%^% 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