%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%                            VerTeX
%                           Hal Varian
%                           August 1987
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%      verbatim macros from TeXbook, page 380--382.
%          to invoke, type: \verbatim# TeX stuff ...#
%          Any character can be used in place of #.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\uncatcodespecials{\def\do##1{\catcode`##1=12}\dospecials}

\def\setupverbatim{\tt%
\def\par{\leavevmode\endgraf}\catcode`\`=\active%
\obeylines\uncatcodespecials\obeyspaces}%
{\obeyspaces\global\let =\ }%
{\catcode`\`=\active \gdef`{\relax\lq}}

\def\verbatim{\begingroup\setupverbatim\doverbatim}
\def\doverbatim#1{\def\next##1#1{##1\endgroup}\next}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Load various fonts
%      there are both computer modern and almost modern fonts
%      available; comment out the ones you aren't using
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%
%  Computer Modern fonts
%%%%%%%%%%%%%%%%%%%%%%%%%

\font\sctwelve=cmcsc10 scaled\magstep1
\font\scten=cmcsc10 

\font\tenrm=cmr10
\font\teni=cmmi10
\font\tensy=cmsy10
\font\tenbf=cmbx10
\font\tenit=cmti10

\font\ninerm=cmr9   \font\eightrm=cmr8    \font\sixrm=cmr6
\font\ninei=cmmi9   \font\eighti=cmmi8    \font\sixi=cmmi6
\font\ninesy=cmsy9  \font\eightsy=cmsy8   \font\sixsy=cmsy6
\font\ninebf=cmbx9  \font\eightbf=cmbx8   \font\sixbf=cmbx6
\font\nineit=cmti9  \font\eightit=cmti8

%%%%%%%%%%%%%%%%%%%%%%%%%
%  Almost Modern fonts
%%%%%%%%%%%%%%%%%%%%%%%%%

%\font\sctwelve=amcsc10 scaled\magstep1
%\font\scten=amcsc10 
%
%\font\tenrm=amr10
%\font\teni=ammi10
%\font\tensy=amsy10
%\font\tenbf=ambx10
%\font\tenit=amti10
%
%\font\ninerm=amr9   \font\eightrm=amr8    \font\sixrm=amr6
%\font\ninei=ammi9   \font\eighti=ammi8    \font\sixi=ammi6
%\font\ninesy=amsy9  \font\eightsy=amsy8   \font\sixsy=amsy6
%\font\ninebf=ambx9  \font\eightbf=ambx8   \font\sixbf=ambx6
%\font\nineit=amti9  \font\eightit=amti8

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Define font families
%       (see TeXbook, p. 414-5)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\catcode`@=11
\newskip\ttglue

\def\tenpoint{\def\rm{\fam0\tenrm}%
\textfont0=\tenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm%
\textfont1=\teni \scriptfont1=\seveni \scriptscriptfont1=\fivei%
\textfont2=\tensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy%
\textfont3=\tenex \scriptfont3=\tenex \scriptscriptfont3=\tenex%
\textfont\itfam=\tenit \def\it{\fam\itfam\tenit}%
\textfont\bffam=\tenbf \scriptfont\bffam=\sevenbf%
\scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\tenbf}%
\tt \ttglue=.5em plus.25em minus.15em%
\ifdouble\normalbaselineskip=1.5pc plus .5pt minus .5pt \else\normalbaselineskip=12pt\fi
\setbox\strutbox=\hbox{\vrule height8.5pt depth3.5pt width0pt}%
\let\sc=\eightrm \normalbaselines\rm}

\def\ninepoint{\def\rm{\fam0\ninerm}%
\textfont0=\ninerm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm%
\textfont1=\ninei\scriptfont1=\sixi\scriptscriptfont1=\fivei%
\textfont2=\ninesy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy%
\textfont3=\tenex \scriptfont3=\tenex \scriptscriptfont3=\tenex%
\textfont\itfam=\nineit\def\it{\fam\itfam\nineit}% 
\textfont\bffam=\ninebf\scriptfont\bffam=\sixbf%
\scriptscriptfont\bffam=\fivebf\def\bf{\fam\bffam\ninebf}% 
\tt \ttglue=.5em plus.25em minus.15em %
\normalbaselineskip=11pt%
\setbox\strutbox=\hbox{\vrule height8pt depth3pt width0pt}% 
\let\sc=\sevenrm\let\big=\ninebig\normalbaselines\rm}

\def\eightpoint{\def\rm{\fam0\eightrm}%
\textfont0=\eightrm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm%
\textfont1=\eighti \scriptfont1=\sixi \scriptscriptfont1=\fivei%
\textfont2=\eightsy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy%
\textfont3=\tenex\scriptfont3=\tenex \scriptscriptfont3=\tenex%
\textfont\itfam=\eightit \def\it{\fam\itfam\eightit}%
\textfont\bffam=\eightbf \scriptfont\bffam=\sixbf%
\scriptscriptfont \bffam=\fivebf \def\bf{\fam\bffam\eightbf}%
\tt \ttglue=.5em plus.25em minus.15em%
\normalbaselineskip=9pt%
\setbox\strutbox=\hbox{\vrule height7pt depth2pt width0pt}%
\let\sc=\sixrm \let\big=\eightbig\normalbaselines\rm}

\def\tenbig#1{{\hbox{$\left#1\vbox to 8.5pt{}\right.\n@space$}}}
\def\ninebig#1{{\hbox{$\textfont0=\tenrm\textfont2=\tensy
   \left#1\vbox to7.25pt{}\right.\n@space$}}}
\def\eightbig#1{{\hbox{$\textfont0=\ninerm\textfont2=\ninesy
   \left#1\vbox to6.5pt{}\right.\n@space$}}}

%Only a partial setup for 6-point, since it is used so rarely
\def\sixpoint{\def\rm{\fam0\sixrm}% switch to 6-point type
 \textfont0=\sixrm \textfont2=\sixsy
 \textfont\itfam=\sixi \def\it{\fam\itfam\sixi}%
 \normalbaselineskip=7.5pt\normalbaselines\rm}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \fnote -- numbered footnotes in small type -- from TeXbook, p. 416
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%register for automatic footnote numbering
\newcount\FootNumber
\FootNumber=1

%insert for holding footnotes to print as endnotes at end of paper

\newinsert\endnoteins        %define a new insert
\skip\endnoteins=0pt         %space added when endnote is present
\count\endnoteins=0          %magnification factor
\dimen\endnoteins=\maxdimen  %maximum endnotes per page

%print endnotes
\def\PrintEndNotes{\vfill\eject\ifvoid\endnoteins
                     \else\centerline{\bf Footnotes}\parskip=\medskipamount
                     \bigskip\unvbox\endnoteins\fi}

%footnote macro
%    Write notes in 8 point
%    Write to \endnotesins for end notes


\def\fnote#1{\footnote{$^{\the\FootNumber}$}{\eightpoint #1\endfnote}
\insert\endnoteins{\tenpoint\medskip\noindent\number\FootNumber. #1\par
\ifdouble\bigskip\fi}%
\global\advance\FootNumber by 1}

%      We must end paragraph to restore original baselines and
%      therefore have to skip up the amount of the baselineskip to keep
%      the space between footnotes right.

\def\endfnote{\par\vskip-\normalbaselineskip}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      \makeheadline -- redefine to omit headline on title pages (p. 364
%                       of TeXBook)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\iftitle                      %true if this is a titlepage
  \global\titlefalse

\def\titlepage{\global\titletrue}  %set flag if this is a Titlepage

\def\titlehead{\hfil}
\def\titlefoot{\hfil}

\def\makeheadline{\vbox to 0pt{\vskip-22.5pt%
    \line{\vbox to8.5pt{}%
    \iftitle\titlehead
    \else\the\headline\fi}\vss}\nointerlineskip}

\def\makefootline{\baselineskip=24pt 
   \iftitle\line{\titlefoot}\global
   \titlefalse\else\line{\the\footline}\fi}

%no footnoterule by default; can reset in sty files.
\def\footnoterule{}

\def\pagecontents{\ifvoid\topins\else
\unvbox\topins\fi
  \dimen@=\dp\@cclv \unvbox\@cclv % open up \box255
  \ifvoid\footins\else % Footnote info is present
    \vskip\skip\footins \footnoterule \unvbox\footins\fi
  \ifr@ggedbottom \kern-\dimen@ \vfil \fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     Create various boxes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newbox\titlebox
\newbox\authorbox
\newbox\affilbox
\newbox\addressbox
\newbox\keywordsbox
\newbox\datebox
\newbox\versionbox
\newbox\thanksbox
\newbox\abstractbox

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Create various counters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcount\SectionNumber\SectionNumber=1
\newcount\SubsectionNumber\SubsectionNumber=1
\newcount\EquationNumber\EquationNumber=0
\newcount\FigureNumber\FigureNumber=0

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \Reset -- to reset all counters and \pageno
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Reset{\global\SectionNumber=1\global\SubsectionNumber=1
\global\EquationNumber=0\global\FigureNumber=0\global\pageno=1
\global\FootNumber=1}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \today -- gives today's date
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\today{\ifcase\month\or
   January\or February\or March\or April\or May\or June\or
   July\or August\or September\or October\or November\or December\fi
   \space\number\day, \number\year}

%can reset this in sty files.
\def\version#1{}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Some math definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%can redefine in .sty files
\def\proof{\medbreak\noindent{\it Proof.  }}

%can redefine in .sty files
\def\qed{\vrule height8pt width4pt depth0pt\par\medskip}

%display mode partial derivatives
\def\D#1#2{{{\partial #1} \over {\partial #2}}}

%math mode partial derivations
\def\d#1#2{\partial #1/\partial #2}

%for naming equations
\def\Equation#1{\global\advance\EquationNumber by 1
	      \global\edef#1{\number\EquationNumber}(#1)}

%for roman text in math or display mode
\def\text#1{\hbox{\rm #1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Figures -- use \Fig\junk the first time you reference a figure, and
%            use \Figure\junk{2in}{This figure is junk.} when you want
%            it to appear.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%  \Fig -- for invoking figure
%%%  #1 is reference name for figure

\def\Fig#1{\global\advance\FigureNumber by 1
           \global\edef#1{\number\FigureNumber}Figure #1}

%%%  \Figure --- to have space reserved for figure.
%%% #1 is reference name for figure
%%% #2 is height of figure
%%% #3 is caption for figure

\def\Figure#1#2#3{
     \midinsert
     \vbox to #2{\vfil}
     \hbox to \hsize{\vbox{\parindent=0pt%
     {\bf Figure \number#1}.\space \rm #3}}
     \endinsert}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      \boxit -- this will surround a box by rules
%                useful for debugging and design purposes 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\ifDoBoxes
\DoBoxestrue

\def\boxit#1{\ifDoBoxes\vbox{\hrule\hbox{\vrule\vbox{#1}\vrule}\hrule}
\else\vbox{\hbox{\vbox{#1}}}\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   References
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%will set hanging indentation in amount specified by \parindent
\def\HangRef{\hangindent\parindent\ignorespaces\noindent}

\newif\ifbook
\newif\ifjour
\newif\ifinbook
\newif\ifunpublished
\newif\ifinbook

\newbox\nobox
\newbox\bybox
\newbox\pagesbox
\newbox\paperbox
\newbox\yrbox
\newbox\datebox
\newbox\volbox
\newbox\jourbox
\newbox\bookbox
\newbox\publbox
\newbox\publaddrbox
\newbox\editorbox
\newbox\paperinfobox
\newbox\bookinfobox

\def\no#1{\setbox\nobox\hbox{#1}}
\def\by#1{\setbox\bybox\hbox{#1}}
\def\pages#1{\setbox\pagesbox\hbox{#1}}
\def\paper#1{\setbox\paperbox\hbox{#1}}
\def\yr#1{\setbox\yrbox\hbox{#1}}
\def\date#1{\setbox\datebox\hbox{#1}}
\def\vol#1{\setbox\volbox\hbox{\bf #1}}
\def\jour#1{\setbox\jourbox\hbox{\it #1}\jourtrue}
\def\book#1{\setbox\bookbox\hbox{\it #1}\booktrue}
\def\inbook#1{\setbox\bookbox\hbox{\it #1}\inbooktrue}
\def\editor#1{\setbox\editorbox\hbox{#1}}
\def\publ#1{\setbox\publbox\hbox{#1}}
\def\publaddr#1{\setbox\publaddrbox\hbox{#1}}
\def\paperinfo#1{\setbox\paperinfobox\hbox{#1}\unpublishedtrue}

\def\ref{\relax}
\def\endref{\SetRef}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Headings
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\runningname#1{\edef\runname{#1}}
\def\runningtitle#1{\edef\runtitle{#1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    \CenterBox and \LeftBox
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\CenterBox creates a vbox with several lines of centered text
%modeled after TeXbook, p. 412
%     #1 name of box
%     #2 font used in box
%     #3 baselineskip in box
%     #4 text for box, lines separated by \cr
%
%\LeftBox does the same for left justified text
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\CenterBox#1#2#3#4{
   \global\setbox#1=\vbox{\baselineskip=#3\halign{#2\hfil##\hfil\cr#4\crcr}}}

\def\LeftBox#1#2#3#4{
   \global\setbox#1=\vbox{\baselineskip=#3\halign{#2##\hfil\cr#4\crcr}}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \section and \subsection
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newbox\sectionbox

\def\Romannumeral#1{\uppercase\expandafter{\romannumeral#1}}

\newif\ifRomanSection\RomanSectionfalse

% taken from TeXbook, p. 355, but changed the parameters so that
%   it won't fill out the page so readily.  If you really want all
%   the pages to be the same size, use \let\BigBreak=\bigbreak

\def\BigBreak{\vskip0pt plus .05\vsize\penalty-250
    \vskip0pt plus-.05\vsize\bigskip\vskip\parskip}

\def\DoCenteredSection#1{
   \BigBreak
   \SubsectionNumber=0
   \CenterBox
        \sectionbox
        \SectionFont
        \normalbaselineskip
        {\ifRomanSection\Romannumeral\SectionNumber
        \else\number\SectionNumber\fi.\enskip#1}
   \line{\hfil\box\sectionbox\hfil}
   \global\advance\SectionNumber by 1
   \nobreak\medskip
   \noindent}

\def\DoLeftSection#1{
   \BigBreak
   \SubsectionNumber=0
   \LeftBox
        \sectionbox
        \SectionFont
        \normalbaselineskip
        {\ifRomanSection{\Romannumeral\SectionNumber}
        \else\number\SectionNumber\fi.\enskip#1}
   \line{\box\sectionbox\hfil}
   \global\advance\SectionNumber by 1
   \nobreak\medskip
   \noindent}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Titles and authors
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\DoCenteredTitle#1{
    \titlepage\global
    \CenterBox
       \titlebox
       \TitleFont
       \normalbaselineskip
       {#1}}

\def\DoLeftTitle#1{
    \titlepage\global
    \LeftBox
       \titlebox
       \TitleFont
       \normalbaselineskip
       {#1}}

\def\DoCenteredAuthor#1{
    \CenterBox
       \authorbox
       \AuthorFont
       \normalbaselineskip
       {#1}}

\def\DoLeftAuthor#1{
     \LeftBox
     \authorbox
     \AuthorFont
     \normalbaselineskip
      {#1}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \prelim -- will write "preliminary verison" on cover
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\ifPreliminaryVersion
 \global\PreliminaryVersionfalse

\def\prelim{\PreliminaryVersiontrue}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   quote mode -- inserts and singlespaces
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\quote#1{\medskip{\normalbaselineskip=12pt\tenpoint
       \narrower #1 \par}\smallskip}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \doublespace -- prints document in doublespace
%   \singlespace -- reverts to singlespace
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\ifdouble\doublefalse 
\def\doublespace{\global\doubletrue\tenpoint}
\def\singlespace{\global\doublefalse\tenpoint}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   define dummys; will be redefined if needed in .sty files
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\runtitle#1{}
\def\runname#1{}
\def\titleheadline{\hfil}
\def\titlefootline{\hfil}
\overfullrule=0pt  %so the black boxes don't print out in margins
\def\enddocument{\relax}