%^% RESOURCEamspptSimple ;
% Assumes AmSTeX(version) loaded, but NOT AmSppt.sty
% These macros are intentionally simple-minded and have
% simple syntax; this permits easy alteration (TeX macros are usually
% very devious). Don't hesitate to make alterations,
% but in that case rename this file!
%% This file will become an %_
%% auxilliary macros file named
%% Kohler.sty
%% needed by the .tex file: Kohler.sty
%% Date: 29 June, 1994
%% Contact: Martine, email: sectop@matups.matups.fr
%^%% DefStrip apparatus:
%% Master posting 1994 on ftp matups.matups.fr
%% DO NOT ALTER DEFSTRIP SIGNS <percent>^ or <percent>_
%% UNLESS YOU UNDERSTAND THEM!
\let\Def\def \let\gDef\gdef \let\Let\let
\def\gLet{\global\let} \let\Font\font
\input auditor.tex %% comment out to suppress audit function. %_
%%% Avoid double input
%%
\bgroup
\catcode`\!=12
\ifx\auxmacros\relax
\immediate\write16{}%
\message{ !!! auxmacros already defined !!!}
\gdef\auxmacros{\endinput}%
\else \global\let\auxmacros\relax
\fi
\egroup
\auxmacros
\catcode`\@=11
%%% The following macros will make you call upon auxiliary files
%% when needed. %_
\bgroup
\catcode`\!=12 %_
\gDef\Acc{%\show\Acc
\errmessage{ !!! You need to input RESOURCEamsAcc.tex !!!}\end
}%_
\gDef\amsCD{%
\errmessage{ !!! You need to input RESOURCEamsCD.tex !!!}\end
}%_
\gDef\gLinefigure{%
\errmessage{ !!! You need to input RESOURCEfig.tex !!!}\end
}%_
\egroup
%^%%% Input following as needed
%%% or better append them to a copy of this file.
%%% before using the DefStrip utility to clean up
% \input RESOURCEamsAcc.tex
% \input RESOURCEamsAcc.tex
% \input RESOURCEamsAcc.tex%_
%%% FONTDEFams stuff defines your fonts;
%% depends on your TeX printing system;
\Font \Bigbf=cmr17 %_
%%TimesB scaled 1500
\Font \bigbf=cmbx12 %_
\Font \biggbf=cmbx12 scaled \magstep 2 %_
\Font \bigbxi=cmbxti10 %at 12pt %_
\Font \textbf=cmb10 %_
\Font \bi=TimesBI%cmbti10 %cmbi10 %_
\Font \smc=cmcsc10 % %_
\Font \smallrm=cmr9 %_
\Font \smallbf=cmbx9 %=cmb9 %_
\Font \smallit=cmti9 %_
%\Font \smallbi=cmbti9 %rare %_
%\Font \smallsmc=cmcsc9 %rare %_
\Font \foliofont=cmr10 %_
%\Font \ss=cmss10 %_
%\Font \ssb=cmssbx10 %_
%\Font \ssi=cmssi10 %_
%\Font \ssbi=cmssbi10 %rare %_
%\def \bi{\textbf}
%\Def \Smc#1{{\smc #1}}%_
\Def \Bbd#1{{\Bbb #1}}%_
\Def \Calig#1{{\Cal #1}}%_
\Def \Frak#1{{\frak #1}}%_
%\Def \Bold#1{{\bold #1}}%_
%%% Improve following
%\Def \Smallfonts {\def\rm{\smallrm} %_
%\Def\it{\smallit}\def\bf{\smallbf}%_
% \def\smc{\smallsmc}}%_
%\Def \Smallfonts {\eightpoint}%_
\Def \Smallfonts {\relax}%_
\Def \Titlefont {\bigbf}%_
\Def \Authorfont {\smc}%_
\Def \Headingfont {\bf}%_
\Def \Subheadingfont {\bf}%_
\Def \Theoremfont {\smc}%_
\Def \TheoremTextfont{\it}%_
\Def \Prooffont {\smc}%_
\Def \Remarkfont {\smc}%_
\Def \Diagramfont {\smc}%_
\Def \Captionfont{\it}%_
% Font macros
\long\def \It #1{{\it{#1}\unskip\/}}%_
\Def \Bi #1{{bi{#1}\unskip\/}}%_
\Def \Bold #1{{\bold #1}}%_
\Def \BF #1{{\bf{#1}\unskip}}%_
\Def \Bf #1{%
{\ifmmode \let\this\Bold
\else \let\this\BF \fi
\this {#1}}}%
%% in math, transcoder provides surrounding brackets,
%% in case of preceding accent, so one superfluous layer here? %_
% \Def\Bbb#1{{\relaxnext@\ifmmode\let\next\Bbb@\else
% \def\next{
% \Err@{Use \string\Bbb\space only in mathmode}}\fi
% \next{#1}}}%_
\Def \Smc#1{{\smc{#1}\unskip}}%_
%\def \leftAdmin{\begingroup\mathsurround=0 pt$}%_
%\def \rightAdmin{$\endgroup}%_
\Def \Admin #1{\begingroup\mathsurround=0 pt
\leavevmode%p222-3: \hskip -\lastskip for \unskip
\ifmmode\hbox{$\roman{{#1}}$}\else$\roman{{#1}}$\fi
\endgroup}%
%%{{}} prevents misinterpretation of naked numbers %_
\Def \Rm #1{{\text{\rm\kern 1pt #1\kern .5pt}}}%
%%outer {} for SwtCD %_
\Def \Displaystyle {\displaystyle}%_
%%% Logical formatting
%%
%mild revision of an AmSTeX definition
\Def \endheading{\cr \egroup \egroup \egroup \nobreak\unvbox
\headingbox@ \nobreak\medskip\nobreak}%_
\Def \Medskip{\vskip 6pt plus 10pt minus 2pt}%_
\Def \Medbreak{\par \ifdim \lastskip <\bigskipamount \removelastskip
\penalty -100\Medskip \fi}%_
\newif\ifAfterHead
\Def \hRule{}%%=\hrule for diagnosis %_
\everypar={\global\AfterHeadfalse}%_
%% \Title block begins
\newskip\TitleLineskip
\TitleLineskip=4pt
\def \DeepCr{\unskip\hfil\egroup\par\hfil\bgroup}%_
\def \\#1{%
\def\test{#1}%
\ifx \test\space\def\this{\DeepCr}\else\def\this{\DeepCr #1}\fi
\this}
\Def \Title{\goodbreak
\ifdim\pagetotal>.70\pagegoal
\def\this{\vfill\eject}
\else\def\this{}\fi \this
\vbox\bgroup\Titlefont\def\cr{\DeepCr}
\parindent=0 pt\parskip= 0 pt
\Titlefont\baselineskip=\fontdimen6\font
\lineskip=\TitleLineskip%
\lineskiplimit=\baselineskip%
\advance\lineskiplimit by -1ex %
\hbox to 0pt{}\vskip15pt plus 15pt\bigskip
\bgroup \hfil}
\def \endTitle {\unskip\hfil\egroup\par \egroup\medskip}
%% end of \Title block %_
%% \Author block begins
\newskip\AuthorLineskip
\AuthorLineskip=5pt plus 5pt
\Def \Author{\nobreak\vskip 20Pt plus 10pt minus 5pt\nobreak
\vbox\bgroup\Authorfont\def\cr{\DeepCr}
\parindent=0 pt\parskip= 0 pt
\Titlefont\baselineskip=\fontdimen6\font
\advance\baselineskip by \AuthorLineskip%
\bgroup \hfil}%
\def \endAuthor {\unskip\hfil\egroup\par \egroup\medskip}%_
%\Def \Heading{\redefine\headingfont{\Headingfont}\heading}%_
%ams ppt sty, not yet used
%\Def \endHeading{\endheading \redefine\headingfont{\smc}}%_
\Def \BoldItemTags{\def\ItemStyle{\Bold}}%_
\Def \PlainItemTags{\def\ItemStyle{\Rm}}%_
\Def \ItemStyle{\Bold}%_
\Def \Item #1{\ifAfterHead\def\this{\nobreak\hRule\nobreak}%\vskip1pt
\else\def\this{\smallskip}\fi
\ifhmode\else\nointerlineskip\fi
\this{\parskip=4pt\noindent
\hbox{$\let\bf\relax
\ItemStyle{{#1}}$}\enskip}\AfterHeadfalse}%_
\Def \Itemitem #1{\itemitem{\hbox{$\def\let\relax\let\bf\relax%
\ItemStyle{\show\bf{#1}}$}}}%_
%\def \Item #1{\item{\def\Bf{}\hbox{$\Bold{{#1}}$}}}%_
%%simpler def with snugness to heading above
% \Def \Itemitem #1{\itemitem{\def\Bf{}\hbox{$\Bold{{#1}}$}}}%
%%The \Bf kill necessitated by some nightmare in AmSTeX?? %_
\Def \Subheading #1{\SubheadingBoldPar{#1}\AfterHeadtrue}%_
\Def \SubheadingA #1{\SubheadingBoldNopar{#1}\AfterHeadfalse}%_
\Def \SubheadingB #1{\SubheadingIndBoldNopar{#1}\AfterHeadfalse}%_
\Def \SubheadingC #1{\SubheadingRmNopar{#1}\AfterHeadfalse}%_
\edef\everymathholder{\noexpand\AfterHeadfalse\the\everymath}%
\expandafter\everymath\expandafter{\everymathholder}%_
\Def \SubheadingBoldPar #1{%
\ifAfterHead\def\this{\nobreak\hRule\nobreak}%
\else\def\this{\goodbreak\vskip 10pt plus 2pt\goodbreak
\vbox to 0pt{\vss}\smallskip\nobreak}\fi\this
\nobreak\noindent{\unskip\bf#1\hfill}\nobreak\vskip0pt
\nobreak
}%_
\Def \SubheadingBoldNopar #1{%
\ifAfterHead\def\this{\nobreak \hRule\nobreak}%
\else\def\this{\Medbreak}\fi
\this\vbox to 0pt{\vss}%
\vskip 4pt\nobreak\nointerlineskip
{\parskip=0pt\noindent\unskip\bf\ignorespaces#1\unskip.\enskip}}%
%%\nointerlineskip is nec! %_
\Def \SubheadingIndBoldNopar #1{\ifAfterHead
\def\this{\nobreak \hRule\nobreak}%
\else\def\this{\Medbreak}\fi
\this\vbox to 0pt{\vss}%
\vskip 4pt\nobreak\nointerlineskip
{\parskip=0pt\noindent\unskip\indent\bf#1\unskip.\enskip}}%
%%\nointerlineskip is nec! %_
\Def \SubheadingRmNopar #1{%
\ifAfterHead\def\this{\nobreak\hRule\nobreak}%
\else\let\this\goodbreak\medskip\fi
\this\nobreak\noindent{\rm #1\unskip.}\enskip}%
%%changeable! %_
%\Def \Theoremfont{\bf}%_
\Def \Theorem #1{\goodbreak\bigskip\par\noindent\Theoremfont #1.
\hskip 2pt plus 1pt minus 1pt
\begingroup\it
\everymath={\ifdim\mathsurround=0pt\def\this{}%
\else\def\this{\kern1.5pt}\fi\this}%
}%_
\Def \endTheorem {\endgroup \rm \goodbreak \smallskip}%_
\Def \Proof#1{\goodbreak \medskip
\par\noindent \Prooffont #1\hskip .7pt:\hskip 3pt\rm}%_
%% A Box for the Quod est demonstrandum:
\Def\qedbox{\hbox{\vbox{
\hrule width0.2cm height0.2pt
\hbox to 0.2cm{\vrule height 0.2cm width 0.2pt
\hfil\vrule height0.2cm width 0.2pt}
\hrule width0.2cm height 0.2pt}\kern1pt}}%_
%% Typing in \qed makes the qedbox right justified:
\Def\qed{\ifmmode\qedbox
\else\unskip\ \hglue0mm\hfill\qedbox\medskip
\goodbreak\fi}%_
\Def \endProof{\qed\goodbreak\vskip10pt}
\Def \Remark#1{\medskip \goodbreak\par\noindent{\Remarkfont #1.}}%_
\Def \endRemark{\medskip \goodbreak}%_
\Def \Example#1{\Remark {#1}}%_
\Def \endExample{\medskip \goodbreak}%_
\Def \Definition#1{\Remark {#1}}%_
\Def \endDefinition{\medskip \goodbreak}%_
\Def \Cite#1{{\rm\cite{#1}}}%_
\Def \cite#1{\cite@#1,\endcite@}%_
\Def \cite@@#1,{#1}%_
\Def \cite@#1,#2\endcite@{\def\temp{#2}%
\ifx\temp\empty\relax
\def \temp{{\bf[#1]}}%
\else\relax
\def\temp{{[\bf #1,\rm\ \cite@@#2]}}%
\fi\temp}%_
\def \Benchmark { }
\Def \References#1{\begingroup \leftskip=25 pt \parskip=4 pt plus 2 pt
\goodbreak \hbox to 1 pt{} \vskip 15 pt plus 10 pt minus 5 pt
\centerline{\Headingfont #1}%
\frenchspacing \Smallfonts \def \Benchmark{\Refmark}%
\def \Refmark##1##2{\par\noindent \llap {##1{##2}\kern 12 pt}\kern 0pt}%
\nobreak\vskip 8pt \nobreak}%
%%##1##2 secretly is \Cite ##2 %_
\Def \endReferences {~\unskip\par\endgroup \medskip\goodbreak}%_
\Def \Footnote #1#2{\plainfootnote{#1}{#2}}%_
%\hbox nec for AMS!!! not Plain
%Symbols macros
\Def \preXbox{\hbox{$
\vcenter{\hbox{
\vrule\vbox to 6.7 pt{
\hrule \vfil \hbox to 12 pt{
\hfil}%
\vfil\hrule}%
\vrule}}\hskip 4pt%
$}}%_
\def \Xbox{\raise -.25pt\hbox{\preXbox}}%
\def \Nonsense {{~\unskip \kern-3.5 pt %
\hbox{\mathsurround=0 pt\Xbox \kern -16.5 pt $>\kern-3pt<$}}}%_
\Def \Blackbox
{\leavevmode\hskip .3pt \vbox{\hrule height 6.9pt
\hbox{\hskip 4.5pt}}\hskip .5pt}%
\Def \<{{$\mathsurround= 0 pt\raise 1.4
pt\hbox{$\scriptscriptstyle
\langle \kern -1 pt \langle\hskip 2 pt $}$}}%_
\Def \>{{\mathsurround= 0 pt$\hskip 2 pt \raise 1.4
pt\hbox{$\scriptscriptstyle
\rangle \kern -1 pt \rangle$}$}}%_
\Def \Matrix #1{\matrix#1\endmatrix}%_
\Def \amsMatrix #1\endamsMatrix{\matrix#1\endmatrix}%_
\Def \amsCases #1\endamsCases{\cases#1\endcases}%_
%\TagsOnRight
\def \tagform@#1{\hbox{\rm\Pretag\ignorespaces#1\unskip\Posttag}}%
\def \Pretag{(}%
\def \Posttag{)}%
\def \Eqno #1$${\def\Pretag{}\def\Posttag{}%
\tag\Admin{#1}$$}%
%^%% too subtle for auditor.tex %_
\Def \Multline#1\endMultline#2$${\def\Pretag{}\def
\Posttag{}\def\Eqno{}
\multline#1\endmultline\tag\Admin{#2\hbox to 1sp{}}$$}%_
\Def \bigMidvert{\kern4pt \big \vert \kern4pt}%_
\Def \Midvert{\kern3pt \vert \kern3pt}%_
\Def \Sharp {\mathord{\#}}%_
\Def \bigConnectedsum {\mathop{\#}\limits}%_
\Def \Coprod {\mathop{\raise 1.2pt \hbox{$\coprod$}}\limits}%_
\Def \Lim {\lim\limits}%_
\Def \Lbrack {{$[\![$}}%_
\Def \Rbrack {{$]\!]$}}%_
%%% Binomial coef trick macros mentioned in Sweet-teX manual (rare)
\Def \Rparen {\right )}%_
\Def \Lparen {\futurelet\next \Lptaupe}%
\def \Lptaupe{\ifx \next ^ \let\this\LLparen
\else \let\this\LLLparen \fi\this}%
\def \LLparen {\left ( \Atop}%
\def \Atop ^#1_#2{{#1\atop#2}}%
\def \LLLparen {\left (}%_
%^%%%%%%%%%%%%%%%% Accents were here%_
\Def \Cdot{\mathbin{\raise .4 ex \hbox to 3pt {\hss\bf .\hss}}}%_
\Def \llonguparrow{\bigg\uparrow}%_
\Def \llongdownarrow{\bigg\downarrow}%_
%\def \Limgadget #1{\mathrel {\kern-2p\mathop
% {\kern3pt #1\kern3pt}\limits}}
%%no; redo correctly to replace following? %_
\Def \llongrightarrow{\kern1pt\mathop
{\kern0pt\longrightarrow\kern1pt}\limits}%_
\Def\llongleftarrow
{\kern-2pt\mathop{\kern3pt\longleftarrow\kern3pt}\limits}%_
\Def \llongtwoheadrarrow {\kern-2pt
\mathop{\kern3pt\longrightarrow \kern-14pt
\longrightarrow\kern3pt}\limits}%_
\Def \llongleftrightarrow {\kern-2pt
\mathop{\kern3pt\longleftrightarrow\kern3pt}\limits}%_
\Def \llongmapsto {\kern-2pt
\mathop{\kern3pt\longmapsto\kern3pt}\limits}%_
\Def \rarrow{\rightarrow}%_
\Def \larrow{\leftarrow}%_
\def\Matrix#1{\matrix #1 \endmatrix}
%tabs inactivated too! %_
%^%%%%%%%%%%%%%%%%%%%%%%%%%% CD macros were here%_
\Def\Trademark{\hbox{\Admin{{}^{\scriptscriptstyle TM}}}}%_
\Def \AmS{{\textfontii A}\kern -.1667em\lower .5ex\hbox {%
\textfontii M}\kern -.125em{\textfontii S}}%_
%\def\LaTeX{{\rm L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em
% T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
\Def\LaTeX{{\rm L\kern-.36em\raise.3ex\hbox
{\smc a}\kern-.15em\TeX}}%_
\Def \Enskip{{\hskip 4pt plus3pt minus2pt}}%_
\def\Undef{\Nonsense}
%The following correspond to rare Sweet-teX symbols,
%and will produce a X'ed box on your TeX printout
%until something better is devised
\Def\Bigasterisk{\Undef}%_
\Def\Control{\Undef}%_
\Def\llongrightarrowtail{\Undef}%_
\Def\llongswarrow{\Undef}%_
\Def\llongsearrow{\Undef}%_
\Def\llongnwarrow{\Undef}%_
\Def\llongnearrow{\Undef}%_
\Def\llongtwoheadrightarrow{\mathbin
{{\longrightarrow} \kern -1850\mu {\rightarrow}}}%_
\Def \Longeq {\mathop{=\kern-5pt=}\limits}%_
\Def\Break{\break}%_
\output{\plainoutput} %%% change if amsppt.sty used
\headline{\hss}
\ifx\undefined\eightpoint
\Def\eightpoint{}
\fi %_
\catcode`\@=13
\Def\dim{\text{\,dim\,}}
\Def\ch{\text{\,ch\,}}
\Def\Td{\text{Td}}
\Def\max{\text{\,max\,}}
\Def\Pf{\text{\,Pf\,}}
\Def\End{\text{\,End\,}}
\Def\loc{\text{\,loc\,}}
\Def\vol {\text{\,vol\,}}
\Def\Tr {\text{\,Tr\,}}
\endinput