COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	%Bob, this is macro.tex  I've copied my macro package into this plus
C00010 ENDMK
C⊗;
%Bob, this is macro.tex  I've copied my macro package into this plus
%some of your new macros that I'm using. The percentage sign in the first
%space means that it is not considered when running TeX. 

\def\drawat#1#2#3{\vtop{\kern#2\rlap{\kern#1#3}}} %#3 goes in hbox
%\def\qtoblank%change ? to invisible digit
%{\newdimen\digitwidth
%\setbox0=\hbox{\rm0}
%\digitwidth=\wd0
%\catcode`?=\active
%\def?{\kern\digitwidth}}
%\qtoblank ... 0.12579?58421?05.
%\catcode'?=\other
%restores normal ?

\def\fnc#1{\mathop{\rm #1}\nolimits}
%usage: to get erf(x), write $\fnc{erf}(x)$

\mathsurround .5pt
\def\dminus{\mathrel{\vbox{\lineskip1pt\baselineskip1pt
 \halign{\ctr{$##$}\cr
 .\cr-\cr}}}}
\def\ldt{\mathinner{\ldotp\ldotp}}
\def\relbuild#1\over#2{\mathrel{\mathop{#1}\limits_{#2}}}%to reverse buildrel
\def\tog{\relbuild \to\over G}%→ over G
\def\Rag{\relbuild \Rightarrow\over G}%double → over G
\def\atog{\buildrel\ast\over\tog}%asterisk over → over g
\def\aRag{\buildrel\ast\over\Rag}%asterisk over → over g
\def\aRa{\buildrel \ast\over\Rightarrow}%asterisk over double→
\def\ato{\buildrel \ast\over\to}%asterisk over →
\def\ld{\mathrel{\hbox{$<$\kern-4pt$\cdot$}}}
\def\gd{\mathrel{\hbox{$\cdot$\kern-4pt$>$}}}
\def\ej{\relbuild \equiv\over{j,k,x}}%≡ over j,k,x
\def\ez{\relbuild \equiv\over z}%≡ over z
\def\ext{\relbuild \equiv\over{x,t}}%≡ over x,t
\def\eqr{\relbuild =\over r}%= over r
\def\eqp{\relbuild =\over p}%= over p
\def\equU{\relbuild =\over U}%= over U
\def\eqq{\relbuild =\over q}%= over q
\def\eqs{\relbuild =\over s}%= over s
\def\eqj{\relbuild =\over j}%= over j
\def\zap{\mathrel{\vbox{\lineskip1pt\baselineskip1pt
 \halign{\ctr{$##$}\cr
 \scriptscriptstyle L\cr \sim\cr}}}}
\def\zzap{\mathrel{\vbox{\lineskip1pt\baselineskip1pt
 \halign{\ctr{$##$}\cr
 \scriptscriptstyle L\cr \approx\cr}}}}
\def\zapp{\mathrel{\vbox{\lineskip1pt\baselineskip1pt
 \halign{\ctr{$##$}\cr
 \scriptscriptstyle L↓2\cr \sim\cr}}}}
\def\zappp{\mathrel{\vbox{\lineskip1pt\baselineskip1pt
 \halign{\ctr{$##$}\cr
 \scriptscriptstyle L↓3\cr \sim\cr}}}}
\def\footnote#1#2{#1botinsert{\hrule width5pc \vskip3pt\baselineskip9pt
 \hbox par size{\eightpoint#1#2}}}
\def\qq{\qquad}
\def\q{\quad}
\def\narp{\buildrel n\over\Rightarrow}
\def\nnap{\buildrel n-1\over\Rightarrow}

\def\ctrline{\centerline}
\def\lft#1{{#1}\hfill}
\def\ctr#1{\hfill{#1}\hfill}
\def\rt#1{\hfill{#1}}
\def\naive{na\"\i ve} %\naive\

\newdimen\unit
\def\point#1 #2 {\rlap{\kern#1\unit
  \raise#2\unit\hbox to 0\unit{\hss$\scriptstyle\bullet$\hss}}}
\def\ycoord#1 {\rlap{\kern -0.2\unit
 \raise#1\unit\hbox{#1}}}
\def\xcoord#1 {\rlap{\kern#1\unit
 \lower0.2\unit\hbox to 0\unit
 {\hss #1\hss}}}

\def\xeq{\buildrel \times\over =}%x over = 
\def\xleq{\buildrel \times\over ≤}%x over ≤ 
\def\xgeq{\buildrel \times\over ≥}%x over ≥ 

\def\twodots{\mathinner{\ldotp\ldotp}} %same as \ldt
\def\derives{\buildrel\ast\over\rightarrow} %same as \ato
\def\transitiveclosure#1{\buildrel\ast\over 1} 

\def\eqaligntwo #1{\,\vcenter{\openup1\jot 
 \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil&\quad
 \hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil\crcr#1\crcr}}\,}


\def\nopagenumber{\output{\shipout\box255}}
\def\upsidea{\mathop{\forall}} % ∀ as math operator in formula
\def\backe{\mathop{\exists}} % ∃ as math operator in displayed formula
\def\therefore{\mathinner{\mskip2mu\raise1pt\vbox{\kern7pt\hbox{.}}
 \mskip2mu\raise7pt\hbox{.}
 \mskip2mu\raise1pt\hbox{.}\mskip6mu}}
\def\per{\mathop{\rm per}\nolimits}
\def\Det{\mathop{\rm Det}\nolimits}
\def\ihat{{\hat\imath}}
\def\jhat{{\hat\jmath}}
\def\xskip{\hskip .7em plus .3em minus .4em}
\def\adx#1:#2\par{\par\halign{\hskip #1##\hfill\cr #2}\par}
\def\disleft#1:#2:#3\par{\par\hangindent#1\noindent
			 \hbox to #1{#2 \hfill \hskip .1em}\ignorespaces#3\par}
\def\display#1:#2:#3\par{\par\hangindent #1 \noindent
			\hbox to #1{\hfill #2 \hskip .1em}\ignorespaces#3 \par}
\def\blackslug{\hbox{\hskip 1pt \vrule width 4pt height 6pt depth 1.5pt \hskip 1pt}}
\def\bib{\noindent\hangindent 20pt}
\def\biba{\par\parindent 20pt\hangindent 40pt}
\def\figbox#1:{\vbox{\null\vskip#1\null}}%cut and paste space
\def\undertext#1{$\underline{\hbox{#1}}$}
\def\table#1{$$\hbox{[Table #1]}$$}
\def\fig#1{$$\hbox{[Figure #1]}$$}
\def\pfbox
 {\hbox{\vbox{
 \def\|{\vrule height 2pt depth 2pt}
 \hrule
 \hbox to 4pt{\|\hfill\|}
 \hrule
 }}\hskip 3pt}
\def\outlineone#1:{\par\hangindent 19pt\noindent
  \hbox to 19 pt{#1\hfill}\ignorespaces}
\def\outlinetwo#1:{\par\hangindent 38pt\noindent
  \hbox to 38 pt{\hbox to 19pt{\hfill}#1\hfill}\ignorespaces}
\def\outlinethree#1:{\par\hangindent 57pt\noindent
  \hbox to 57 pt{\hbox to 38pt{\hfill}#1\hfill}\ignorespaces}
\uchyph 1 % hyphenate Capital letter words