \by in a \ref is now possible without getting unwanted
punctuation at the very beginning after the key.

---\rom now handles preceding ~, not just preceding space.

---\subsubheadfont@ added to facilitate font switching.

---\document does some font setup if \topmatter is omitted.

---Fixed a problem with running heads and \chapter\nofrills.

---Eliminated spurious error message from \roster \widestnumber inside
a \proclaim.

Version 2.1c:

---Fixed a bug introduced in version 2.1b: lost punctuation and space
at the beginning of a \moreref.