COMMENT ⊗   VALID 00006 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	\chcode'173←1 \chcode'176←2 \chcode'44←3 \chcode'26←4
C00007 00003	\font @←cmathx \font a←cmr10 \font b←cmr9 \font c←cmr8
C00011 00004	\def\tpage{F} \def\rhead{} \def\frstx{F} \def\csec{} \def\chd{} % "global variables"
C00014 00005	\def\quoteformat#1{\baselineskip 11pt \def\rm{\:>} \def\sl{\:←}
C00018 00006	\def\MIX{{\tt MIX}}
C00021 ENDMK
C⊗;
\chcode'173←1 \chcode'176←2 \chcode'44←3 \chcode'26←4
\chcode'45←5 \chcode'43←6 \chcode'136←7 \chcode 1←8
\chcode'27←13 \def↔{\penalty999\ }
\chpar10←250

\def\lft#1{#1\hfill}
\def\ctr#1{\hfill#1\hfill}
\def\rt#1{\hfill#1}
\def\top#1{#1\vfill}
\def\mid#1{\vfill#1\vfill}
\def\bot#1{\vfill#1}

\def\rjustline#1{\hbox to size{\hss#1}}
\def\ctrline#1{\hbox to size{\hss#1\hss}}

\def\trace{\chpar0←}
\def\jpar{\chpar1←}

\def\log{\mathop{\char l\char o\char g}\limitswitch}
\def\lg{\mathop{\char l\char g}\limitswitch}
\def\ln{\mathop{\char l\char n}\limitswitch}
\def\lim{\mathop{\char l\char i\char m}}
\def\limsup{\mathop{\char l\char i\char m\,\char s\char u\char p}}
\def\liminf{\mathop{\char l\char i\char m\,\char i\char n\char f}}
\def\sin{\mathop{\char s\char i\char n}\limitswitch}
\def\cos{\mathop{\char c\char o\char s}\limitswitch}
\def\tan{\mathop{\char t\char a\char n}\limitswitch}
\def\cot{\mathop{\char c\char o\char t}\limitswitch}
\def\sec{\mathop{\char s\char e\char c}\limitswitch}
\def\csc{\mathop{\char c\char s\char c}\limitswitch}
\def\max{\mathop{\char m\char a\char x}}
\def\min{\mathop{\char m\char i\char n}}
\def\sup{\mathop{\char s\char u\char p}}
\def\inf{\mathop{\char i\char n\char f}}
\def\det{\mathop{\char d\char e\char t}}
\def\exp{\mathop{\char e\char x\char p}\limitswitch}
\def\Pr{\mathop{\char P\char r}}
\def\gcd{\mathop{\char g\char c\char d}}
\def\lcm{\mathop{\char l\char c\char m}}
\def\xch{\mathrel{\char '444}}

\def\ldots{{.\≥.\≥.}}
\def\cdots{{\char'401\≥\char'401\≥\char'401}}
\def\ldotss{{.\≥.\≥.\≥}}
\def\cdotss{\cdots\≥}
\def\ldotsm{{\≥.\≥.\≥.\≥}}
\def\vdots{\vbox{\baselineskip 4pt\vskip 6pt\hbox{.}\hbox{.}\hbox{.}}}

\def\leftset{\mathopen{\{\,}}
\def\rightset{\mathclose{\,\}}}

\def\neqv{\mathrel{\not≡}}

\def\%{\char'45 }	% Note, the space after 45 is needed!
\def\deg{↑{\hbox{\hskip-1pt\:w\char5}}}

\def\choose{\comb()}

\def\mod{\<\,\mathbin{\char m\char o\char d}\penalty900\<\,}
\def\modulo#1{\penalty0\;(\char m\char o\char d\char u\char l\char o\,\,#1)}

\def\cpile#1{\vcenter{\halign{\hfill$## $\hfill\cr#1}}}
\def\lpile#1{\vcenter{\halign{$## $\hfill\cr#1}}}
\def\rpile#1{\vcenter{\halign{\hfill$## $\cr#1}}}
\def\eqalign#1{\baselineskip15pt\lineskip3pt
  \vcenter{\halign{\hfill$\dispstyle{##}$⊗$\dispstyle{\null##}$\hfill\cr#1}}}
\def\teqalign#1{
  \vcenter{\halign{\hfill$\dispstyle{##}$⊗$\dispstyle{\null##}$\hfill\cr#1}}}
\def\eqalignno#1{\baselineskip15pt\lineskip3pt
  \vbox{\tabskip 0pt plus 1000pt minus 1000pt
    \halign to size{\hfill$\dispstyle{##}$\tabskip 0pt
    ⊗$\dispstyle{\null##}$\hfill\tabskip 0 pt plus 1000pt minus 1000pt
    ⊗\hfill$ ##$\tabskip 0pt\cr#1}}}
\def\null{\hbox{}}
\def\twoline#1#2#3{\vbox{\hbox to size{$\quad\dispstyle{#1}$\hfill}
    \vskip#2\hbox to size{\hfill$\dispstyle{#3}\quad$}}}

\def\chop to#1pt#2{\hbox{\lower#1pt
\null\vbox{\hbox{\lower100pt\hbox{\raise100pt
\hbox{$\dispstyle{#2}$}}}\vskip-100pt}}} % pretends that #2 is #1pt deep
\def\spose#1{\hbox to 0pt{#1\hss}}
\font @←cmathx \font a←cmr10 \font b←cmr9 \font c←cmr8
\font d←cmr7   \font e←cmr6  \font f←cmr5 \font g←cmi10
\font h←cmi9   \font i←cmi8  \font j←cmi7 \font k←cmi6
\font l←cmi5   \font m←cmsc10 \font n←cms10 \font o←cms9
\font p←cms8  \font q←cmb10 \font r←cmb9 \font s←cmb8
\font t←cmtt   \font u←cmsy10 \font v←cmsy9 \font w←cmsy8
\font x←cmsy7  \font y←cmsy6 \font z←cmsy5 \font ;←cmtitl
\font <←cmssb  \font =←cmss12 \font >←cmss8 \font ←←cmsss8
\font T←cmtt9  \font U←cmtt8 \font M←cmsc9

\hsize 29pc \vsize 45pc \maxdepth 2pt \parindent 19pt \topbaseline 10pt
\parskip 0pt plus 1 pt \lineskip 1pt
\topskip 24pt plus 6pt minus 10pt  \botskip 3pt plus 6pt

\def\tenpoint{\baselineskip 12pt \dispskip 12pt plus 3pt minus 9pt
	\dispaskip 0pt plus 3pt \dispbskip 7pt plus 3pt minus 4pt
	\def\rm{\:a} \def\sl{\:n} \def\bf{\:q} \def\it{\:g} \def\tt{\:t}
	\def\biglp{\mathopen{\vcenter{\hbox{\:@\char'0}}}}
	\def\bigrp{\mathclose{\vcenter{\hbox{\:@\char'1}}}}
	\mathrm adf \mathit gjl \mathsy uxz \rm}
\def\ninepoint{\baselineskip 11pt \dispskip 11pt plus 3pt minus 8pt
	\dispaskip 0pt plus 3pt \dispbskip 6pt plus 3pt minus 3pt
	\def\rm{\:b} \def\sl{\:o} \def\bf{\:r} \def\it{\:h} \def\tt{\:T}
	\def\biglp{\mathopen{\hbox{\:a(}}}
	\def\bigrp{\mathclose{\hbox{\:a)}}}
	\mathrm bef \mathit hkl \mathsy vyz \rm}
\def\eightpoint{\baselineskip 9pt \dispskip 9pt plus 3pt minus 7pt
	\dispaskip 0pt plus 3pt \dispbskip 5pt plus 3pt minus 2pt
	\def\rm{\:c} \def\sl{\:p} \def\bf{\:s} \def\it{\:i} \def\tt{\:U}
	\def\biglp{\mathopen{\hbox{\:a(}}}
	\def\bigrp{\mathclose{\hbox{\:a)}}}
	\mathrm cef \mathit ikl \mathsy wyz \rm}
\mathex @  \def\tt{\:t}
\def\bigglp{\mathopen{\vcenter{\hbox{\:@\char'22}}}}
\def\biggrp{\mathclose{\vcenter{\hbox{\:@\char'23}}}}
\def\biggglp{\mathopen{\vcenter{\hbox{\:@\char'40}}}}
\def\bigggrp{\mathclose{\vcenter{\hbox{\:@\char'41}}}}

\def\qquad{\hskip 2em}
\def\9{\hskip .5em}
\def\xskip{\hskip 7pt plus 3pt minus 4pt}
\def\yskip{\penalty-50\vskip 3pt plus 3pt minus 2pt}
\def\yyskip{\penalty-100\vskip 6pt plus 6pt minus 4pt}
\def\sectionskip{\penalty-200\vskip 24pt plus 12pt minus 6pt}

\def\textindent#1{\noindent\hbox to 19pt{\hss#1\ }\!}
\def\hang{\hangindent 19pt}
\def\tpage{F} \def\rhead{} \def\frstx{F} \def\csec{} \def\chd{} % "global variables"
\def\titlepage{\gdef\tpage{T}}   % \titlepage sets tpage to T
\def\runninglefthead#1{\gdef\rhead{\:M#1}} %\runninglefthead sets rhead
\def\acpmark#1#2{\mark
	{\ifeven0{\hbox to .45 in{\:a\count0\hfill}\rhead\hfill\:a#2}
	\else{\:a\csec\hfill\:M#1\hbox to .45 in{\:a\hfill\count0}}}}
\def\runningrighthead#1 \section#2{\acpmark{\chd}{#2}
	\gdef\csec{#2} \gdef\chd{#1}} %\runningrighthead sets csec and chd
\output{\baselineskip 0pt\lineskip0pt	% beginning of output routine, resets skips
	\vbox to 48pc{         % prepare the full page of this fixed height
	\if T\tpage		% the next is used when tpage is "T" (title pages)
		{\gdef\tpage{F} % reset tpage
		\vskip 24pt	% blank space in place of headlines
		\page		% insert the page contents
		\vfill		 % extra space before the page number
		\ctrline{\:c\count0}} % "drop folio", the page number in 8pt type
	\else{\baselineskip 12pt \hbox{} % empty line to position next baseline
		\hbox to size{\ifeven0{\topmark}\else{\botmark}}
		\hbox{}	% empty line whose baseline is exactly 24pt from top
		\page\vfill}	% insert the page contents
	}			% completion of the \vbox
	\setcount1\count0	% set up page number counter for indexing macros
	\advcount0}		% increase page number by 1 and end output routine
\def\corners{\vbox to 0pt{\baselineskip0pt\lineskip 0pt \vskip -24pt
	\hbox to size{\vrule height .2pt width 11pt \hfill \vrule width 11pt}
	\hbox to size{\vrule height 11pt width .2pt \hfill \vrule width .2pt}
	\vfill}}		% this will indicate true top corners on title page
\def\quoteformat#1{\baselineskip 11pt \def\rm{\:>} \def\sl{\:←}
	\def\bf{\error} \def\it{\:←}
	\vskip 6pt plus 2pt minus 2pt
	{\sl\halign{\rjustline{##}\cr#1}}}
\def\author#1{\penalty1000\vskip 6pt plus 2pt minus 2pt
	\rm\rjustline{---#1}
	\vskip 8pt plus 4pt minus 2pt}
\def\tablehead#1{\ctrline{\:<#1}\penalty1000\vskip2pt\eightpoint}
\def\sectionbegin#1{\hbox{\:<#1}
	\penalty 1000 \vskip 6pt plus 3pt
	\acpmark{\chd}{\csec}
	\noindent\tenpoint\!}
\def\subsectionbegin#1{\yyskip\noindent
	\tenpoint{\bf#1.}\xskip\!}
\def\dimsectionbegin#1{\sectionskip
	\acpmark{\chd}{\csec}
	\tenpoint\noindent{\bf#1.}\xskip\!}
\def\exbegin#1{\sectionskip
	\hbox{\:<#1}
	\penalty 1000 \vskip 8pt minus 5pt
	\gdef\frstx{T}
	\ninepoint}
\def\ansbegin#1{\runningrighthead{ANSWERS TO EXERCISES}
	\section{#1}
	\sectionskip
	\hbox{\:<SECTION #1}
	\penalty 1000 \vskip 8pt minus 5pt
	\acpmark{\chd}{\csec}
	\gdef\frstx{T}
	\ninepoint}
\def\algbegin#1(#2). {\yyskip\noindent
	{\bf #1}({\sl#2\/}){\bf.}\xskip}
\def\thbegin#1. {\yyskip\noindent
	{\bf#1.}\xskip}
\def\proofbegin{\penalty25\vskip 6pt plus 12pt minus 4pt\noindent{\sl Proof.}\xskip}
\def\dproofbegin{\penalty25\noindent{\sl Proof.}\xskip}

\def\anskip{\par\if T\frstx{\gdef\frstx{F}}\else{\penalty-200}
	\vskip 3pt plus 3pt minus 1pt}
\def\annskip{\par\if T\frstx{\gdef\frstx{F}}\else{\penalty-200}
	\vskip 6pt plus 6pt minus 3pt}
\def\exno #1. [#2]{\anskip\textindent{\bf#1.}[{\it#2\/}]\hskip6pt}
\def\trexno #1. [#2]{\anskip\noindent\hbox to 19pt{\hskip-3.5pt\:@\char'170\hfill
	\bf#1.\ }[{\it#2\/}]\hskip6pt}
\def\HM{H\hskip-1pt M}
\def\ansno #1. {\anskip\textindent{\bf#1.}}
\def\ansnos #1,#2. {\anskip\textindent{\bf#1,}\hbox{\bf\!#2.\ }}
\def\algstep #1. [#2]{\par\yskip \hang
	\textindent{\bf#1.}\hskip-.08em[#2]\xskip\!}
\def\aalgstep #1. [#2]{\par\yskip\hangindent 24pt
	\noindent\hbox to 24pt{\hss\bf#1.\ }\hskip-.08em[#2]\xskip\!}

\def\caption Fig.\ #1.{\ninepoint{\bf Fig.\ #1.}\xskip\!}
\def\footnote#1#2{#1\botinsert{\hrule width 5pc
	\vskip 3pt \baselineskip 9pt\hbox par size{\eightpoint#1#2}}}

\def\star{\hbox to 0pt{\hskip 0pt minus 100pt *}}
\def\blackslug{\hbox{\hskip 1pt \vrule width 4pt height 6pt depth 1.5pt
	\hskip 1pt}}
\def\MIX{{\tt MIX}}
\def\.#1{\hbox{\tt#1}}
\def\rA{\hbox{\rm rA}}
\def\rX{\hbox{\rm rX}}
\def\rAX{\hbox{\rm rAX}}
\def\rI{\hbox{\rm rI}}
\def\rJ{\hbox{\rm rJ}}

\def\mixtwo#1{\let\ttt=\tt\ninepoint\def\\{\noalign{\penalty-200}}
	\halign{\lft{\ttt##}\quad\tabskip0pt⊗\lft{\ttt##}\qquad
	⊗\lft{\rm##}\cr#1}}
\def\mixthree#1{\let\ttt=\tt\ninepoint\def\\{\noalign{\penalty-200}}
	\halign{\lft{\ttt##}\quad\tabskip0pt
	⊗\lft{\ttt##}\quad⊗\lft{\ttt##}
	\qquad⊗\lft{\rm##}\cr#1}}
\def\mixfour#1{\let\ttt=\tt\ninepoint\def\\{\noalign{\penalty-200}}
	\halign{\rt{\it##}\quad\tabskip0pt⊗\lft{\ttt##}\quad⊗\lft{\ttt##}\quad
	⊗\lft{\ttt##}\qquad⊗\lft{\rm##}\cr#1\\}}
\def\mixfive#1{\let\ttt=\tt\ninepoint\def\\{\noalign{\penalty-200}}
	\halign{\rt{\it##}\quad\tabskip0pt⊗\lft{\ttt##}\quad⊗\lft{\ttt##}\quad
	⊗\lft{\ttt##}\quad⊗\ctr{$ ##$}\quad⊗\lft{\rm##}\cr#1\\}}
\def\mixans #1. #2{\def\\{\noalign{\penalty-200}}\annskip
\halign{\hbox to 19pt{##}⊗\lft{\tt##}\quad⊗\lft{\tt##}\quad⊗\lft{\tt##}\quad
⊗\lft{\rm##}\cr
{\hfill\bf #1.\ }#2}}
\def\mixansfour #1. #2{\def\\{\noalign{\penalty-200}}\annskip
\halign{\hbox to 19pt{##}⊗\lft{\tt##}\quad⊗\lft{\tt##}\quad⊗\lft{\tt##}\quad
⊗$\ctr{##}$⊗\quad\lft{\rm##}\cr
{\hfill\bf #1.\ }#2}}

\def\understep#1{$\underline{\hbox{\sl#1}}$}

\def\inx#1{\send0{#1→\count1}\ifhmode{\!}\else{}}
\def\inxf#1{\send0{#1→\count1f}\ifhmode{\!}\else{}}
\def\α#1{\send0{#1→\count1}#1}
\def\β#1{\send0{#1→\count1f}#1}