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authorKarl Berry <karl@freefriends.org>2009-05-23 00:04:36 +0000
committerKarl Berry <karl@freefriends.org>2009-05-23 00:04:36 +0000
commit1e748bf04d4470ebb06521adedd4d3f5c7f3c45e (patch)
tree9788a0b9c80ed5097265901bb111a6ac327c5f89 /Master/texmf-doc/doc
parent20d25e62ad99344ee37e88fb0787319391107640 (diff)
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-
-
-%% Thanks for your interest in A Gentle Introduction to TeX.
-%% Any comments on this manual would be appreciated. These may
-%% be typesetting, English, or TeX criticisms. If you decide to
-%% translate this document into another language, I'd appreciate
-%% receiving a copy.
-%%
-%% This file is a complete TeX input file. Just run it
-%% through TeX and print out the resulting "DVI" file. If you are
-%% familiar with TeX, the macros at the top of the file have a few
-%% switches which you may want to set. If you have problems or
-%% can't run TeX at all, write to me and I'll send you a hard copy.
-%% You can get a bound copy from the TeX Users Group at the address
-%% given below.
-%%
-%% You should feel free to photocopy and/or distribute this manual.
-%% My only request is that it remain in one piece and not be chopped
-%% up. The only machine dependent section (#1.2) may need to be
-%% rewritten for your local site, of course.
-%%
-%%% Michael Doob
-%% Department of Mathematics
-%% The University of Manitoba
-%% Winnipeg, Manitoba R3T 2N2
-%% Canada
-%% mdoob@uofmcc (bitnet)
-%% mdoob@ccu.umanitoba.ca (internet)
-%%
-%% Here is a character listing to check to be sure that no
-%% unwanted translations took place within the bowels of the net.
-%% Upper case letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ
-%% Lower case letters: abcdefghijklmnopqrstuvwxyz
-%% round parentheses, square brackets, curly braces: () [] {}
-%% Exclaim, at, sharp, dollar, percent: ! @ # $ %
-%% Caret, ampersand, star, underscore, hyphen: ^ & * _ -
-%% vertical bar, backslash, tilde, backprime, plus: | \ ~ ` +
-%% plus, equal, prime, quote, colon: + = ' " :
-%% less than, greater than, slash, question, comma: < > / ? ,
-%% period, semicolon: . ;
-%%
-%%
-%%
-%% Now here come the macros used in this manual. If you are
-%% already familiar with TeX, you may want to fiddle with them.
-%% In particular, the hooks are left to generate a new control
-%% word index and table of contents if you change section 1.2.
-%%
-%%
-
-
-
-%%%%%%%% Here are the fonts other than the sixteen defined in %%%%%%%%
-%%%%%%%%%%%%% plain.tex that are used %%%%%%%%%%%%%%%%%%
-
- %%%% first, choose between amr or cmr fonts %%%
-\newif \ifamrfonts
-\amrfontsfalse % use this line if you use the cmr fonts
-%\amrfontstrue % use this line if you use the old amr fonts
-
-\ifamrfonts \font\brm=amr10 scaled \magstep1
- \else \font\brm=cmr10 scaled \magstep1 \fi
-\ifamrfonts \font\halfrm=amr10 scaled \magstephalf
- \else \font\halfrm=cmr10 scaled \magstephalf \fi
-\ifamrfonts \font\bbrm=amr10 scaled \magstep2
- \else \font\bbrm=cmr10 scaled \magstep2 \fi
-\ifamrfonts \font\bbbrm=amr10 scaled \magstep3
- \else \font\bbbrm=cmr10 scaled \magstep3 \fi
-\ifamrfonts \font\bbbbrm=amr10 scaled \magstep4
- \else\font \bbbbrm=cmr10 scaled \magstep4 \fi
-\ifamrfonts \font\bbbbbrm=amr10 scaled \magstep5
- \else \font\bbbbbrm=cmr10 scaled \magstep5 \fi
-\ifamrfonts \font\sf = amssmc10
- \else \font\sf = cmss10 \fi
-\ifamrfonts \font\chapfont=ambx10 scaled \magstep2
- \else \font\chapfont=cmbx10 scaled \magstep2 \fi
-\ifamrfonts \font\secfont=ambx10 scaled \magstep1
- \else \font\secfont=cmbx10 scaled \magstep1 \fi
-\ifamrfonts \font\sc= amcsc10
- \else \font\sc= cmcsc10 \fi
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%%%%\vbadness=10000 %%%%%% I don't want to hear about underfull vboxes
-\raggedbottom %%%%% delete this line for aligned page bottoms
-\hsize=5.5in
-\vsize=7in
-\voffset=.75in
-\parskip=\baselineskip
-\widowpenalty=1000 \clubpenalty=1000 %%% I hate widows and orphans! %%%
-
-%%%%%%%%% choosing between Canadian and American spellings %%%%%%%%%
-\newif \ifcanspell
-\canspelltrue %%%% Canadian spelling
-%\canspellfalse %%% use this line for American spelling
-
-\def\aesthetic{\ifcanspell \ae{}sthetic\else esthetic\fi}
-\def\analogue{\ifcanspell analogue\else analog\fi}
- \let\analog=\analogue
-\def\cancelled{\ifcanspell cancelled\else canceled\fi}
- \let\canceled=\cancelled
-\def\centimetre{\ifcanspell centimetre\else centimeter\fi}
- \let\centimeter=\centimetre
-\def\centre{\ifcanspell centre\else center\fi}
- \let\center=\centre
-\def\centred{\ifcanspell centred\else centered\fi}
- \let\centered=\centred
-\def\our{\ifcanspell our\else or\fi}
-\def\postcode{\ifcanspell postalcode\else zipcode\fi}
-\def\province{\ifcanspell province\else state\fi}
-\def\theatre{\ifcanspell theatre\else theater\fi}
- \let\theater=\theatre
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%% First check to see if using plain format %%%%%%%%%%%%%%%%%
-
-\def\shouldbefmt{plain}
-\ifx\shouldbefmt\fmtname
-\else
-\immediate\write16{}
-\immediate\write16{***** WARNING WARNING WARNING *****}
-\immediate\write16{You probably need to use the command}
-\immediate\write16{tex \string<filename\string>}
-\immediate\write16{to make your dvi file (not latex).}
-\immediate\write16{***** WARNING WARNING WARNING *****}
-\immediate\write16{}
-\fi
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%% headline routines %%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\def\gentleheadline{%
- \vbox {\hrule%
- \line {\strut \vrule \quad \tenrm A \TeX{} intro
- \ifcanspell (Canadian \else (U.S. \fi spelling)
- \hfil
- \ifnum \secnum > 0 Section \the\secnum: \fi \sectiontitle \quad
- \vrule}%
- \hrule}%
-}
-
-\newif \iftitlepage \titlepagetrue
-\headline=
- {\iftitlepage \hfil \global\titlepagefalse \else \gentleheadline \fi}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%% define contents and index files %%%%%%%%%%%%%%%%%%%%%%
-%%% Normally the contents and index are hard coded into the input file. %%%
-%% To generate new ones, use \writingcontentstrue and \writingindextrue. %%
-
-\newif \ifwritingcontents
-\newif \ifwritingindex
-\newwrite\contents \newwrite\index
-
-\writingcontentsfalse \writingindexfalse
-%%% \writingcontentstrue %%% use this line to make the contents
-%%% \writingindextrue %%% use this line to make the index
-
-\ifwritingcontents \openout\contents=contents.tex \fi
-\ifwritingindex \openout\index=index.tex
- \def\toindex#1{\immediate\write\index{#1 \the\pageno}}
- \else \def\toindex#1{} \fi
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%% determine whether answers are printed %%%%%%%%%%%%%%%%
-\newif \ifwritinganswers
-\writinganswersfalse %%% use this line to suppress answer section
-\writinganswerstrue %%% use this line to include answer section
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%% footnote macro with counter %%%%%%%%%%%%
-\newcount\footnotenum \footnotenum=0
-\def\fnote#1{\advance \footnotenum by 1%
-\footnote{$^{\the\footnotenum}$}{#1}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-%%%%%%%%%%%%%%%% exercise, section, and subsection macros %%%%%%%%%%%%
-\newcount\exno %%%%%% counter for exercises %%%%%%%%
-\newcount\secnum \secnum=0 %%%% counter for section numbers %%%%
-\newcount\subsecnum
-
-\def\section#1{
- \vfill\eject %%%%% new section starts on a new page
- %%%\ifodd\pageno \else\ \vfill\eject \fi %start on an odd page
- \advance\secnum by 1 \subsecnum=0 \exno=0
- \ifnum \secnum = 1 \pageno=1 \fi
- \ifnum \secnum > 0
- \leftline{\chapfont Section \the\secnum}
- \vskip 3pt \fi
- \leftline{\chapfont #1}
- \def\sectiontitle{#1}
- \vskip\baselineskip
- \hrule
- \vskip 1cm
- \ifwritingcontents \write\contents{\string\line\string{#1
- \string\dotfill{}
- \ifnum \pageno < 0 \romannumeral-\pageno
- \else \the\pageno \fi
- \string}}\fi
- \titlepagetrue}
-
-\def\subsection#1{\advance\subsecnum by 1
- \vskip 30pt
- \leftline{\secfont \the\secnum .\the\subsecnum\ #1}
- \nobreak
- \ifwritingcontents
- \write\contents{\string\line\string{\string\qquad{}#1
- \string\dotfill{} \the\pageno\string}}\fi
- }
-
-\def\exercise{\global\advance \exno by 1
- \vskip\baselineskip
- \noindent $\triangleright$ Exercise \the\secnum.\the\exno\quad
- }
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%% definitions of control sequences for characters in the typewriter font %%%
-%%%% for short phrases this is easier than using a literal construction %%%%
-\def\\{\char92{}} %%%%% backslash %%%%%
-\def\lb{\char'173{}} %%%%% left brace %%%%%
-\def\rb{\char'175{}} %%%%% right brace %%%%%
-\def\sp{\char32{}} %%%%% special space symbol %%%%%
-
-\def\beginliteral{
-\vskip\baselineskip
-\begingroup
-\tt
-\obeylines
-%{\obeyspaces\global\let =\ }
-\catcode`\@=0
-\parskip=0pt\parindent=0pt
-\catcode`\$=12\catcode`\&=12\catcode`\^=12\catcode`\#=12
-\catcode`\_=12\catcode`\~=12
-\def\par{\leavevmode\endgraf}
-\catcode`\{=12\catcode`\}=12\catcode`\%=12\catcode`\\=12
-}
-
-\def\endliteral{\endgroup}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%%%%%%%%%%%%%% inhibit hyphenation of typewriter text %%%%%%%%%%%%%%
-\hyphenchar\tentt=-1
-
-
-%%%%%%%%%%%% grouping to make input listing in typewriter type %%%%%%%
-\def\beginuser{\vskip\parskip
- \everypar={\nobreak}
- \begingroup
- \tt \obeylines \parskip=0pt \parindent=0pt}
-
-\def\enduser{\endgroup}
-
-
-%%%%%%%%%%% macro to construct tables (easily) %%%%%%%%%%%%%%%%
-%%% parameters: title goes between brackets, rest of the
-%%% paragraph is the table
-\def\maketable[#1]#2\par{
-\setbox1=\vbox{#2}
-$$\vbox{
- \hbox to \wd1{\bf \hss #1 \hss}
- \vskip 12pt
- \box1
- }
-$$
-}
-%%%%%%%%%%% end of macro to construct tables %%%%%%%%%%%%%%%%
-
-
-
-%%%%%%%%%%% macro to put a box around the text %%%%%%%%%%%%%%%%
-\def\makebox#1#2#3% vsize, hsize, inserted text
-{\hbox{\vrule
- \vbox to #1{\hrule \vss
- \hbox to #2{\hss#3\hss}\vss
- \hrule}\vrule}}
-
-\def\displaytext#1{$$\hbox{#1}$$}
-
-\def\LaTeX{{\rm L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em
- T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
-
-\def\AMSTeX{{$\cal A$}\kern-.1667em\lower.5ex\hbox
- {$\cal M$}\kern-.125em{$\cal S$}-\TeX}
-
-
-%%%%%%%%%%%% macro to put TeX references in right margin %%%%%%%%
-\newdimen\theight
-\def \TeXref#1{%
- \vadjust{\setbox0=\hbox{\sevenrm\quad\quad\TeX book: #1}%
- \theight=\ht0
- \advance\theight by \dp0 \advance\theight by \lineskip
- \kern -\theight \vbox to \theight{\rightline{\rlap{\box0}}%
- \vss}%
- }}%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\def\version{1.1}
-
-%%%%%%%%%%%% macro to write the date out the date and time %%%%%%%%%%%
-%%%%%%%%%%%% TeXbook p. 406 for 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}
-
-\newcount\hour \newcount\minute
-\hour=\time \divide \hour by 60
-\minute=\time
-\loop \ifnum \minute > 59 \advance \minute by -60 \repeat
-\def\writetime{\ifnum \hour<13 \number\hour:% % supresses leading 0's
- \ifnum \minute<10 0\fi% % so add it it
- \number\minute
- \ifnum \hour < 12 \ A.M. \else \ P.M. \fi
- \else \advance \hour by -12 \number\hour:% % supresses leading 0's
- \ifnum \minute<10 0\fi% % add it in
- \number\minute \ P.M. \fi}
-
-\def\datestamp{\vfill
- \rightline{\sevenrm Gentle Intro \version{} run through \TeX{}
- on \today{} at \writetime}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\titlepagetrue
-{\nopagenumbers
-\def\sectiontitle{Introduction}
-\topinsert \vskip 6 cm \endinsert
-\centerline{\chapfont A Gentle Introduction to \TeX{}}
-\vskip 15 pt
-\centerline{\secfont A Manual for Self-study}
-\vskip 3cm
-\leftline{Michael Doob}
-\leftline{Department of Mathematics}
-\leftline{The University of Manitoba}
-\leftline{Winnipeg, Manitoba, Canada R3T 2N2}
-\vskip\baselineskip
-\leftline{MDOOB@UOFMCC.BITNET}
-\leftline{MDOOB@CCU.UMANITOBA.CA}
-
-\vfill\eject
-\titlepagetrue.
-\vfill\eject
-}
-\secnum=-2 \pageno=-1
-
-\section{Introduction}
-
-First the bad news: \TeX{} is a large and complicated program that
-goes to extraordinary lengths to produce attractive typeset material.
-This very complication can cause unexpected things to happen at times.
-Now the good news: straightforward text is very easy to typeset using
-\TeX\null. So it's possible to start with easier text and work up to
-more complicated situations.
-
-The purpose of this manual is to start from the very beginning and
-to move towards these more complicated situations. No previous knowledge
-of \TeX{} is assumed. By proceeding a section at a time, greater
-varieties of text can be produced.
-
-Here are a few suggestions: there are some exercises in each
-section. Be sure and do them! The only way to learn \TeX{} is
-by using it. Better yet, experiment on your own; try to make
-some variations on the exercises. There is no way that you can
-damage the \TeX{} program with your experiments. You can find a
-complete answer to most exercises by looking at the \TeX{} source
-file that was used to produce this document. You'll notice that
-there are references in the right margin to {\bf The \TeX
-book}\fnote{Addison-Wesley, Reading,Massachusetts, 1984, ISBN
-0-201-13488-9}\null. When you feel that you want more
-information on a topic, that's where to look.
-
-Incidentally, there are a few fibs that appear in this manual;
-they are used to hide complications (I look at this as something
-like poetic license). As you become more experienced at using
-\TeX{}, you'll be able to find them.
-
-\TeX{} is a public domain program that is available for no
-license fee. It was developed by Donald Knuth at Stanford
-University as a major project. In the profit-oriented market
-place, the program would certainly cost many thousands of
-dollars. The \TeX{} Users Group (TUG) is a nonprofit
-organization which distributes copies of \TeX{}, this manual,
-updates software, and gives information about new developments in
-both hardware and software in its publications TUGboat and \TeX
-niques. Joining this users group is inexpensive; please consider
-doing so. The address is:
-\vskip\baselineskip
-\centerline{\TeX{} Users Group}
-\centerline{P.O. Box 869}
-\centerline{Santa Barbara, CA 93102}
-\centerline{U.S.A.}
-
-This manual would not have come into being without the aid of others.
-In particular the proofreading and suggestions of the following
-people have been invaluable:
-\begingroup
-\frenchspacing
-Waleed A.~Al-Salam (University of Alberta),
-Debbie L.~Alspaugh (University of California),
-Nelson H.~F.~Beebe (University of Utah),
-Barbara Beeton (American Mathematical Society),
-Anne Br\"uggemann-Klein (University of Freiburg),
-Bart Childs (Texas A.~\&~M\null. University),
-Mary Coventry (University of Washington),
-Dimitrios Diamantaras (Temple University),
-Roberto Dominimanni (Naval Underwater Systems Center),
-Lincoln Durst (Providence, RI),
-Victor Eijkhout (University of Nijmegen),
-Moshe Feder (St. Lawrence University),
-Josep~M.~Font (Universidad Barcelona),
-Jonas de Miranda Gomes
- (Instituto de Matematica Pura e Aplicada - Brazil),
-Rob Gross (Boston College),
-Klaus Hahn (University of Marburg),
-Anita Hoover (University of Delaware),
-J\"urgen Koslowski (Macalester College),
-Kees van der Laan (Rijksuniversiteit Groningen),
-John Lee (Northrop Corporation),
-Silvio Levy (Princeton University),
-Robert Messer (Albion College),
-Emily H.~Moore (Grinnell College),
-Young Park (University of Maryland),
-Craig Platt (University of Manitoba),
-Kauko Saarinen (University of Jyv\"askyl\"a),
-Jim Wright (Iowa State University),
-and
-Dominik Wujastyk (Wellcome Institute for the History of Medicine).
- \endgroup
-
-In addition several people have sent me parts or all of their local
-manuals. I have received a few others on the rebound.
-In particular
-\begingroup
-\frenchspacing
-Elizabeth Barnhart (TV Guide),
-Stephan v.~Bechtolsheim (Purdue University),
-Nelson H.~F.~Beebe (University of Utah)
- and Leslie Lamport (Digital Equipment Corporation),
-Marie McPartland-Conn and Laurie Mann (Stratus Computer),
-Robert Messer (Albion College),
-Noel Peterson (Library of Congress),
-Craig Platt (University of Manitoba),
-Alan Spragens (Stanford Linear Accelerator Center, now of Apple Computers),
-Christina Thiele (Carleton University),
-and Daniel M.~Zirin (California Institute of Technology)
-\endgroup
-have written various types of lecture notes that have been most helpful.
-
-\vfill \eject
-\section{Contents}
-
-\line{Introduction \dotfill{} i}
-\line{Contents \dotfill{} iii}
-\line{1.~Getting Started \dotfill{} 1}
-\line{\qquad{}1.1 What \TeX{} is and what \TeX{} isn't \dotfill{} 1}
-\line{\qquad{}1.2 From \TeX{} file to readable output,
- the big set up \dotfill{} 2}
-\line{\qquad{}1.3 Let's do it! \dotfill{} 4}
-\line{\qquad{}1.4 \TeX{} has everything under control \dotfill{} 7}
-\line{\qquad{}1.5 What \TeX{} won't do \dotfill{} 8}
-\line{2.~All characters great and small \dotfill{} 9}
-\line{\qquad{}2.1 Some characters are more special than others \dotfill{} 9}
-\line{\qquad{}2.2 Typesetting with an accent \dotfill{} 10}
-\line{\qquad{}2.3 Dots, dashes, quotes,
- $\textfont0=\tenbf \mathinner {\ldotp \ldotp \ldotp }$ \dotfill{} 13}
-\line{\qquad{}2.4 Different fonts \dotfill{} 15}
-\line{3.~The shape of things to come \dotfill{} 19}
-\line{\qquad{}3.1 Units, units, units \dotfill{} 19}
-\line{\qquad{}3.2 Page shape \dotfill{} 20}
-\line{\qquad{}3.3 Paragraph shape \dotfill{} 22}
-\line{\qquad{}3.4 Line shape \dotfill{} 26}
-\line{\qquad{}3.5 Footnotes \dotfill{} 27}
-\line{\qquad{}3.6 Headlines and footlines \dotfill{} 28}
-\line{\qquad{}3.7 Overfull and underfull boxes \dotfill{} 29}
-\line{4.~$\Bigl\{$Groups, $\bigl\{$Groups, $\{$and More%
- \setbox0=\hbox{$\biggl\{$} \vrule height \ht0 depth \dp0 width 0pt
- Groups$\}\bigr\}\Bigr\}$ \dotfill{} 31}
-\line{5.~No math anxiety here! \dotfill{} 33}
-\line{\qquad{}5.1 Lots of new symbols \dotfill{} 33}
-\line{\qquad{}5.2 Fractions \dotfill{} 37}
-\line{\qquad{}5.3 Subscripts and superscripts \dotfill{} 38}
-\line{\qquad{}5.4 Roots, square and otherwise \dotfill{} 39}
-\line{\qquad{}5.5 Lines, above and below \dotfill{} 39}
-\line{\qquad{}5.6 Delimiters large and small \dotfill{} 40}
-\line{\qquad{}5.7 Those special functions \dotfill{} 41}
-\line{\qquad{}5.8 Hear ye, hear ye! \dotfill{} 42}
-\line{\qquad{}5.9 Matrices \dotfill{} 43}
-\line{\qquad{}5.10 Displayed equations \dotfill{} 45}
-\line{6.~All in a row \dotfill{} 48}
-\line{\qquad{}6.1 Picking up the tab \dotfill{} 48}
-\line{\qquad{}6.2 Horizontal alignment with more sophisticated patterns
- \dotfill{} 51}
-\line{7.~Rolling your own \dotfill{} 55}
-\line{\qquad{}7.1 The long and short of it \dotfill{} 55}
-\line{\qquad{}7.2 Filling in with parameters \dotfill{} 57}
-\line{\qquad{}7.3 By any other name \dotfill{} 60}
-\line{8.~To err is human \dotfill{} 62}
-\line{\qquad{}8.1 The forgotten bye \dotfill{} 62}
-\line{\qquad{}8.2 The misspelled or unknown control sequence \dotfill{} 62}
-\line{\qquad{}8.3 The misnamed font \dotfill{} 64}
-\line{\qquad{}8.4 Mismatched mathematics \dotfill{} 64}
-\line{\qquad{}8.5 Mismatched braces \dotfill{} 65}
-\line{9.~Digging a little deeper \dotfill{} 68}
-\line{\qquad{}9.1 Big files, little files \dotfill{} 68}
-\line{\qquad{}9.2 Larger macro packages \dotfill{} 69}
-\line{\qquad{}9.3 Horizontal and vertical lines \dotfill{} 70}
-\line{\qquad{}9.4 Boxes within boxes \dotfill{} 72}
-\line{10.~Control word list \dotfill{} 77}
-\ifwritinganswers
- \line{11.~I get by with a little help\dotfill{} 80}
-\fi
-
-
-
-\section{Getting Started}
-
-\subsection{What \TeX{} is and what \TeX{} isn't}
-
-First of all, let's see what steps are necessary to produce a
-document using \TeX\null. The first step is to type the file
-that \TeX{} reads. This is usually called the \TeX{} file or the
-input file, and it can be created using a simple text editor (in
-fact, if you're using a fancy word processor, you have to be sure
-that your file is saved in ASCII or nondocument mode without any
-special control characters). The \TeX{} program then reads your
-input file and produces what is called a DVI file (DVI stands for
-DeVice Independent). This file is not readable, at least not by
-humans. The DVI file is then read by another program (called a
-device driver) that produces the output that is readable by
-humans\TeXref{23}. Why the extra file? The same DVI file can be
-read by different device drivers to produce output on a dot
-matrix printer, a laser printer, a screen viewer, or a
-phototypesetter. Once you have produced a DVI file that gives
-the right output on, say, a screen viewer, you can be assured
-that you will get exactly the same output on a laser printer
-without running the \TeX{} program again.
-
-The process may be thought of as proceeding in the following way:
-$$
-{\hbox{edit text\quad} \atop \longrightarrow}
-\lower .6cm \makebox{1.5cm}{1.8cm}%
-{\vbox{\hbox{\TeX{}}
- \hbox{input}
- \hbox{file}
- }%
-}%
-{\hbox{\quad \TeX{} program\quad} \atop \longrightarrow}
-\lower .6cm \makebox{1.5cm}{1.8cm}%
-{\vbox{\hbox{DVI}
- \hbox{file}}
-}%
-{\hbox{\quad device driver\quad} \atop \longrightarrow}
-\lower .6cm \makebox{1.5cm}{1.8cm}%
-{\vbox{\hbox{readable}
- \hbox{output}}
-}%
-$$
-
-This means that we don't see our output in its final form when it
-is being typed at the terminal. But in this case a little
-patience is amply rewarded, for a large number of symbols not
-available in most word processing programs become available. In
-addition, the typesetting is done with more precision, and the
-input files are easily sent between different computers by
-electronic mail or on a magnetic medium.
-
-Our focus will be on the first step, that is, creating the \TeX{}
-input file and then running the \TeX{} program to produce
-appropriate results. There are two ways of running the \TeX{}
-program; it can be run in batch mode or interactively. In
-batch mode you submit your \TeX{} input file to your computer;
-it then runs the \TeX{} program without further intervention and
-gives you the result when it is finished. In interactive mode
-the program can stop and get further input from the user, that
-is, the user can interact with the program. Using \TeX{}
-interactively allows some errors to be corrected by the user,
-while the \TeX{} program makes the corrections in batch mode as
-best it can. Interactive is the preferred mode, of course. All
-personal computer and many mainframe implementations are
-interactive. On some mainframes, however, the only practical
-method of running \TeX{} is in batch mode.
-
-
-\subsection{From \TeX{} file to readable output, the big set up}
-\vskip\baselineskip
-
-{\parskip = 0pt \noindent
-[Note from MD:
-{\sl This is the only system dependent section in the manual and
-may be replaced by a local guide. No reference is made to it
-outside of the section itself. The following local information
-should be included:
-\item{$\bullet$} What initial steps, if any, should be taken by the reader
-to permit the running of \TeX{} and your local device driver(s).
-\item{$\bullet$} How to run \TeX\null.
-\item{$\bullet$} How to read the log file.
-\item{$\bullet$} How to preview and/or print the dvi file.
-
-The following sample is applicable here at the University of
-Manitoba. We use a locally written editor (MANTES) on an
-Amdahl running MVS; I'm fairly certain that it's the worst possible case.}]
-}
-
-
-In this section we'll see how to run \TeX{} at the University of
-Manitoba. It is assumed that the reader is familiar with MANTES
-and can create text files using it.
-
-First, there are several things that must be done {\bf one time
-only}. To start you must do the following (you type in the
-material that looks like typewriter type):
-\item{(1)} allocate the files that \TeX{} will use by typing the
-following lines (while in MANTES):
-\itemitem{} C: {\tt alloc da=source.tex format=vb,256,6144}
-\itemitem{} C: {\tt alloc da=dvi format=fb,1024,6144}
-
-\item{(2)} Create a file called RUNTEX in your MANTES aggregate
-containing the following JCL:
-
-\beginuser
-// JOB ,'RUN TEX'
-// EXEC TEXC
-//SRC DD DSN=<userid>.SOURCE.TEX,DISP=SHR
-//DVI DD DSN=<userid>.DVI,DISP=OLD
-\enduser
-
-
-The name {\tt <userid>} is replaced by your own user id, of
-course. The use of upper case and the spaces must be followed
-exactly.
-
-\item{(3)} Create a file called PRINTTEX in your MANTES aggregate
-containing the following JCL:
-
-\beginuser
-// JOB ,'PRINT TEX'
-// EXEC TEXP
-//DVIFILE DD DSN=<userid>.DVI,DISP=SHR
-\enduser
-
-
-Once you have completed these three steps, you are ready to run a
-\TeX{} job. The files you have created will allow you to produce
-about ten pages of ordinary text.
-
-Here are the steps you use {\bf each time you run a job}.
-
-\item{(1)} create a MANTES file containing your \TeX{} input.
-\item{(2)} save and submit your file using the commands
-\itemitem{} C: {\tt save f/l to da=source.tex noseq}
-\itemitem{} C: {\tt submit runtex}
-\item{(3)} when you get a message saying that your job is finished,
-enter the command
-\itemitem{} C: {\tt out <jobname>; list ttyout}
-
-In this command, {\tt <jobname>} is replaced by your user id with
-a dollar sign appended. This file listing will tell you of any
-errors that might have occurred. It is an abbreviated version of
-what is called the ``log file''; we will use the term ``log
-file'' to refer to the ttyout file produced by \TeX\null.
-
-If you want, you can check on the status of your job while it is
-executing by using the command
-\itemitem{} C: {\tt q <jobname>}
-
-When you are finished looking at the log file, the command {\tt
-end scratch} will throw away the log file while the command {\tt
-end release} will send the log file to the printer, and it can
-then be picked up with your \TeX{} output.
-
-\item{(4)} when your output from RUNTEX program is error free, \TeX{}
-will have created a legal DVI file. To print it, use the
-command
-\itemitem{} C: {\tt submit printtex nohold}
-
-As in (3), you can check on the status of your job while it is
-executing.
-\item{(5)} Pick up your output at the I/O window, sixth floor
-Engineering building. It usually takes about twenty minutes for the
-output to be ready. Ask for it by ``{\tt <jobname>}''.
-
-The files created are large enough for running \TeX{} jobs of about
-10 pages. A job of that size will take about one second of CPU time
-to run through \TeX\null. It will take about 15 seconds of CPU time to
-print 10 pages on the Xerox 8600 using the current device driver.
-
-You can print your own copy of this manual using the command
-{\tt \%docu tex}. You can also find lots of other useful
-online information about \TeX{} by using {\tt \%texinfo}.
-
-\subsection{Let's do it!}
-
-So, from our viewpoint, the name of the game is to create the \TeX{}
-file that produces the right readable output. What does
-a \TeX{} file look like? It consists of characters from an
-ordinary terminal, that is, upper and lower case letters,
-numbers, and the usual punctuation and accent characters (these
-are the usual ASCII characters). Text, for the most part, is just
-typed normally. Special instructions usually start with one of a
-few special symbols such as {\tt \#} or {\tt \&} (these will be
-described in more detail later). Here is an example of a \TeX{}
-input file:
-
-\beginuser
-Here is my first \\TeX\\ sentence.
-\\bye
-\enduser
-\toindex{TeX{} } \toindex{ }
-
-
-First note that the characters in this example look like
-typewriter type. We use these characters with all examples that
-are meant to be typed from the computer terminal. Second, note
-that the backslash appears three times in the text. We'll soon
-see that this is one of the special symbols mentioned
-previously, and it is used very frequently when making \TeX{}
-documents. Make a file containing this example. Use the \TeX{}
-program to make a DVI file and a device driver to see what you
-have produced. If all goes well, you'll have a single page with
-the following single sentence:
-
-Here is my first \TeX\ sentence.
-
- There will also be a page number at the bottom of the page. If
-you've gotten this far, congratulations! Once you can produce one
-\TeX{} document, it's just a matter of time before you can do
-more complicated ones. Now let's compare what we typed in with
-what we got out. The straightforward words were just typed in
-normally, and \TeX{} set them in ordinary type. But the word ``\TeX'',
-which can't be typed in on a terminal because the letters
-aren't on the same line, is entered by using a word starting with
-a backslash, and \TeX{} made the proper interpretation. Most
-symbols that are not ordinary letters, numbers, or punctuation
-are typeset by entering a word starting with a backslash. If we
-look a little closer, we'll note that the word ``first'' is also
-changed.
-\TeXref{4}
-The first two letters have been joined together and there isn't
-a separate dot over the letter ``i''. This is standard
-typesetting practice: certain letter combinations are joined up
-to form what are called {\sl ligatures}. There is actually a good
-\aesthetic{} reason for this. Compare the first two letters of
-``first'' and ``{f}irst'' to see the difference. We note that
-{\tt \\bye} appears in the input file with no corresponding word
-in the final copy.
-\toindex{bye}
-This a typesetting instruction that tells \TeX{} that the input
-is finished. We'll learn about lots of different typesetting
-instructions as we go along.
-
-Let's look at the log file that was created when we ran \TeX
-\null. It may vary slightly at your site, but should look
-something like this:
-\beginuser
- 1.
- 2. This is TeX, MVS Version 2.9 (no format preloaded)
- 3. ** File PLAIN.FMT <-- DD=FMTLIB MEM=PLAIN
- 4.
- 5. ** File SRC.TEX <-- DD=SRC
- 6. (src.tex [1]
- 7. Output written on DVI (1 page, 256 bytes).
- 8. Transcript written on TEXLOG.
-\enduser
-
-
-This is the file that will contain any error messages. On line 6,
-{\tt (src.tex\ } indicated that \TeX{} has started reading that
-file. The appearance of {\tt [1]} indicates that page 1 has been
-processed. If there were errors on page 1, they would be listed
-at that point.
-
-\vskip .5cm
-\exercise Add a second sentence to your original \TeX{} file to get:
-\beginuser
-Here is my first \\TeX\\ sentence.
-I was the one who typeset it!
-\\bye
-\enduser
-
-Use \TeX{} and look at your output. Is the second sentence on a
-new line?
-
-
-\exercise Now add this line to the beginning of your file:
-\beginuser
-\\nopagenumbers
-\enduser
-\noindent
-Guess what will happen when you run the new file through
-\TeX\null. Now try it and see what happens.
-\toindex{nopagenumbers}
-
-\exercise Add three or four more sentences to your file.
-Use letters, numbers, periods, commas, question marks,
-and exclamation points, but don't use any other symbols.
-
-
-\exercise Leave a blank line and add some more sentences.
-You can now get new paragraphs.
-\medskip
-
-We have now seen a major principle concerning the preparation of
-\TeX{} input files. The placement of the text on your computer
-terminal does not necessarily correspond to the placement of the
-text on your output. You can not, for example, add space between
-words in your output by adding spaces in your input file. Several
-consecutive spaces and one space will produce exactly the same
-output. As would be expected, a word at the end of one line will
-be separated from the first word of the following line. In fact,
-sometimes when working on a file that will be heavily edited, it
-is convenient to start each sentence on a separate line. Spaces
-at the beginning of a line, however, are always ignored.
-
-\exercise Add the following sentence as a new paragraph, and then
-typeset it:
-\beginuser
-Congratulations! You received a grade of 100\% on your latest
-examination.
-\enduser
-\noindent
-The {\tt\%} sign is used for comments in your input file.
-Everything on a line following this symbol is ignored. Notice
-that even the space that normally separates the last word on one
-line from the first word on the next line is lost. Now put a
-backslash in front of the {\tt\%} sign to correct the
-sentence. \toindex{\$} \toindex{\%}
-
-\exercise Add the following sentence as a new paragraph:
-\beginuser
-You owe me \$10.00 and it's about time you sent it to me!
-\enduser
-\noindent
-This will produce an error in your log file (if your
-implementation of \TeX{} is interactive, that is, sends you
-messages and waits for answers, just hit the carriage return or
-enter key when you get the error message). You will get output,
-but not what you might expect. Look at the log file and see
-where the error messages are listed. Don't worry about the
-actual messages. We'll have a lot more to say about errors
-(including this one) later. Now fix the error by putting a
-backslash in front of the {\tt \$} sign, and typeset the result
-(there are a small number of characters like the per cent and
-dollar signs that \TeX{} uses for its own purposes. A table of
-these characters will be provided shortly).
-
-\subsection{\TeX{} has everything under control}
-
-We have seen that the backslash has a special role. Any word
-starting with a backslash will be given a special interpretation
-when \TeX{} reads it from your input file. Such a word is called
-a {\sl control sequence}. There are, in fact, two types of
-control sequences: a {\sl control word\/} is a backslash followed
-by letters only (for example, {\tt \\TeX}) and a {\sl control
-symbol\/} is a backslash followed by a single nonletter (for
-example, {\tt \\\$})\null. Since a space is a nonletter, a
-backslash followed by a space is a legitimate control symbol.
-\TeXref{7--8}
-When we want to emphasize that a space is present, we will use a
-special symbol {\tt\sp} to indicate the space, as in the control
-symbol {\tt\\\sp}. This convention is used in {\bf The \TeX
-book} as well as in this manual.
-
-When \TeX{} is reading your input file and comes to a backslash
-followed by a letter, it knows that a control word is being
-read. So it continues reading the name of the control word until
-a nonletter is read. So if your file contains
-
-\displaytext{\tt I like \\TeX!}
-
-\noindent
-the control word {\tt \\TeX} is terminated by the exclamation
-point. But this presents a problem if you want to have a space
-after a control word. If you have, for example, the sentence
-
-\displaytext{\tt I like \\TeX and use it all the time.}
-
-\noindent
-in your input file, the control word {\tt\\TeX} is terminated by
-the space (which is, of course, a nonletter). But then you won't
-have a space between the words ``\TeX{}'' and ``and''; inserting
-more spaces won't help, since \TeX{} doesn't distinguish between
-one space and several consecutive spaces. But if you put the
-control symbol {\tt\\\sp} after a control word, you will both
-terminate the control word and insert a space. It's really easy
-to forget to put in something like {\tt\\\sp} after a control
-word. I promise you that you will do it at least once while
-you're learning to use \TeX\null.
-
-\exercise Make an input file that will produce the following
-paragraph:
-
-I like \TeX! Once you get the hang of it, \TeX{} is really easy
-to use. You just have to master the \TeX nical aspects.
-
-Most control words are named so as to give a hint of their uses.
-You can use {\tt \\par} to make a new paragraph, for example,
-instead of putting in a blank line.
-\toindex{par}
-
-\subsection{What \TeX{} won't do}
-
-\TeX{} is very good at setting type, but there are things that \TeX{}
-can't do well. One is making figures. Space can be left
-to insert figures, but there are no graphic procedures built into
-the language (at present). Some implementations allow graphic
-instructions to be inserted using the {\tt \\special} control
-word but these are exceptional and definitely site dependent.
-
-\TeX{} sets type in horizontal straight lines and not in
-straight lines at other angles. In particular, it is generally
-not possible to make insertions in ``landscape mode'', that is,
-with the text rotated so that the baseline is parallel with
-the long edge of the paper, or to include text that has a curve for
-a baseline. Perspective type (gradually increasing or
-decreasing in height) is not handled well by \TeX\null.
-
-We have seen that there is an ``edit, \TeX{}, driver'' cycle that
-is necessary for each different copy of output. This is true
-even when the output device is a terminal. In particular, it's
-not possible to type the input file and see the results on the
-screen immediately without going through the full cycle. Some
-implementations have both text and graphics displays with
-reasonably quick turnaround (a few seconds for a single page); as
-hardware becomes less expensive and processors become faster, we
-may see improvement.
-
-
-
-
-
-
-\section{All characters great and small}
-
-\subsection{Some characters are more special than others}
-
-We saw in the last section that most text is entered at the
-terminal as sentences of ordinary words just as when typing with
-a typewriter. But we also saw that, in particular, the backslash
-could be used for at least two different purposes. It can be
-used for symbols (or combinations of symbols) that don't appear
-on the keyboard such as typing {\tt \\TeX} to get \TeX\null. It
-can also be used to give \TeX{} special instructions such as
-typing {\tt \\bye} to indicate the end of the input file. In
-general, a word starting with a backslash will be interpreted by
-\TeX{} as one requiring special attention. There are several
-hundred words that \TeX{} knows, and you can define more
-yourself, and so the backslash is very important. We'll spend a
-lot of time as we proceed learning some of these words;
-fortunately we'll only need to use a small number of them most of
-the time.
-
-There are ten characters which, like the backslash, are used
-by \TeX{} for special purposes, and we now want to give the
-complete list.
-\TeXref{37--38}What if we want to use a sentence with one of these
-special characters in it? With this in mind we'll ask the following
-questions:
-\item{(1)} What are the different special characters?
-\item{(2)} How do we use a special character if we really want to
-typeset it in our text?
-
-Here is a table of each special character, its purpose, and the
-method of typesetting the special character itself if you need
-it:
-
-
-\maketable [Characters requiring special input]
-\halign{
- \strut \hfil#\hfil & \quad # \hfil & \quad\tt # \hfil\cr
- \bf Character & \bf Purpose & \bf Input for literal output \cr
- \noalign{\hrule} \noalign{\smallskip}
- $\backslash$ & Special symbols and instructions & \$\\backslash\$ \cr
- $\{$ & Open group & \$\\\lb\$ \cr
- $\}$ & Close group & \$\\\rb\$ \cr
- \% & Comments & \\\% \cr
- \& & Tabs and table alignments & \\\& \cr
- \~{} & Unbreakable space & \\\~{}\lb\rb \cr
- \$ & Starting or ending math text & \\\$ \cr
- \^{} & Math superscripts & \\\^{}\lb\rb \cr
- \_{} & Math subscripts & \\\_{}\lb\rb \cr
- \# & Defining replacement symbols & \\\# \cr
- }
-
-\toindex{\lb}
-\toindex{\rb}
-\toindex{\%}
-\toindex{\&}
-\toindex{\~{}}
-\toindex{\$}
-\toindex{\^{}}
-\toindex{\_{}}
-\toindex{\#}
-
-\subsection{Typesetting with an accent}
-
-Now we're going to start using some of \TeX{}'s goodies! So far
-we've just been using \TeX{} to make our output look attractive,
-but now we'll start to do things that are difficult or impossible
-on the typewriter. In particular, we're going to look at accents
-now. How do you produce an accent when the symbol doesn't appear on
-the keyboard? Just as with the symbol \TeX{}, it is necessary to
-enter a word starting with a backslash. For the word ``premi\`ere'',
-as a first example, you need to type in {\tt premi\\`ere}
-(you may have to hunt around to find the ``back prime''
-or ``grave'' symbol {\tt `} on your keyboard, but it's there
-somewhere\fnote{If you have a very old or obscure
-keyboard and the back prime is {\it really\/} not there, you can
-use {\tt \\lq\lb\rb} instead. Similarly {\tt \\rq\lb\rb} can be
-used for the symbol {\tt '}. You can think of the symbols as
-being abbreviations for ``left quote'' and ``right quote.'' In
-addition, {\tt \\lq\\lq\lb\rb} and {\tt \\rq\\rq\lb\rb} give the
-usual quotation marks. But this won't work as a method to produce
-an accent over the following letter, so you're really better off
-with a proper keyboard.}). In general, to put an accent
-on a letter, the appropriate control sequence precedes the letter.
-
-Here are some examples:
-$$\vbox{
-
-\halign{
-\strut \hfil\tt # & \quad # \hfil\cr
-\bf \TeX{} input & \bf \TeX{} output \cr
-\noalign{\hrule} \noalign{\smallskip}
-\\`a la mode & \`a la mode \cr
-r\\'esum\\'e & r\'esum\'e \cr
-soup\\c{\sp}con & soup\c con \cr
-No\\"el & No\"el \cr
-na\\"\\i{\sp}ve & na\"\i ve \cr
-}
-}$$
-
-
-We see several principles illustrated by these examples. Most
-accents are produced by using a control symbol with a similar
-shape. A few of them are produced by control words containing a
-single letter. Some care must be used in this case, for a space
-must be used to terminate the control word. If you have {\tt
-soup\\ccon} in your file, for example, \TeX{} will look for the
-control word {\tt\\ccon}\fnote{We'll see that there is another
-method when we look at the grouping concept in Section~4.}.
-\TeXref{52--53}
-
-Notice that there is a control word {\tt\\i} also. This produces
-the letter ``i'' without the dot over it; this allows an accent
-to be put over the lower part of the letter. There is an
-analogous control word {\tt\\j} that produces a dotless ``j''
-for accenting purposes.
-
-\maketable [Accents that may be immediately followed by a letter]
-\halign{
- \strut \hfil # \hfil & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Name & \bf \TeX{} input & \bf \TeX{} output \cr
- \noalign{\hrule} \noalign{\smallskip}
- grave & \\`o & \`o \cr
- acute & \\'o & \'o \cr
- circumflex & \\\^{}o & \^o \cr
- umlaut/dieresis/tr\'emat & \\"{}o & \"o \cr
- tilde & \\\~{}o & \~o \cr
- macron & \\={}o & \=o \cr
- dot & \\\char'056{}o & \.o \cr
- }
-
-\toindex{`}
-\toindex{'}
-\toindex{\^{}}
-\toindex{"}
-\toindex{i}
-\toindex{j}
-\toindex{=}
-\toindex{.}
-
-\maketable [Accents requiring an intervening space]
-\halign{
- \strut \hfil # \hfil & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Name & \bf \TeX{} input & \bf \TeX{} output \cr
- \noalign{\hrule} \noalign{\smallskip}
- cedilla & \\c o & \c{o} \cr
- underdot & \\d o & \d{o} \cr
- underbar & \\b o & \b{o} \cr
- h\'a\v{c}ek & \\v o & \v{o} \cr
- breve & \\u o & \u{o} \cr
- tie & \\t oo & \t oo \cr
- Hungarian umlaut& \\H o & \H{o} \cr
- }
-
-\toindex{c}
-\toindex{d}
-\toindex{b}
-\toindex{v}
-\toindex{u}
-\toindex{t}
-\toindex{H}
-
-\TeX{} also allows some letters from languages other than English to
-be typeset.
-
-\maketable [A\kern-1pt vailable foreign language symbols]
-\halign{
- \strut \hfil # \hfil & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Example& \bf \TeX{} input & \bf \TeX{} output \cr
- \noalign{\hrule} \noalign{\smallskip}
- \AE gean, \ae sthetics & \\AE, \\ae & \AE, \ae \cr
- \OE uvres, hors d'\oe uvre & \\OE \\oe & \OE, \oe \cr
- \AA ngstrom & \\AA, \\aa & \AA, \aa \cr
- \O re, K\o benhavn & \\O, \\o & \O, \o \cr
- \L odz, \l\'odka & \\L, \\l & \L, \l \cr
- Nu\ss & \\ss & \ss \cr
- ?`Si? & {?}{`} & ?` \cr
- !`Si! & {!}{`} & !` \cr
- Se\~nor & \\\~{} & \~{} \cr
- & \lb\\it\\\$\rb & {\it\$} \cr
- }
-
-\toindex{AE}
-\toindex{ae}
-\toindex{OE}
-\toindex{oe}
-\toindex{AA}
-\toindex{aa}
-\toindex{O}
-\toindex{o}
-\toindex{L}
-\toindex{l}
-\toindex{ss}
-
-Typeset the sentence in each of the following exercises:
-
-\exercise Does \AE schylus understand \OE dipus?
-
-\exercise The smallest internal unit of \TeX{} is about 53.63\AA.
-
-\exercise They took some honey and plenty of money wrapped up in a
-{\it \$}5 note.
-
-\exercise \'El\`eves, refusez vos le\c cons! Jetez vos cha\^\i nes!
-
-\exercise Za\v sto tako polako pijete \v caj?
-
-\exercise Mein Tee ist hei\ss.
-
-\exercise Peut-\^etre qu'il pr\'ef\`ere le caf\'e glac\'e.
-
-\exercise ?`Por qu\'e no bebes vino blanco? !`Porque est\'a avinagrado!
-
-\exercise M\'\i\'\j n idee\"en worden niet be\"\i nvloed.
-
-\exercise Can you take a ferry from \"Oland to \AA land?
-
-\exercise T\"urk\c ce konu\c san ye\u genler nasillar?
-
-
-\def\bdots{$\textfont0=\tenbf \ldots$} %%% boldface version of \ldots
-
-\subsection{Dots, dashes, quotes, \bdots}
-
-Typing has always been a compromise: the small number of keys
-(compared to the number of typeset symbols available) has forced
-some changes on the typist. When preparing material using \TeX{},
-there is no need to be so restricted. In this section we'll look
-at some differences between typing and using \TeX\null.
-
-There are four types of dashes that are used. The hyphen is used
-for combining words into one unit as with mother-in-law.
-\TeXref{3--5}
-The en-dash is used to indicate a sequence of page numbers, years
-or such things. The em-dash is a grammatical symbol. The minus
-sign is used for negative numbers. Here they are with their uses:
-
-\maketable [Different types of dashes]
-\halign{
- \strut \hfil # \hfil & \quad \hfil \tt # \hfil & \hfil \quad # \hfil
- & \hfil # \hfil\cr
- \bf Name& \bf \TeX{} input & \bf \TeX{} output & \bf Example\cr
- \noalign{\hrule} \noalign{\smallskip}
- hyphen & - & - & The space is 3-dimensional. \cr
- en-dash & {-}{-} & -- & Read pages 3--4. \cr
- em-dash & {-}{-}{-} & --- & I saw them---there were 3 men alive. \cr
- minus sign & \$-\$ & $-$ & The temperature dropped to $-$3 degrees. \cr
- }
-
-\exercise I entered the room and---horrors---I saw both my
-father-in-law and my mother-in-law.
-
-\exercise The winter of 1484--1485 was one of discontent.
-\bigskip
-
-
-Another difference between typing and using \TeX{} is the use of
-quotation marks. Opening and closing quotation marks are the
-same on a typewriter. They are produced in \TeX{} by using the
-apostrophe or prime key {\tt '} and backprime key {\tt `}\null.
-An open quote is produced by {\tt ``} and the
-close quote by {\tt ''}\null.\TeXref{3} Similarly the
-opening single quote is produced by {\tt `} and the closing
-single quote by {\tt '}\null. Notice that there is no need
-to use the usual typing quotation mark (it normally gives a close
-quote, but don't count on it).
-
-\exercise His ``thoughtfulness'' was impressive.
-
-\exercise Frank wondered, ``Is this a girl that can't say `No!'?''
-\bigskip
-
-Sometimes ellipses (three dots) are used to indicate a passage
-of time or missing material. Typing three periods will give
-three dots very close together. The dots with proper spacing will
-be produced by having {\tt \\dots} in your input file.
-\TeXref{173}
-\toindex{dots}
-
-\exercise He thought, ``\dots and this goes on forever, perhaps to the
-last recorded syllable.''
-
-Another problem with dots is that the period after an
-abbreviation normally has less space after it than does the
-period at the end of a sentence. There are two ways to solve this
-problem: the dot can be followed by either {\tt\\\sp} or {\tt\~{}}
-to change the spacing.
-\TeXref{91--92}
-The second alternative will give an unbreakable space; when such
-a space is between two words, these words must typeset on the
-same line. The input {\tt Prof.\~{}Knuth} would cause those two
-words to be typeset on one line. This is desirable for names
-like Vancouver, B.~C. and Mr.~Jones so that ``Mr.'' and ``Jones''
-do not end up on separate lines. Notice that no backslash is used
-with the unbreakable space.
-
-\exercise Have you seen Ms.~Jones?
-
-\exercise Prof.~Smith and Dr.~Gold flew from
-\ifcanspell
-Halifax N.~S. to Montr\'eal, P.~Q. via Moncton, N.~B.
-\else
-L.~A. to Washington, D.~C., via Fargo, N.~D.
-\fi
-
-
-\subsection{Different fonts}
-
-The most obvious difference between typewritten text and \TeX{}
-output is undoubtedly the different fonts or types of symbols
-used. When \TeX{} starts up it has sixteen fonts available. Some
-of these are used for technical purposes, but even so there are
-several different typefaces available as can be seen in the
-following table. A complete list of the sixteen fonts is given in
-Appendix F of {\bf The \TeX{}book}.
-\TeXref{427--432}
-Most of them are used automatically; a mathematical subscript,
-for example, is put in smaller type by \TeX{} with no special
-user intervention.
-
-To change from the usual (roman) typeface to italic, the control
-word {\tt \\it} is used. To change back to the usual roman
-typeface, use {\tt \\rm}. For example, you could have the
-following sentence: {\tt I started with roman type, \\it switched
-to italic type, \\rm and returned to roman type}. This would give
-the following: I started with roman type, \it switched to italic
-type,\fnote{Notice that the comma and this footnote are in
-italic type, and this looks a little funny. We'll see that there
-is another method for changing fonts when we talk about grouping
-in Section 4.}
-\rm and returned to roman type.
-
-Typefaces other than italic are also available. Those given below
-are the ones most commonly used. They are available immediately
-when \TeX{} starts. A little later we'll see how to use other
-typefaces that aren't available when \TeX{} starts.
-
-\global\advance\footnotenum by 1
-\maketable [Font Samples]
-\halign{
- \strut \hfil # \hfil & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Font name & \bf \TeX{} switch sequence & \bf Sample of typeface \cr
- \noalign{\hrule} \noalign{\smallskip}
- Roman & \\rm & \rm This is roman type. \cr
- Boldface & \\bf & \bf This is boldface type. \cr
- Italic & \\it & \it This is italic type. \cr
- Slanted & \\sl & \sl This is slanted type. \cr
- Typewriter & \\tt & \tt This is typewriter type. \cr
- Math symbol${}^\the\footnotenum$ & \\cal & $\cal SOME\hbox{\quad}SCRIPT
- \hbox{\quad}LETTERS$\rm. \cr
- }
-
-\footnote{}{\llap{$^\the\footnotenum$}%
-This example is cheating since you need to know a little about
-mathematics input to use it, but I wanted to include it anyway.
-You'll be able to use these letters after you study the use of
-mathematical symbols.}
-\nobreak
-\toindex{it}
-\toindex{rm}
-\toindex{bf}
-\toindex{sl}
-\toindex{tt}
-
-The slanted and italic fonts seem quite similar at first. It is
-easy to see the difference between the letter ``a'' in each
-sample. When changing from a slanted or italic font to a roman
-font, the last letter in the first font will lean towards the
-first letter of the roman font; this looks cramped, and to
-compensate there is a little extra space that can be added called
-the {\sl italic correction}. This is done using the control
-symbol {\tt \\/}.
-\toindex{/}
-In the following sentence, there is no italic correction after
-the first sequence of italic letters but there is after the
-second sequence; see the difference: {\it If} the italic
-correction is not used the letters are too close together, but
-{\it if\/} the correction is used, the spacing is better. There
-is no need for the italic correction when the italic characters
-are followed by a comma or a period, but your text will
-definitely look better if you use it before quotation marks or
-parentheses.
-
-
-It is possible to use fonts other than those initially defined in
-\TeX{} when desired (assuming that they are available on
-your computer system, of course). Different sizes can be used
-with the aid of the control word {\tt \\magstep}. To define your
-new font you will have to know its name on your computer system.
-For example, the roman typeface is called ``cmr10'' on most
-systems. If you use {\tt \\font\\bigrm = cmr10 scaled \\magstep
-1}, you can then use {\tt\\bigrm} in exactly the same way as you
-use {\tt\\it} or {\tt\\rm}.
-\TeXref{13--17}
-\toindex{magstep}
-\toindex{font}
-\toindex{scaled}
-
-Switching via {\tt\\bigrm} will give roman type that is larger
-than the usual by 20\%\null. {\tt \\font\\bigbigrm = cmr10
-scaled \\magstep 2} will define a font that is about 44\% larger
-than the usual roman typeface. The sizes {\tt \\magstep~0} to
-{\tt \\magstep~5} are available. On most computers {\tt \\magstephalf}
-is also available; this represents an enlargement of
-about 9.5\%\null. Here are some samples at various sizes:
-
-\maketable [Different Font Magnifications]
-\halign{
- \strut \tt # \hfil & \quad # \hfil \cr
- \bf Magnification & \bf Sample \cr
- \noalign{\hrule} \noalign{\smallskip}
- \\magstep 0 & \rm Sample text at magstep 0. \cr
- \\magstephalf & \halfrm Sample text at magstephalf. \cr
- \\magstep 1 & \brm Sample text at magstep 1. \cr
- \\magstep 2 & \bbrm Sample text at magstep 2. \cr
- \\magstep 3 & \bbbrm Sample text at magstep 3. \cr
- \\magstep 4 & \bbbbrm Sample text at magstep 4. \cr
- \\magstep 5 & \bbbbbrm Sample text at magstep 5. \cr
- }
-\bigskip
-
-It's also possible to use completely new typefaces. These
-are dependent on system availability, of course. Many systems
-have a file called CMSS10 which is a font that contains sans
-serif letters. Using {\tt \\font\\sf = cmss10} will allow the
-control word {\tt\\sf} to be used in the same manner as {\tt\\bf}.
-Having made this definition, the input
-\displaytext{\tt \\sf Here is a sample of our new Sans Serif font.}
-will produce
-\displaytext{\sf Here is a sample of our new Sans Serif font.}
-
-\exercise What problem might have arisen if we had used {\tt \\ss}
-instead of {\tt \\sf} to turn on the Sans Serif font? Hint: if
-the answer doesn't occur to you at first, think about the German
-alphabet and it will finally come to you.
-
-\exercise Typeset a paragraph of magnified sans serif text.
-
-The extra fonts available may vary from site to site. The ones
-in the following table are available at most places.
-
-\maketable [External Fonts Names]
-\halign{
-\strut \tt # \hfil & \quad \tt # \hfil & \quad \tt # \hfil
- & \quad \tt # \hfil & \quad \tt # \hfil
- & \quad \tt # \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-CMBSY10 &CMBXSL10 &CMBXTI10 &CMBX10 &CMBX12 &CMBX5 \cr
-CMBX6 &CMBX7 &CMBX8 &CMBX9 &CMB10 &CMCSC10 \cr
-CMDUNH10 &CMEX10 &CMFF10 &CMFIB8 &CMFI10 &CMITT10 \cr
-CMMIB10 &CMMI10 &CMMI12 &CMMI5 &CMMI6 &CMMI7 \cr
-CMMI8 &CMMI9 &CMR10 &CMR12 &CMR17 &CMR5 \cr
-CMR6 &CMR7 &CMR8 &CMR9 &CMSLTT10 &CMSL10 \cr
-CMSL12 &CMSL8 &CMSL9 &CMSSBX10 &CMSSDC10 &CMSSI10 \cr
-CMSSI12 &CMSSI17 &CMSSI8 &CMSSI9 &CMSSQI8 &CMSSQ8 \cr
-CMSS10 &CMSS12 &CMSS17 &CMSS8 &CMSS9 &CMSY10 \cr
-CMSY5 &CMSY6 &CMSY7 &CMSY8 &CMSY9 &CMTCSC10 \cr
-CMTEX10 &CMTEX8 &CMTEX9 &CMTI10 &CMTI12 &CMTI7 \cr
-CMTI8 &CMTI9 &CMTT10 &CMTT12 &CMTT8 &CMTT9 \cr
-CMU10 &CMVTT10 \cr
-}
-\bigskip
-
-Here's a little background about these names. The first two
-letters {\tt CM} stands for Computer Modern, the name given to
-this font family by the designer. The number at the end is the
-point size: 10 point type is the normal size, 7 point is the
-normal size for subscripts, and 5 point is the normal size for
-subscripts of subscripts, 12 point is 20\% larger than 10 point,
-etc. If the letters {\tt CM} are followed by {\tt B}, it is a
-boldface type. Similarly {\tt R} indicates roman, {\tt I} is for
-italics, {\tt CSC} is for small caps, {\tt SL} is for slanted,
-{\tt SS} is for sans serif, {\tt SY} is for symbols,
-and {\tt TT} is for typewriter type.
-
-\exercise Find the fonts available on your system, and print out
-all the letters and numbers in several of them.
-
-\exercise The font {\tt CMR12} is 20\% larger than {\tt CMR10}.
-Also {\tt \\magstep~1} magnifies the type by 20\%. Take some
-text and print it using {\tt CMR12} then using {\tt CMR10} scaled
-by {\tt \\magstep~1}. The results are quite different!
-
-
-
-
-\section{The shape of things to come}
-
-In this section we want to see how to make text have different
-shapes or sizes. One may use \TeX{} with the default sizes, of
-course, just as we have been doing so far. We'll now become more
-creative with our output. In discussing the size of various
-parts of a page of text, there are several units of measure we
-can use.
-
-\subsection{Units, units, units}
-
-\TeX{} can measure length using many types of units. The most
-common are the inch, the \centimeter, the point, the pica. The
-abbreviations for these units are {\tt in}, {\tt cm}, {\tt pt},
-and {\tt pc} respectively. The point is defined by the equation 1
-inch = 72.27 points, and the pica by 1 pica = 12 points. Thus a
-point is rather small and is about the size of a decimal point.
-Here is a sample to give an idea of the comparative sizes:
-\def\pip{\vrule height 4 true pt }
-\TeXref{57}
-
-$$ \hbox{1 inch: } \hbox to 1 true in{\pip\hrulefill\pip}$$
-$$ \hbox{1 \centimeter: }\hbox to 1 true cm{\pip\hrulefill\pip}$$
-$$ \hbox{20 points: }\hbox to 20 true pt{\pip\hrulefill\pip}$$
-$$ \hbox{1 pica: } \hbox to 1 true pc{\pip\hrulefill\pip}$$
-
-Thus points are used to make fine changes; a pica is about the
-distance between the baselines of two consecutive lines of
-(unmagnified) normal text. \TeX{} is quite exact about
-dimensions; internally its smallest unit is less than one
-four-millionth of an inch. Hence it is the resolution of the
-output device that will determine the accuracy of the output.
-
-There are two other units that are sometimes useful that have
-different sizes in different fonts. The {\tt ex} is about the
-height of a small ``x'' and the {\tt em} is a little smaller than
-the width of a capital ``M''\null.
-\TeXref{60}
-
-The shape of the output is generally determined by control
-words. There are many such words; these allow very fine control
-of the resulting text. But most of the time only a small number
-of them are necessary.
-
-\subsection{Page shape}
-
-The text on a page consists of three basic parts. There is the
-headline above the main text; this often contains a chapter
-title, section title, or a page number, and may differ on odd and
-even pages. Below this is the main text, which includes any
-footnotes. And finally there is the footline that might contain a
-page number.
-
-In the examples we have seen so far, the headline has been blank.
-The footline has contained either a \centred{} number or, if {\tt
-\\nopagenumbers} had been used, has also been blank. We'll have
-more to say about headlines and footlines later in this section.
-For the moment let's concentrate on the main text.
-
-To finish one page and start a new one, {\tt \\vfill \\eject} can
-be used. The control word {\tt \\eject} forces the completion of
-the current page, while {\tt \\vfill} causes any left over
-vertical space to be gathered at the bottom of the page (you might
-try leaving out the {\tt \\vfill} as an experiment to see how the
-vertical \analog{} of justified horizontal lines of text works).
-\toindex{vfill}
-\toindex{eject}
-
-
-{\hsize=4in
-The current horizontal width of the text on the page is described
-by the control word {\tt \\hsize}. It can be changed, say to 4
-inches, by {\tt \\hsize = 4 in\ } at any desired time using
-methods to be described in the next few sections. The value of
-{\tt \\hsize} in effect when the paragraph is completed
-determines the width of the paragraph. As can be seen in this
-paragraph, the text width can be changed (in this case to 4
-inches) for a single paragraph. Because it represents the
-current value of the horizontal width, expressions such as {\tt
- \\hsize = 0.75\\hsize} can make a new value that is relative
-to the old one. \par}
-\toindex{hsize}
-
-The vertical \analog{} of {\tt \\hsize} is {\tt \\vsize}, which
-is the current height of the main text. It can be reset, just
-like {\tt \\hsize}. Thus, {\tt \\vsize = 8 in\ } can be used to
-change the vertical height of the main text. Note that {\tt \\vsize}
-is the size of the text exclusive of any headline or
-footline material.
-\toindex{vsize}
-
-Text can also be shifted across the page. The upper left corner
-of the text is one inch down and one inch in from the upper left
-corner of the page. The control words {\tt \\hoffset} and {\tt \\voffset}
-are used to shift the text horizontally and
-vertically. Thus {\tt \\hoffset = .75 in} and {\tt \\voffset =
--.5 in} would shift the text an additional .75 inches to the
-right and .5 inches up. Most of the time you'll need to set {\tt
-\\hoffset}, {\tt \\voffset}, and {\tt \\vsize} at the beginning
-of your document only.
-\TeXref{251}
-\toindex{hoffset}
-\toindex{voffset}
-
-\global\advance\footnotenum by 1
-\maketable [Control words for page sizes]
-\halign{
- \strut \hfil # & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Name & \bf \TeX{} Control Word & \bf \TeX{} default value (inches)\cr
- \noalign{\hrule} \noalign{\smallskip}
- horizontal width & \\hsize & 6.5 \cr
- vertical width & \\vsize & 8.9 \cr
- horizontal offset${}^\the\footnotenum$ & \\hoffset & 0 \cr
- vertical offset${}^\the\footnotenum$ & \\voffset & 0 \cr
- }
-
-\footnote{}{\llap{$^\the\footnotenum$}The text is initially 1 inch
-down and 1 inch in from upper left corner of the page.}
-\nobreak
-
-\exercise Enter a paragraph of text that is a few lines long.
-Take several copies of your paragraph and put {\tt \\hsize = 5
-in\ } before one and {\tt \\hsize = 10 cm\ } in front of a second
-one. Try a few other values for {\tt \\hsize}.
-
-\exercise Put {\tt \\hoffset = .5 in\ } and {\tt \\voffset = 1
-in\ } before the first paragraph of your previous exercise.
-
-\exercise Take your previous exercise and put {\tt \\vsize = 2
-in\ } before the first paragraph.
-\bigskip
-
-In the previous section we saw that it is possible to use fonts
-of larger size by using the {\tt \\magstep} control word. It's
-also possible to magnify the entire document at once. If {\tt
-\\magnification = \\magstep 1} appears at the top of your document,
-then all of your output is magnified by 20\%\null. The other
-values of {\tt \\magstep} can be used, too. {\bf It should be
-emphasized that {\tt \\magnification} can only be used before
-even a single character is typeset.} This magnification creates
-a problem in units; if the document is to be magnified by 20\%
-and {\tt \\hsize = 5 in} appears in the \TeX{} input file, should
-the final output have an {\tt \\hsize} of 5 inches or should it
-be magnified by 20\% to 6 inches? Unless told otherwise, all the
-dimensions will be magnified so that, in this case, {\tt \\hsize}
-would be 6 inches in the final output. This means that all the
-dimensions will increase uniformly when {\tt \\magnification} is
-used. But for some special situations it might not be desirable
-for this to happen; for example, you might want to leave a space
-of exactly 3 inches to insert a figure. In this case any unit
-can be modified by {\tt true} so that {\tt \\hsize = 5 true in}
-will always set the line width to 5 inches, regardless of
-magnification. \TeXref{59--60} \toindex{magnification}
-
-\exercise Put {\tt \\magnification = \\magstep 1} as the first
-line in one of your input files and see how the output changes.
-
-\subsection{Paragraph shape}
-
-When \TeX{} is reading the text to be typeset from your input
-file, it reads in a paragraph at a time and then typesets it.
-This means that there is a lot of control over paragraph shapes,
-but also that some care must be taken. We've already seen that
-{\tt \\hsize} can be used to control the width of a single
-paragraph. But suppose the following appeared as part of your
-input file:
-
-\beginuser
-\\hsize = 5 in
-Four score and seven years $\ldots$
-$\vdots$
-$\ldots$ from this earth.
-\\hsize = 6.5 in
-
-\enduser
-
-What is the width of the paragraph? The {\tt \\hsize} was
-changed at the start of the paragraph and again at the end.
-Since the paragraph was not completed (by putting in a blank line
-or {\tt \\par}) until after the second change, the paragraph
-would be typeset with a width of 6.5 inches. However, if a blank
-line were inserted before {\tt \\hsize = 6.5 in}, then the
-paragraph would be typeset with a width of 5 inches. So, in
-general, when a paragraph is set, the values of the parameters
-that are in effect when the paragraph is completed are the ones
-that are used.
-
-Here is a table with some paragraph parameters:
-
-\maketable [Some paragraph shape parameters]
-\halign{
- \strut \hfil # & \quad \hfil \tt # \hfil & \hfil \quad # \hfil\cr
- \bf Function & \bf \TeX{} Control Word & \bf \TeX{} default\cr
- \noalign{\hrule} \noalign{\smallskip}
- width & \\hsize & 6.5 inches \cr
- indentation on first line & \\parindent & 20 points\cr
- distance between lines & \\baselineskip & 12 points\cr
- distance between paragraphs & \\parskip & 0 points \cr
- }
-
-\toindex{parindent}
-\toindex{parskip}
-\toindex{baselineskip}
-
-The control word {\tt \\noindent} may be used at the beginning of
-a paragraph to avoid the automatic indentation on the first line.
-This control word will only affect the paragraph being set when
-it is invoked (of course {\tt \\parindent = 0 pt} will cause no
-indentation for all paragraphs).
-\toindex{noindent}
-
-{\narrower
-A more flexible way to control the width of a paragraph is to use
-{\tt \\rightskip} and {\tt \\leftskip}. Setting {\tt \\leftskip
-= 20 pt} causes the left margin of the paragraph to be moved in
-an extra twenty points. Negative values may be assigned to {\tt
-\\leftskip} to move the left margin out. The control word {\tt
-\\rightskip} does the same to the right side of the paragraph.
-The single control word {\tt \\narrower} is the equivalent of
-setting both {\tt \\leftskip} and {\tt \\rightskip} equal to {\tt
-\\parindent}. This is quite useful for long quotations, and
-this paragraph is an example of its use. As with {\tt \\hsize},
-the value of {\tt \\leftskip} and {\tt \\rightskip} in effect
-when the paragraph is completed is the one which will apply to
-the whole paragraph.
-\TeXref{100}
-
-}
-\toindex{leftskip}
-\toindex{rightskip}
-\toindex{narrower}
-
-\exercise Make two paragraphs with the following specifications:
-the left margin of both paragraphs is indented by 1.5 inches,
-the right margin of the first paragraph is indented by 0.75
-inches, and the right margin of the second paragraph is indented
-by 1.75 inches.
-\bigskip
-
-\def\hangparagraph{ Lines can be made with different lengths
-within one paragraph by using {\tt \\hangindent} and {\tt
-\\hangafter}. The amount of the indentation is determined by value
-of {\tt \\hangindent}. If {\tt \\hangindent} is positive, the
-indentation is made from the left, and if it is negative it is
-made from the right. The lines on which the indentation occurs is
-controlled by {\tt \\hangafter}. If {\tt \\hangafter} is
-positive then it determines the number of lines at full width
-before the indentation starts. Thus if {\tt \\hangindent = 1.75
-in} and {\tt \\hangafter = 6}, then the first six lines will be
-at full width and the rest will be indented by 1.75 inches from
-the left. On the other hand if {\tt \\hangindent = \hbox{-1.75}
-in} and {\tt \\hangafter = -6}, then the first six lines will be
-indented by 1.75 inches from the right and the rest will be at
-full width. \TeX{} resets to the default values {\tt \\hangindent
-= 0 pt} and {\tt \\hangafter = 1} after each paragraph. These
-control words are useful for paragraphs with ``hanging indents''
-and for flowing a paragraph around space reserved for a figure.
-\TeXref{355}The control word {\tt \\hang} at the beginning of the
-paragraph will cause the first line to be of full width ({\tt
-\\hangafter=1}) and the rest of the paragraph to be indented by
-the current value of {\tt \\parindent}. But you do have to use
-{\tt \\noindent} if you want the first line to extend all the way
-to the left margin.
-\TeXref{102}
-\par}
-
-\hangafter=6 \hangindent=1.75in
-\hangparagraph
-\toindex{hangindent}
-\toindex{hangafter}
-\toindex{hang}
-
-Here is the previous paragraph repeated with {\tt \\hangafter = -6}
-and {\tt \\hangindent = -1.75 in}.
-
-\hangafter=-6 \hangindent=-1.75in \hangparagraph
-
-
-The control word {\tt \\parshape} can be used to make paragraphs with
-a greater variety of shapes.
-\TeXref{101}
-\toindex{parshape}
-
-Another useful control word for setting paragraphs is {\tt \\item}.
-It can be used to make various types of itemized lists,
-and is invoked using the pattern {\tt \\item\lb$\ldots$\rb}\null.
-This causes the next paragraph to be formed with every line
-indented by {\tt \\parindent} and, in addition, the first line
-labeled on the left by whatever is between the braces. It is
-usually used with {\tt \\parskip = 0 pt}, since that control word
-determines the vertical space between the different items. The control
-word {\tt \\itemitem} is the same as {\tt \\item} except that the
-indentation is twice as far, that is, twice the value of
-{\tt \\parindent}.
-\TeXref{102}Here is an example:
-\toindex{item}
-\toindex{itemitem}
-
-\beginliteral
-\parskip = 0pt \parindent = 30 pt
-\noindent
-Answer all the following questions:
-\item{(1)} What is question 1?
-\item{(2)} What is question 2?
-\item{(3)} What is question 3?
-\itemitem{(3a)} What is question 3a?
-\itemitem{(3b)} What is question 3b?
-@endliteral
-
-
-\noindent
-will produce
-\vfill\eject
-
-{\parskip = 0pt \parindent = 30 pt
-\noindent
-Answer all the following questions:
-\item{(1)} What is question 1?
-\item{(2)} What is question 2?
-\item{(3)} What is question 3?
-\itemitem{(3a)} What is question 3a?
-\itemitem{(3b)} What is question 3b?
-
-}
-
-\exercise Make a paragraph several lines long and use it with
-the {\tt \\item} control word to see the ``hanging indent.'' Now
-take the same paragraph and use it with different values of {\tt
-\\parindent} and {\tt \\hsize}.
-\bigskip
-
-Now let's see how to put space between paragraphs. The control
-word {\tt \\parskip} is used to determine how much space is
-normally left between paragraphs. So if you put {\tt \\parskip =
-12 pt} at the beginning of your \TeX{} source file, there will be
-12 points between paragraphs unless other instructions are
-given. The control word {\tt \\vskip} can be used to insert extra
-vertical space between paragraphs. If {\tt \\vskip 1 in} or {\tt
-\\vskip 20 pt} appears between two paragraphs, then the extra
-space is inserted.
-
-There are a couple of peculiarities of {\tt \\vskip} that seem
-quite strange at first. If you have {\tt \\vskip 3 in} and the
-skip starts two inches from the bottom of the page, the rest of
-the page is skipped, but the extra one inch is {\it not\/}
-skipped at the top of the next page. In other words, {\tt \\vskip}
-{\bf will not insert space across page boundaries}. In
-fact, {\tt \\vskip~1~in} will have no effect at all if it happens
-to appear at the top of a page! For many types of vertical
-spacing this is quite appropriate. The space before a section
-heading, for example, should not continue across page boundaries.
-
-A similar phenomenon occurs at the beginning of your document.
-If, for example, you want a title page with the title about half
-way down the page, you can not insert the space at the top of the
-page using {\tt \\vskip}.
-
-But what if you really want some blank space at the top of a
-page? You could start the page with {\tt\\\sp} but this in effect
-typesets a one line paragraph containing a blank. So while
-nothing is typeset, the extra space due to the values of {\tt
-\\baselineskip} and {\tt \\parskip} will add extra space. An easier
-method is to use {\tt \\vglue} instead of {\tt \\vskip} to get
-the desired result. Thus {\tt \\vglue 1 in\ }will leave one inch
-of blank space at the top of the page.\TeXref{352}
-\toindex{vglue}
-
-
-We can note in passing that there is another more general method
-to put material at the top of a page using the control words {\tt
-\\topinsert} and {\tt \\endinsert}. If {\tt \\topinsert $\ldots$
-\\endinsert} is used within a page, the material between
-{\tt \\topinsert} and {\tt \\endinsert} will appear at the top
-of the page, if possible. For example:
-
-\vbox{
- \beginuser
- \\topinsert
- \\vskip 1 in
- \\centerline\lb Figure 1\rb
- \\endinsert
- \enduser
-}
-\noindent
-is useful for inserting figures of a prescribed size.
-\TeXref{115}
-\toindex{topinsert}
-\toindex{endinsert}
-
-There are also some special control words for making small
-vertical skips. They are {\tt \\smallskip}, {\tt \\medskip}, and
-{\tt \\bigskip}. Here is the size of each one:
-
-\def\hrl{\hrule width .5 in}
-
-\centerline{{\tt \\smallskip}: \vbox{\hrl \smallskip \hrl} \quad
- {\tt \\medskip}: \vbox{\hrl \medskip \hrl} \quad
- {\tt \\bigskip}: \vbox{\hrl \bigskip \hrl}
- }
-\toindex{smallskip}
-\toindex{medskip}
-\toindex{bigskip}
-
-\subsection{Line shape}
-
-For most material \TeX{} does a good job of breaking up a
-paragraph into lines. But sometimes it's necessary to add
-further instructions. It's possible to force a new line by
-inserting {\tt \\hfill \\break} in your input file. It's also
-possible to put some text on a line by itself using the control
-word {\tt \\line\lb $\ldots$\rb}; then the material between the
-braces will be restricted to one line (although the result will
-be spread out over the whole line and may be horrible). The
-control words {\tt \\leftline\lb $\ldots$\rb}, {\tt \\rightline\lb
-$\ldots$\rb}, and {\tt \\centerline\lb $\ldots$\rb} will,
-respectively, set the material between the braces on a single
-line on the left margin, on the right margin, or \centred. Thus
-\toindex{hfill}
-\toindex{break}
-\toindex{centerline}
-\toindex{leftline}
-\toindex{rightline}
-\toindex{line}
-
-
-\beginliteral
-\leftline{I'm over on the left.}
-\centerline{I'm in the @centre.}
-\rightline{I'm on the right.}
-\line{I just seem to be spread out all over the place.}
-@endliteral
-
-\noindent
-produces the four lines:
-\vskip\baselineskip
-
-
-{
-\hbadness = 10000
-\leftline{I'm over on the left.}
-\centerline{I'm in the \center.}
-\rightline{I'm on the right.}
-\line{I just seem to be spread out all over the place.}
-
-Other types of spacing can be obtained by using the control word {\tt
-\\hfil}. This causes all the extra space in the line to be
-accumulated at the position where {\tt \\hfil} appears.
-Thus if we alter our last example to
-{\tt \\line\lb I just seem to be spread out \\hfil all over the place.\rb}
-we will get \hfil\break
-\medskip
-\line{I just seem to be spread out \hfil all over the place.}
-\medskip
-If we have more than one {\tt \\hfil}, they will divide any extra
-space among themselves equally. Hence
-{\tt \\line\lb left text \\hfil \centre{} text \\hfil right text.\rb}
-will produce
-\medskip
-\line{left text \hfil \centre{} text \hfil right text.}
-\toindex{hfil}
-}
-
-\exercise Typeset the following line:
-
-\line{left end \hfil left tackle \hfil left guard \hfil \centre{} \hfil
-right guard \hfil right tackle \hfil right end}
-
-\exercise Typeset the following line with twice as much space between
-``left'' and ``right-\centre{}'' as between ``right-\centre{}'' and
-``right'':
-
-\line{left \hfil \hfil right-\centre{} \hfil right}
-
-It's possible to move horizontally using {\tt \\hskip} in a
-manner analogous with {\tt \\vskip}.
-\toindex{hskip}
-
-\exercise What happens with the following input:\hfil\break
-{\tt \\line\lb\\hskip 1 in ONE \\hfil TWO \\hfil THREE\rb}
-\bigskip
-
-The right justification can be canceled by using the
-control word {\tt \\raggedright}.
-\toindex{raggedright}
-
-\subsection{Footnotes}
-
-The general pattern to make footnotes using \TeX{} is
-{\tt \\footnote\lb$\ldots$\rb\lb$\ldots$\rb}\null.
-
-The footnote mark goes in between the first set of braces. Some
-available marks are {\tt \\dag (\dag)}, {\tt \\ddag (\ddag)}, {\tt \\S
-(\S)}, and {\tt \\P (\P)}\null. The text of the footnote
-goes between the second set of braces. The use of numbers as
-marks is a little less straightforward. The footnote%
-\footnote{${}^{21}$}{This is the footnote at the bottom of the page.}
-at the bottom of the page was produced by using {\tt \\footnote\lb\$\lb
-\rb\^{}\lb{21}\rb\$\rb\lb This is the footnote at the
-bottom of the page.\rb} after the word ``footnote'' in the
-text. This construction is somewhat complicated; we'll see why
-it's this way when we know a little more about typesetting
-mathematics. But for the moment we can look at it as a way of
-getting the job done. You may want to use {\tt \\rm} within the
-footnote to ensure that the right font appears. Usually you will
-not want a space between the text and the control word {\tt
-footnote}.\TeXref{117}
-\toindex{footnote}
-\toindex{ddag}
-\toindex{S}
-\toindex{P}
-
-\exercise Make up a page with a relatively long footnote spanning
-several lines.
-
-\exercise Make up a page with two different footnotes on it.
-
-\subsection{Headlines and Footlines}
-
-\headline={\hfil \tenrm Page \the\pageno} %example for this section
-
-The lines for title and page numbers that go above and below the
-main text are produced by using {\tt \\headline=\lb$\dots$\rb}
-and {\tt \\footline=\lb$\dots$\rb}\null.
-\TeXref{252--253}
-
-The principle is the same as using the control word {\tt \\line\lb
-$\dots$\rb} within the usual text on the page. A helpful
-control word is {\tt \\pageno} which represents the current page
-number. Thus {\tt \\headline=\lb\\hfil \\tenrm Page \\the\\pageno\rb}
-would cause the page number to appear in the upper
-right corner preceded by the word ``Page'' (now look at the upper
-right corner of this page). It is safer to explicitly name the
-font that you want to use (in this case {\tt \\tenrm} to use the
-10 point roman font), since you are never guaranteed that a
-particular font will be in use when the headline or footline is
-set. The control word {\tt \\the} takes the internal value of the
-next word if it is an appropriate control word and prints it as
-text. You can also use the control word {\tt \\folio} instead of
-{\tt \\the \\pageno}. The difference is that {\tt \\folio} will
-give roman numerals when {\tt \\pageno} is negative.
-\toindex{headline}
-\toindex{footline}
-\toindex{pageno}
-\toindex{the}
-\toindex{folio}
-
-You can also assign values to {\tt \\pageno} if you want your
-document to use a different sequence of page numbers from the
-usual. Roman numerals can be produced by using negative numbers;
-{\tt \\pageno=-1} at the beginning of a document will cause page
-numbers to be in roman numerals.
-\TeXref{252}
-
-Different headlines can be produced for even and odd pages in
-the following manner:
-
-{\tt
-\\headline=\lb\\ifodd \\pageno \lb$\dots$\rb \\else \lb$\dots$\rb
-\\fi\rb}
-
-\noindent
-where the material between the first set of braces is for the
-right-hand pages and the material between the second set of
-braces is for the left-hand pages.
-
-\exercise Change the footline so that the page number is \centred{}
-with an en-dash on either side.
-
-\subsection{Overfull and underfull boxes}
-
-One of the most frustrating experiences for the new \TeX{} user
-is the occurrence of overfull and underfull boxes. They are duly
-noted in the log file and are also written to the screen when \TeX{}
-is being run interactively. Overfull boxes are also marked
-on the output by a slug (a large filled-in black rectangle that
-looks like this: \vrule width \overfullrule) in the right
-margin. Various obscene terms are applied to this slug. It
-appears even though there is nothing wrong with the \TeX{} input.
-So why is the slug there and what can be done about it?
-
-A good way to visualize the way \TeX{} organizes a page is to
-think of the printed material as being put into boxes. There are
-two types of boxes: {\sl hboxes\/} and {\sl vboxes}. Most of the
-time these correspond to the organization of horizontal text
-into lines and vertical paragraphs into pages. In particular, it
-is the spacing of the words in a hbox corresponding to a line of
-text that causes the slug to appear.
-
-Recall that \TeX{} reads in the complete paragraph before
-deciding how to break it up into lines. This is better than
-working a line at a time, since a slight improvement in one line
-might cause catastrophic changes farther down in the paragraph.
-When words are gathered together to form a line, space is added
-between the words to justify the right margin. Very large spaces
-between words is obviously undesirable; the badness of the line
-is a measure of how badly the words are spaced. An underfull
-hbox means that there is too much space between words. More
-specifically, the badness of any line is a number between 0
-(perfect) and 10000 (horrible). There is a parameter called {\tt
-\\hbadness} whose default value is 1000\null. Any line whose
-badness is greater than {\tt \\hbadness} is reported as an
-underfull hbox. If the value of {\tt \\hbadness} is increased,
-then fewer underfull hboxes will be reported. In fact {\tt
-\\hbadness = 10000} will suppress the reporting of underfull
-hboxes altogether. Similarly, if the words must be squeezed into
-a line so that the spaces are very small or even so the words
-extend a little into the right margin, then an overfull hbox
-results. \toindex{hbadness}
-
-%%%%%%%%%%%%%% restore original headline %%%%%%%%%%%%%%%%%%%%%%%%
-\headline={\iftitlepage \hfil \global\titlepagefalse
- \else \gentleheadline \fi}
-
-In a similar way, sometimes \TeX{} allows a line to be slightly
-longer than {\tt \\hsize} in order to achieve a more balanced
-appearance. The control word {\tt \\tolerance} determines when
-this happens. If the badness of a line is greater than {\tt
-\\tolerance}, \TeX{} will make the line longer by adding a new word
-at the end of the line, even though it might exceed the value of
-{\tt \\hsize}. A line which is only slightly longer is set
-without being reported. The control word {\tt \\hfuzz} determines
-how much excess is allowed; the default is {\tt \\hfuzz
-=~0.1~pt}. A line that is more than slightly longer than {\tt \\hsize}
-is obviously a serious problem; \TeX{} puts a slug in
-the margin to make its point forcefully. It's possible to avoid
-overfull hboxes altogether by increasing the value of {\tt \\tolerance}.
-With {\tt \\tolerance = 10000} there will never be
-overfull boxes or slugs. The default is {\tt \\tolerance = 200}\null.
-\TeXref{29}
-\toindex{hfuzz}
-\toindex{tolerance}
-
-The width of the slug is determined by the control word {\tt
-\\overfullrule}. Including {\tt \\overfullrule = 0 pt} in your
-file will delete any further printing of the slugs. The
-overfull boxes will still be there, of course, and they will
-probably be harder to spot.
-\toindex{overfullrule}
-
-So we see why overfull boxes and underfull boxes are reported; we
-can also change the reporting by changing the values of {\tt
-\\badness}, {\tt \\hfuzz}, and {\tt \\tolerance}. In addition, a
-small value of {\tt \\hsize} obviously makes it more difficult to
-set lines and causes more overfull and underfull hboxes to be
-reported. These are warnings that you ignore at your own peril!
-
-Adding new possibilities of hyphenation will sometimes eliminate
-an overfull box. \TeX{} has automatic hyphenation and usually
-finds good places to hyphenate a word; however, it's possible to
-add hyphenations to let lines break at new places. For example,
-the automatic hyphenation will never put a hyphen in the word
-``database''. If you type in {\tt data\\-base}, it will allow a
-hyphen to be inserted after the second letter ``a'' in the word.
-More generally, if you put {\tt \\hyphenation\lb data-base\rb} in
-the beginning of your input file, then all occurrences of the
-word ``database'' will allow hyphenation after the letter ``a''.
-\TeXref{28} The log file will show the possible hyphenations on
-the line containing the overfull or underfull box. Sometimes the
-best solution to an overfull or underfull hbox is a little
-judicious editing of the original document.
-\toindex{hyphenation}
-
-Our discussion has involved the setting of type into lines, that is,
-the horizontal page structure. There are several vertical \analog{}s.
-Overfull and underfull hboxes indicate how well words are gathered
-into lines. Similarly, overfull and underfull vboxes are reported
-when paragraphs are gathered to form pages. A large table that
-can't be broken in the middle, for example, can produce an underfull
-vbox that is reported in the log file when the page being typeset is
-completed. The control word {\tt \\vbadness} works for the vertical
-placement of text in the same way as {\tt \\hbadness} works for
-horizontal text.
-\toindex{vbadness}
-
-\exercise Take a few paragraphs and print them using various (small)
-values of {\tt \\hsize} to see what kind of overfull boxes result.
-Repeat with various values of {\tt \\hbadness}, {\tt \\hfuzz}, and
-{\tt \\tolerance}.
-
-
-
-
-
-
-\section{$\Bigl\{$Groups, $\bigl\{$Groups,
- $\{$and More Groups$\}\bigr\}\Bigr\}$}
-
-The concept of gathering text into groups allows \TeX{} input
-files to be greatly simplified. A new group is started by the
-character {\tt\lb} and terminated by the character {\tt \rb}\null.
-Changes made within a group will lose their effect when the
-group terminates. So, for example if {\tt \lb \\bf three
-boldface words\rb} appears in your text, the opening brace starts
-the group, the {\tt \\bf} control word changes to a boldface
-font, and the closing brace finishes up the group. Upon
-completion of the group the font being used is the one in effect
-before the group started. This is the (easier) way of having a
-few words in a different font. It's also possible to have groups
-nested within groups.
-
-
-As another example, size changes can be made in the text that are
-only temporary. For example
-\beginuser
-\lb
-\\hsize = 4 in
-\\parindent = 0 pt
-\\leftskip = 1 in
-will produce a paragraph that is four
-$\vdots$
-(this is an easy mistake to make).
-\\par
-\rb
-\enduser
-
-{\hsize = 4 in
-\parindent = 0 pt
-\leftskip = 1 in
-will produce a paragraph that is four inches wide with the text
-offset into the paragraph by one inch regardless of the settings
-in effect before the start of the group. This paragraph is set
-with those values. After the end of the group, the old settings
-are in effect again. Note that it is necessary to include
-{\tt \\par} or to use a blank line before the closing brace to end
-the paragraph, since otherwise the group will end and \TeX{} will
-go back to the old parameters before the paragraph is actually
-typeset (this is an easy mistake to make). \par}
-
-When line-spacing control words (like {\tt \\centerline}) act on text
-following it in braces, that text is implicitly in a group. Thus
-{\tt \\centerline\lb\\bf A bold title\rb} will produce a \centred{}
-boldface line, and the text following that line will be in
-whatever font was in effect before the {\tt \\centerline} was
-invoked.
-
-The empty group {\tt\lb\rb} is useful. One use allows accents to be
-typeset with no accompanying letter. For example, {\tt \\\~{}\lb\rb}
-will print a tilde with no letter under it. It can also be used to
-stop \TeX{} from eating up consecutive spaces. Hence {\tt I use
-\\TeX\lb\rb{} all the time} will leave a space after ``\TeX'' in the
-output. This is an alternative to using {\tt \\\sp} as we did in
-Section~1.
-\TeXref{19--21}
-
-Grouping can also be used to avoid spaces in the middle of a word
-when including accents. Either {\tt soup\\c\sp con} or {\tt
-soup\\c\lb c\rb on} will produce the word soup\c{c}on.
-
-\exercise Change the dimensions of one paragraph on a page using the
-grouping idea.
-
-\exercise Mathematicians sometime use the word ``i{f}f'' as an
-abbreviation for ``if and only if''\null. In this case it looks
-better if the first and second letter ``f'' are {\sl not\/}
-joined as a ligature. How do you do this (there are several
-solutions)?
-
-It's really easy to forget to match braces properly. The effect
-can be dramatic; if you get output that suddenly changes to an
-italic font for the rest of the document, a mismatched brace is
-probably the cause. If you have an extra {\tt \lb} \TeX{} will
-give a message in the log file: {\tt (\\end occurred inside a
-group at level 1)}. An extra {\tt\rb} will result in the message
-\hbox{\tt! Too many \rb's.}
-
-Here's a little hint to help you keep track of the braces in more
-complicated groups: put the opening brace on a line by itself and
-do the same for the closing brace. If there are braces nested
-within the original ones, put them on separate lines also, but
-indent them a few spaces. The text within the nested braces can
-also be indented since \TeX{} ignores all spaces at the beginning
-of a line. The matching braces will then stand out when you look
-at your \TeX{} source file. In fact, if your editor is smart
-enough, you can create the two lines with the braces first and
-then insert the appropriate material within them with automatic
-indenting.
-
-\exercise In section 2 we changed fonts the following method:
-{\tt I started with roman type, \\it switched to italic type,
-\\rm and returned to roman type}. Get the same result using the
-idea of grouping.
-
-
-\section{No math anxiety here!}
-
-\TeX{} is at its best when typesetting mathematics. The
-conventions for doing this are many and complex, and the ability
-of \TeX{} to take them into account makes the production of high
-quality, attractive mathematical output possible. If you plan to
-produce papers with mathematical symbols in them, this section
-will give you all the basics necessary for creating beautiful
-output in almost all circumstances; \TeX{} may be used without
-any mathematics, of course, and if this is your goal, then the
-following two subsections are probably sufficient for your needs.
-
-\subsection{Lots of new symbols}
-
-Mathematical text is inserted into normal text in two possible
-ways: it can be {\sl in-line\/}, that is, as part of the usual
-lines of text. It can also be {\sl displayed}, that is, \centred{}
-in a gap between the usual text. The results in the spacing and
-placement of symbols can be quite different in each case. The
-in-line equation $\sum_{k=1}^{\infty} {1\over k^2} = {\pi^2\over6}$
-is easily seen to be different from the same equation when
-displayed:
-$$\sum_{k=1}^{\infty} {1\over k^2} = {\pi^2\over6}.$$
-
-Since the spacing and the fonts used for mathematics are quite
-different from those of ordinary text, \TeX{} needs to be told
-when mathematics rather than normal text is being typeset. This
-is done using the {\tt\$} symbol. More specifically, mathematics
-is typeset in-line by surrounding the symbols to be entered by
-single dollar signs: {\tt \$$\ldots$\$}, and is typeset displayed
-by surrounding the symbols to be entered by double dollar signs:
-{\tt \$\$$\ldots$\$\$}\null. Hence {\tt \$x = y+1\$} will give
-$x=y+1$ in-line while {\tt \$\$x = y+1.\$\$} will display
-$$x=y+1.$$
-
-The spacing for both in-line and displayed mathematics is
-completely controlled by \TeX\null. Adding spaces to your input
-has no effect at all. What if you need a space or some text in
-the middle of some mathematics? You can insert text by inserting
-it into an hbox (don't worry about the definition of an hbox for
-now): {\tt \\hbox\lb$\ldots$\rb}\null. This is particularly
-useful for displayed mathematics. Hence ``$x=y+1 \hbox{ whenever
-} y=x-1$'' can be typeset using {\tt \$x=y+1 \\hbox\lb\ whenever
-\rb y=x-1\$}. Note the spaces on either side of the word within
-the braces. Usually it isn't necessary to insert spaces into
-mathematical text, but here are the control sequences that do the
-job.
-\TeXref{167}
-
-\maketable [Adding space to mathematical text]
-\halign{
-\strut \hfil # & \quad \hfil\tt# \hfil \quad
- & \hbox to 2cm{\hrulefill\vrule height 8pt#\vrule height 8pt\hrulefill} \cr
- Name & \rm Control Sequence & \hfil{}$\gets$Size$\to$\cr
- \noalign{\hrule} \noalign{\smallskip}
- Double quad & \\qquad &\qquad \cr
- Quad & \\quad &\quad \cr
- Space & \\\sp\ &\ \cr
- Thick space & \\; &$\;$\cr
- Medium space & \\> &$\>$\cr
- Thin space & \\, &$\,$\cr
- Negative thin space & \ \\!\ &$\!$\cr
- }
-
-\toindex{quad}
-\toindex{qquad}
-\toindex{\sp}
-\toindex{;}
-\toindex{>}
-\toindex{,}
-\toindex{!}
-
-If you look closely at the negative thin space, you'll notice
-that, unlike the other entries, the two arms overlap. This is
-because the negative space is one in the opposite direction, that
-is, while the other control sequences increase the amount of
-space between two symbols being typeset, the negative thin space
-decreases the space between them, even if it causes them to
-overlap.
-
-\exercise Typeset the following: $C(n,r) = n!/(r!\,(n-r)!)$\null. Note the
-spacing in the denominator.
-\bigskip
-
-You shouldn't have any blank lines between the dollar signs
-delimiting the mathematical text. \TeX{} assumes that all the
-mathematical text being typeset is in one paragraph, and a blank
-line starts a new paragraph; consequently, this will generate an
-error message. This turns out to be useful, for one of the
-easiest errors to make is to forget to put in the trailing dollar
-sign(s) after the mathematical input (I promise that you'll do it
-at least once while learning \TeX{}); if \TeX{} allowed more than
-one paragraph to be between the dollars signs, then one omitted
-trailing dollar sign might cause the rest of the document to be
-typeset as mathematics.
-
-Most mathematical text is entered in exactly the same way for
-in-line typesetting as for displayed typesetting (except for the
-surrounding dollar signs, of course). The exceptions, such as
-aligning multiline displays and placing equation numbers at the
-left or right margin will be discussed in the last part of this
-section.
-
-Many new symbols can appear when typesetting mathematics. Most
-of the ones that actually appear on the keyboard can be used
-directly. The symbols {\tt + - / * = ' | < > (} and {\tt )} are
-all entered directly. Here they are as mathematics: $+ - / * =\>
-'\> | <\> >\> ( \> )$.
-
-\exercise Typeset the equation $a+b=c-d=xy=w/z$ as in-line and
-displayed mathematical text.
-
-\exercise Typeset the equation $(fg)' = f'g + fg'$ as in-line and
-displayed mathematical text.
-\bigskip
-
-Many other symbols, as you would expect, are predefined control
-words. All Greek letters are available. Here is a table of them:
-\TeXref{434}
-
-\maketable [Greek letters]
-\halign{
-\strut \hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \qquad
- &\hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-\alpha & \\alpha &\beta & \\beta &\gamma & \\gamma &\delta & \\delta \cr
-\epsilon & \\epsilon & \varepsilon & \\varepsilon & \zeta & \\zeta &
-\eta & \\eta \cr
-\theta & \\theta & \vartheta & \\vartheta & \iota & \\iota & \kappa &
-\\kappa \cr
-\lambda & \\lambda & \mu & \\mu & \nu & \\nu & \xi & \\xi \cr
-o & o & \pi & \\pi & \rho & \\rho & \varrho & \\varrho \cr
-\sigma & \\sigma & \varsigma & \\varsigma & \tau & \\tau & \upsilon &
-\\upsilon \cr
-\phi & \\phi & \varphi & \\varphi & \chi & \\chi & \psi & \\psi \cr
-\omega & \\omega & \Gamma & \\Gamma & \Delta & \\Delta & \Theta &
-\\Theta \cr
-\Lambda & \\Lambda & \Xi & \\Xi & \Pi & \\Pi & \Sigma & \\Sigma \cr
-\Upsilon & \\Upsilon & \Phi & \\Phi & \Psi & \\Psi & \Omega & \\Omega \cr
- }
-
-\toindex{alpha}
-\toindex{beta}
-\toindex{gamma}
-\toindex{delta}
-\toindex{epsilon}
-\toindex{varepsilon}
-\toindex{zeta}
-\toindex{eta}
-\toindex{theta}
-\toindex{vartheta}
-\toindex{iota}
-\toindex{kappa}
-\toindex{lambda}
-\toindex{mu}
-\toindex{nu}
-\toindex{xi}
-\toindex{pi}
-\toindex{rho}
-\toindex{varrho}
-\toindex{sigma}
-\toindex{varsigma}
-\toindex{tau}
-\toindex{upsilon}
-\toindex{phi}
-\toindex{varphi}
-\toindex{chi}
-\toindex{psi}
-\toindex{omega}
-\toindex{Gamma}
-\toindex{Delta}
-\toindex{Theta}
-\toindex{Lambda}
-\toindex{Xi}
-\toindex{Pi}
-\toindex{Sigma}
-\toindex{Upsilon}
-\toindex{Phi}
-\toindex{Psi}
-\toindex{Omega}
-
-
-\exercise Typeset $\alpha\beta=\gamma+\delta$ as in-line and displayed
-mathematical text.
-
-\exercise Typeset $\Gamma(n) = (n-1)!$ as in-line and displayed
-mathematical text.
-
-Sometimes accents are put above or below symbols. The control
-words used for accents in mathematics are different from those
-used for normal text. The normal text control words may not be
-used for mathematics and vice-versa.
-\TeXref{135--136}
-
-\maketable [Mathematical accents]
-\halign{
- \strut \hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ &
- \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \qquad \cr
- \noalign{\hrule} \noalign{\smallskip}
- \hat o & \\hat o & \check o & \\check o & \tilde o & \\tilde o \cr
- \acute o & \\acute o & \grave o & \\grave o & \dot o & \\dot o \cr
- \ddot o & \\ddot o &\breve o & \\breve o & \bar o & \\bar o \cr
- \vec o & \\vec o & \widehat {abc} & \\widehat \lb abc\rb
- & \widetilde {abc} & \\widetilde \lb abc\rb\cr
- }
-
-\toindex{hat}
-\toindex{check}
-\toindex{tilde}
-\toindex{acute}
-\toindex{grave}
-\toindex{dot}
-\toindex{ddot}
-\toindex{breve}
-\toindex{bar}
-\toindex{vec}
-\toindex{widehat}
-\toindex{widetilde}
-
-
-
-Binary operators combine two mathematical objects to get another
-object. Ordinary addition and multiplication, for example,
-combine two numbers to get another number, and so they are binary
-operators. When a binary operator such as $+$ or $\times$ is
-typeset, a little extra space is put around it. Here is a list of
-some of the available binary operators:
-\TeXref{436}
-
-\maketable [Binary operators]
-\halign{
-\strut \hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \qquad
- &\hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-\cdot & \\cdot &\times & \\times &\ast & \\ast &\star & \\star \cr
-\circ & \\circ & \bullet & \\bullet & \div & \\div & \diamond & \\diamond \cr
-\cap & \\cap & \cup & \\cup & \vee & \\vee & \wedge & \\wedge \cr
-\oplus & \\oplus &\ominus & \\ominus & \otimes &\\otimes &\odot &\\odot \cr
- }
-
-\toindex{cdot}
-\toindex{times}
-\toindex{ast}
-\toindex{star}
-\toindex{circ}
-\toindex{bullet}
-\toindex{div}
-\toindex{diamond}
-\toindex{cap}
-\toindex{cup}
-\toindex{vee}
-\toindex{wedge}
-\toindex{oplus}
-\toindex{ominus}
-\toindex{otimes}
-\toindex{odot}
-
-Ellipses are commonly used with binary operators. The control
-word {\tt \\cdots} will raise the dots so that they are level
-with the binary operator. Thus {\tt \$a + \\cdots + z\$} will
-produce $a + \cdots + z$. The control word {\tt \\ldots} will
-put the dots on the baseline, and so {\tt \$1\\ldots n\$}
-produces $1\ldots n$.
-\toindex{cdots}
-\toindex{ldots}
-
-\exercise Typeset: $x\wedge (y\vee z) = (x\wedge y) \vee (x\wedge z)$.
-
-\exercise Typeset: $2+4+6+\cdots +2n = n(n+1)$.
-\bigskip
-
-A relation indicates a property of two mathematical objects. We
-already know how to show two objects equal, or how to show one
-number less than or greater than another number (since these are
-symbols on most terminal keyboards). To negate a relation, the
-control word {\tt \\not} is put in front of the relation. Here
-are some relations:
-\TeXref{436}
-\toindex{not}
-
-\maketable [Relations ]
-\halign{
-\strut \hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \qquad
- &\hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-\leq & \\leq &\not\leq & \\not \\leq
- & \geq & \\geq & \not\geq & \\not \\geq \cr
-\equiv & \\equiv & \not\equiv & \\not \\equiv
- & \sim & \\sim & \not\sim & \\not \\sim \cr
-\simeq & \\simeq & \not\simeq & \\not \\simeq
- & \approx & \\approx & \not\approx & \\not \\approx \cr
-\subset & \\subset & \subseteq & \\subseteq
- & \supset & \\supset & \supseteq & \\supseteq \cr
-\in & \\in & \ni & \\ni & \parallel & \\parallel & \perp & \\perp \cr
- }
-
-\toindex{leq}
-\toindex{geq}
-\toindex{equiv}
-\toindex{sim}
-\toindex{simeq}
-\toindex{approx}
-\toindex{subset}
-\toindex{subseteq}
-\toindex{supset}
-\toindex{supseteq}
-\toindex{in}
-\toindex{ni}
-\toindex{parallel}
-\toindex{perp}
-
-
-\exercise
-Typeset: $\vec x\cdot \vec y = 0$ if and only if $\vec x \perp \vec y$.
-
-\exercise
-Typeset: $\vec x\cdot \vec y \not= 0$ if and only if $\vec x \not\perp \vec y$.
-
-Here are some other available mathematical symbols:\TeXref{435--438}
-
-\maketable [Miscellaneous symbols ]
-\halign{
-\strut \hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \qquad
- &\hfil$#$ & \quad \tt# \hfil \qquad &\hfil$#$ & \quad \tt# \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-\aleph & \\aleph & \ell & \\ell & \Re & \\Re & \Im & \\Im \cr
-\partial & \\partial & \infty & \\infty & \| & \\| & \angle & \\angle \cr
-\nabla & \\nabla & \backslash &\\backslash & \forall & \\forall
- & \exists & \\exists \cr
-\neg & \\neg & \flat & \\flat & \sharp & \\sharp & \natural & \\natural \cr
- }
-
-\toindex{aleph}
-\toindex{ell}
-\toindex{Re}
-\toindex{Im}
-\toindex{partial}
-\toindex{infty}
-\toindex{|}
-\toindex{angle}
-\toindex{nabla}
-\toindex{backslash}
-\toindex{forall}
-\toindex{exists}
-\toindex{neg}
-\toindex{flat}
-\toindex{sharp}
-\toindex{natural}
-
-\exercise Typeset: $(\forall x\in \Re)(\exists y\in\Re)$ $y>x$.
-
-\subsection{Fractions}
-
-There are two methods of typesetting a fraction: it can be
-typeset either in the form $1/2$ or in the form ${1\over2}$\null.
-The first case is just entered with no special control sequences,
-that is, {\tt \$1/2\$}\null. The second case uses the control
-word {\tt \\over} and the following pattern: {\tt \lb
-<numerator> \\over <denominator>\rb}\null. Hence {\tt \$\$\lb a+b
-\\over c+d\rb.\$\$} gives \TeXref{139--140}
-\toindex{over} $${a+b\over c+d}.$$
-
-\exercise Typeset the following: ${a+b\over c}\quad {a\over b+c}
-\quad {1\over a+b+c} \not= {1\over a}+{1\over b}+{1\over c}$.
-
-\exercise Typeset: What are the points where
-${\partial \over \partial x} f(x,y) = {\partial \over \partial y}
-f(x,y) = 0$?
-
-\subsection{Subscripts and superscripts}
-
-Subscripts and superscripts are particularly easy to enter using
-\TeX\null. The characters {\tt \_{}} and {\tt \^{}} are used to
-indicate that the next character is a subscript or a superscript.
-Thus {\tt \$x\^{}2\$} gives $x^2$ and {\tt \$x\_{}2\$} gives
-$x_2$\null. To get several characters as a subscript or
-superscript, they are grouped together within braces. Hence we
-can use {\tt \$x\^{}\lb 21\rb\$} to get $x^{21}$ and {\tt \$x\_{}\lb
-21\rb\$} to get $x_{21}$\null. Notice that the
-superscripts and subscripts are automatically typeset in a
-smaller type size. The situation is only slightly more
-complicated for a second layer of subscripts or superscripts.
-You can {\sl not\/} use {\tt \$x\_{}2\_{}3\$} since this could
-have two possible interpretations, namely, {\tt \$x\_{}\lb 2\_{}3\rb\$}
-or {\tt \$\lb x\_{}2\rb\_{}3\$}; this gives two
-different results: $x_{2_3}$ and ${x_2}_3$, the first of which is
-the usual mathematical subscript notation. Thus you must put in
-the complete braces to describe multiple layers of subscripts and
-superscripts. They may be done to any level.
-\TeXref{128--130}
-
-To use both subscripts and superscripts on one symbol, you use
-both the {\tt \_{}} and {\tt \^{}} in either order. Thus either
-{\tt \$x\_{}2\^{}1\$} or {\tt\$x\^{}1\_{}2\$} will give $x_2^1$.
-
-\exercise
-Typeset each of the following: $e^x \quad e^{-x} \quad
-e^{i\pi}+1=0 \quad x_0 \quad x_0^2 \quad {x_0}^2 \quad 2^{x^x}$.
-
-\exercise Typeset:
-$\nabla^2 f(x,y) = {\partial^2 f \over\partial x^2}
-+ {\partial^2 f \over\partial y^2}$.
-\bigskip
-
-A similar method is used for summations and integrals. The input
-of {\tt \$\\sum\_{}\lb k=1\rb\^{}n k\^{}2\$} will give $\sum_{k=1}^n
-k^2$, and {\tt \$\\int\_{}0\^{}x f(t) dt\$} will
-give $\int_0^x f(t) dt$.
-\TeXref{144--145}
-\toindex{sum}
-\toindex{int}
-
-Another use of this type of input is for expressions
-involving limits. You can use
-{\tt \$\\lim\_\lb n\\to \\infty\rb (\lb n+1 \\over n\rb)\^{}n = e\$}
-to get $\lim_{n\to \infty} ({n+1\over n})^n = e$.
-\toindex{lim}
-
-\exercise Typeset the following expression: $\lim_{x\to 0}
-(1+x)^{1\over x}=e$.
-
-\exercise Typeset: The cardinality of $(-\infty, \infty)$ is $\aleph_1$.
-
-\exercise Typeset: $\lim_{x\to {0^+}} x^x = 1$.
-\bigskip
-
-Here's a hint to make integrals look a little nicer: look at the
-difference between $\int_0^x f(t) dt$ and $\int_0^x f(t)\, dt$\null.
-In the second case there is a little extra space after
-$f(t)$, and it looks nicer; {\tt \\,} was used to add the
-additional space.
-\toindex{,}
-
-\exercise Typeset the following integral: $\int_0^1 3x^2\,dx = 1$.
-
-\subsection{Roots, square and otherwise}
-
-To typeset a square root it is only necessary to use the construction
-{\tt \\sqrt\lb$\ldots$\rb}\null. Hence {\tt \$\\sqrt\lb x\^{}2+y\^{}2\rb\$}
-will give $\sqrt{x^2+y^2}$\null. Notice that \TeX{} takes care of the
-placement of symbols and the height and length of the radical.
-To make cube or other roots, the control words {\tt \\root} and {\tt
-\\of} are used. You get $\root n \of {1+x^n}$ from the
-input\TeXref{130--131} {\tt \$\\root n \\of \lb1+x\^{}n\rb\$}.
-\toindex{root}
-\toindex{sqroot}
-
-A possible alternative is to use the control word {\tt \\surd}; the
-input {\tt \$\\surd 2\$} will produce $\surd 2$.
-\toindex{surd}
-
-\exercise Typeset the following: $\sqrt2 \quad \sqrt {x+y\over x-y}
-\quad \root 3 \of {10}$ \quad $e^{\sqrt x}$.
-
-\exercise Typeset: $\|x\| = \sqrt{x\cdot x}$.
-
-\exercise Typeset:
-$\phi(t) = {1 \over \sqrt{2\pi}} \int_0^t e^{-x^2/2}\,dx$.
-
-
-\subsection{Lines, above and below}
-
-Use the constructions {\tt \\overline\lb$\ldots$\rb} and
-{\tt \\underline\lb$\ldots$\rb} to put lines above or below mathematical
-expressions. Hence {\tt \$\\overline\lb x+y\rb=\\overline x + \\overline
-y\$} gives $\overline{x+y}=\overline x + \overline y$\null.
-But notice that the lines over the letters are at
-different heights, and so some care is necessary. The use of {\tt
-\\overline\lb\\strut x\rb} will raise the height of the line
-over\TeXref{130--131} $x$\null.
-\toindex{overline}
-\toindex{underline}
-
-To underline non-mathematical text, use {\tt \\underbar\lb$\dots$\rb}.
-\toindex{underbar}
-
-\exercise Typeset the following: $\underline x \quad \overline y
-\quad \underline{\overline{x+y}}$.
-
-
-\subsection{Delimiters large and small}
-
-The most commonly used mathematical delimiters are brackets,
-braces, and parentheses. As we have seen, they may be produced
-by using {\tt [ ] \\\lb\ \\\rb\ ( )} to get
-$[\>]\>\{\>\}\>(\>)\>$. Sometimes larger delimiters increase the
-clarity of mathematical expressions, as in
-$$\bigl(a\times(b+c)\bigr) \bigl((a\times b)+c\bigr).$$ To make
-larger left delimiters the control words {\tt \\bigl}, {\tt
-\\Bigl}, {\tt \\biggl}, and {\tt \\Biggl} are used in front of
-the delimiter; similarly, {\tt \\bigr}, {\tt \\Bigr}, {\tt
-\\biggr}, and {\tt \\Biggr} are used\TeXref{145--147} for the
-right delimiters. Hence {\tt \$\\Bigl[\$} and {\tt \$\\Bigr]\$}
-will produce $\Bigl[$ and $\Bigr]$.
-
-\toindex{bigl}
-\toindex{Bigl}
-\toindex{biggl}
-\toindex{Biggl}
-\toindex{bigr}
-\toindex{Bigr}
-\toindex{biggr}
-\toindex{Biggr}
-
-Here is a table to compare the size of some of the delimiters.
-
-%% \everycr can add 4 points between lines in the following table %%
-\everycr={\noalign{\vskip 4 pt}}
-\maketable [Delimiters of various sizes]
-\halign{
-\strut \hfil$#$ & \quad \tt# \hfil \quad\qquad
- &\hfil$#$ & \quad \tt# \hfil \quad\qquad
- &\hfil$#$ & \quad \tt# \hfil \quad\qquad
- &\hfil$#$ & \quad \tt# \hfil \cr
-\noalign{\hrule} \noalign{\smallskip}
-\{ & \\\lb & \} & \\\rb & ( & ( & ) & )\cr
-\bigl\{ & \\bigl\\\lb & \bigr\} & \\bigr\\\rb & \bigl( & \\bigl( & \bigr) &
-\\bigr)\cr
-\Bigl\{ & \\Bigl\\\lb & \Bigr\} & \\Bigr\\\rb & \Bigl( & \\Bigl( & \Bigr) &
-\\Bigr)\cr
-\biggl\{ & \\biggl\\\lb & \biggr\} & \\biggr\\\rb & \biggl(
- & \\biggl( & \biggr) & \\biggr) \cr
-\Biggl\{ & \\Biggl\\\lb & \Biggr\} & \\Biggr\\\rb & \Biggl(
- & \\Biggl( & \Biggr) & \\Biggr)\cr
- }
-
-\everycr={}
-
-If you want, you can let \TeX{} choose the size of delimiter by
-using the control words {\tt \\left} and {\tt \\right} before
-your delimiters.
-\TeXref{148}Thus {\tt \\left[$\ldots$\\right]} will cause the material
-to be enclosed by brackets that are appropriately big. {\bf Note
-well:} each use of a {\tt \\left} delimiter must have a matching
-{\tt \\right} delimiter (although the delimiters themselves may be
-different). Hence {\tt \$\$\\left|\lb a+b \\over
-c+d\rb\\right|.\$\$} gives $$\left|{a+b \over c+d}\right|.$$
-
-\maketable [Mathematical delimiters]
-\halign{
-\strut \hfill$#$ & \quad \tt # \qquad\qquad &
- \hfill$#$ & \quad \tt # \qquad\qquad &
- \hfill$#$ & \quad \tt # \cr
-\noalign{\hrule} \noalign{\smallskip}
-( & ( & ) & ) & [ & [ \cr
-] & ] &\{ & \\\lb & \} & \\\rb \cr
-\lfloor & \\lfloor &\rfloor &\\rfloor & \lceil & \\lceil \cr
-\rceil & \\rceil &\langle & \\langle & \rangle & \\rangle \cr
-/ & / & \backslash & \\backslash &| & | \cr
-\| & \\| &\uparrow & \\uparrow & \Uparrow & \\Uparrow \cr
-\downarrow & \\downarrow & \Downarrow & \\Downarrow
- & \updownarrow & \\updownarrow \cr
-\Updownarrow & \\Updownarrow \cr
- }
-
-\toindex{lfloor}
-\toindex{rfloor}
-\toindex{lceil}
-\toindex{rceil}
-\toindex{langle}
-\toindex{rangle}
-\toindex{|}
-\toindex{uparrow}
-\toindex{Uparrow}
-\toindex{downarrow}
-\toindex{Downarrow}
-\toindex{updownarrow}
-\toindex{Updownarrow}
-
-\exercise Typeset $\bigl \lceil \lfloor x \rfloor \bigr \rceil
- \leq \bigl \lfloor \lceil x \rceil \bigr \rfloor$.
-
-\subsection{Those special functions}
-
-There are several types of functions that appear frequently in
-mathematical text. In an equation like ``$\sin^2x + \cos^2x =
-1$'' the trigonometric functions ``sin'' and ``cos'' are in roman
-rather than italic type. This is the usual mathematical
-convention to indicate that it is a function being described and
-not the product of three variables. The control words {\tt
-\\sin} and {\tt \\cos} will use the right typeface automatically.
-Here is a table of these and some other special functions:
-\TeXref{162}
-
-\maketable [Special mathematical functions]
-\halign{
- \strut \tt {\\}#\hfil && \quad \tt {\\}#\hfil \cr
- \noalign{\hrule} \noalign{\smallskip}
- sin & cos & tan & cot & sec & csc & arcsin & arccos \cr
- arctan & sinh & cosh & tanh & coth & lim & sup & inf \cr
- limsup & liminf & log & ln & lg & exp & det & deg \cr
- dim & hom & ker & max & min & arg & gcd & Pr \cr
- }
-
-\toindex{sin}
-\toindex{cos}
-\toindex{tan}
-\toindex{cot}
-\toindex{sec}
-\toindex{csc}
-\toindex{arcsin}
-\toindex{arccos}
-\toindex{arctan}
-\toindex{sinh}
-\toindex{cosh}
-\toindex{tanh}
-\toindex{coth}
-\toindex{lim}
-\toindex{sup}
-\toindex{inf}
-\toindex{limsup}
-\toindex{liminf}
-\toindex{log}
-\toindex{ln}
-\toindex{lg}
-\toindex{exp}
-\toindex{det}
-\toindex{deg}
-\toindex{dim}
-\toindex{hom}
-\toindex{ker}
-\toindex{max}
-\toindex{min}
-\toindex{arg}
-\toindex{gcd}
-\toindex{Pr}
-
-\exercise Typeset: $\sin(2\theta) = 2\sin\theta\cos\theta \quad
-\cos(2\theta) = 2\cos^2\theta - 1 $.
-
-\exercise Typeset: $$\int \csc^2x\, dx = -\cot x+ C
-\qquad \lim_{\alpha\to 0} {\sin\alpha \over \alpha} = 1
-\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0.$$
-
-\exercise Typeset: $$\tan(2\theta) = {2\tan\theta \over
-1-\tan^2\theta}.$$
-
-
-\subsection{Hear ye, hear ye!}
-
-There is a particular macro that is used in almost every
-mathematical paper, and is different enough to require a special
-explanation. This is the {\tt \\proclaim} macro. It is used when
-stating theorems, corollaries, propositions, and the like. The
-paragraph following {\tt \\proclaim} is broken into two parts:
-the first part goes up to and including the first period that is
-followed by a space, and the second part is the rest of the
-paragraph. \TeXref{202--203}The idea is that the first part
-should be something like ``Theorem 1.'' or ``Corollary B.'' The
-second part is the statement of the theorem or corollary. Here
-is an example:
-\toindex{proclaim}
-
-\beginliteral
-\proclaim Theorem 1 (H.~G.~Wells). In the country of the blind,
-the one-eyed man is king.
-@endliteral
-
-\noindent gives
-
-\proclaim Theorem 1 (H.~G.~Wells). In the country of the blind,
-the one-eyed man is king.
-
-The statement of the theorem may contain mathematical expressions, of
-course.
-
-\vfill\eject
-\exercise Typeset:
-\nobreak
-\proclaim Theorem (Euclid). There exist an infinite number of
-primes.
-
-\exercise Typeset:
-\proclaim Proposition 1.
-$\root n \of {\prod_{i=1}^n X_i} \leq {1 \over n} \sum_{i=1}^n X_i$
-with equality if and only if $X_1=\cdots=X_n$.
-
-\subsection{Matrices}
-
-Matrices are typeset using combinations of the alignment
-character {\tt \&} and the control word {\tt \\cr} to indicate
-the end of the line. Start with {\tt \$\$\\pmatrix\lb$\dots$\rb\$\$}.
-Into the space between the braces go the rows of the matrix, each
-one ended by {\tt \\cr}. The entries are separated by the
-{\tt \&}\null. For example the input
-\TeXref{176--178}
-
-\beginliteral
-$$\pmatrix{
-a & b & c & d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab & cd \cr
-}.$$
-@endliteral
-
-\noindent
-gives as printed output
-$$\pmatrix{
-a & b & c & d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab & cd \cr
-}.$$
-\toindex{pmatrix}
-
-The matrix entries in our examples have all been \centred{}
-within their columns with a little space on each side. They can
-be made flush right or flush left by inserting {\tt \\hfill}
-before or after the entry. Notice the differences between the
-following example and the previous one.
-
-\beginliteral
-$$\pmatrix{
-a & b & c \hfill & \hfill d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab \hfill & \hfill cd \cr
-}.$$
-@endliteral
-
-\noindent
-gives as printed output
-
-$$\pmatrix{
-a & b & c \hfill & \hfill d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab \hfill & \hfill cd \cr
-}.$$
-
-
-\vbox{
-\exercise Typeset
-$$ I_4 = \pmatrix{ 1 &0 &0 &0 \cr
- 0 &1 &0 &0 \cr
- 0 &0 &1 &0 \cr
- 0 &0 &0 &1 \cr}$$
-}
-
-It's possible to have matrices that use other delimiters. Using
-{\tt \\matrix} instead of {\tt \\pmatrix} will leave off the
-parentheses, so the delimiters must be explicitly included using
-{\tt \\left} and {\tt \\right}. Here is how we can change the
-matrix of our first example.
-\toindex{matrix}
-\toindex{left}
-\toindex{right}
-
-\beginliteral
-$$ \left |
-\matrix{
-a & b & c & d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab & cd \cr
-}
-\right | $$
-@endliteral
-
-\noindent
-gives as printed output
-$$ \left |
-\matrix{
-a & b & c & d \cr
-b & a & c+d & c-d \cr
-0 & 0 & a+b & a-b \cr
-0 & 0 & ab & cd \cr
-}
-\right | $$
-
-It's even possible to use {\tt \\left.} and {\tt \\right.} to
-indicate that the opening or closing delimiter is deleted (note
-the use of the period).
-
-\exercise Use a matrix construction to typeset
-
-$$ |x| = \left\{ \matrix{ x & x \ge 0 \cr
- -x & x \le 0 \cr} \right.$$
-
-This exercise and more general constructions of this type
-may also be typeset using the {\tt \\cases} macro.
-\TeXref{175}
-
-Sometimes ellipses are used within matrices. The control words
-{\tt \\cdots}, {\tt \\vdots}, and {\tt \\ddots} can be used to
-insert horizontal, vertical, and diagonal dots.
-
-Thus we can use
-\beginliteral
-$$ \left [
-\matrix{
-aa & \cdots & az \cr
-\vdots & \ddots & \vdots \cr
-za & \cdots & zz \cr
-}
-\right ] $$
-@endliteral
-
-\noindent
-to get as printed output
-$$ \left [
-\matrix{
-aa & \cdots & az \cr
-\vdots & \ddots & \vdots \cr
-za & \cdots & zz \cr
-}
-\right ] $$
-
-
-Matrices may also be typeset in-line, but they are pretty ugly
-unless they have a small number of rows.
-
-
-\subsection{Displayed equations}
-
-All of the mathematics covered so far has identical input whether
-it is to be typeset in-line or displayed. At this point we'll
-look at some situations that apply to displayed equations only.
-
-The first is that of aligning multiline displays. This is done with
-the alignment character {\tt \&} and the control words {\tt \\cr} and
-{\tt \\eqalign}. Starting with {\tt \$\$\\eqalign\lb$\dots$\rb\$\$},
-the equations to be aligned are entered with each one terminated by
-{\tt \\cr}. In each equation there should be one alignment symbol
-{\tt \&} to indicate where the alignment should take place. This is
-usually done at the equal signs, although it is not necessary to do
-so. For example
-\TeXref{190--192}
-\toindex{eqalign}
-
-\beginliteral
-$$\eqalign{
-a+b &= c+d \cr
-x &= w + y + z \cr
-m + n + o + p &= q \cr
-}$$
-@endliteral
-
-
-\noindent
-yields
-$$\eqalign{
-a+b &= c+d \cr
-x &= w + y + z \cr
-m + n + o + p &= q \cr
-}$$
-
-Displayed equations can be numbered at either the right or left
-margin. When the control word {\tt \\eqno} appears in a displayed
-equation, everything after the control word is put at the right
-margin. Hence {\tt \$\$ x+y=z. \\eqno (1)\$\$} yields
-$$ x+y=z. \eqno (1)$$
-To number an equation at the left margin, use {\tt \\leqno}
-in place of {\tt \\eqno}.
-\toindex{eqno}
-\toindex{leqno}
-
-It's possible to number aligned equations by using the control
-word {\tt \\eqalignno}. The alignment character {\tt \&} is
-used to separate the equation from the equation number.
-\beginliteral
-$$\eqalignno{
-a+b &= c+d & (1) \cr
-x &= w + y + z \cr
-m + n + o + p &= q & * \cr
-}$$
-@endliteral
-
-\noindent
-yields
-$$\eqalignno{
-a+b &= c+d & (1) \cr
-x &= w + y + z \cr
-m + n + o + p &= q & * \cr
-}$$
-
-Use {\tt \\leqalignno} to put the equation numbers on the left.
-\TeXref{192--193}
-\toindex{eqalignno}
-\toindex{leqalignno}
-
-Finally, suppose some text needs to appear in the middle of a
-displayed equation. This can be done by putting it in an hbox.
-We will describe hboxes in more detail in the next section.
-For now we want to use them to temporarily resume using ordinary
-roman type and to also allow the insertion of space between
-words (remember that all spaces are ignored when typesetting
-mathematics). Hence
-{\tt \$\$X=Y \\hbox\lb{} if and only if \rb x=y.\$\$} will give
-$$X=Y \hbox{ if and only if } x=y.$$
-Note carefully the spaces in the hbox.
-
-\exercise Do some of the challenge problems on pages 180--181 of The
-\TeX book.
-
-
-
-
-\section{All in a row}
-
-It's not uncommon to want to put a table in the middle of some
-text. Fortunately \TeX{} makes it easy to do this. In fact there
-are two separate methods of aligning text. The first is by using
-the tabbing environment. This is similar to setting the tab
-stops on a typewriter. Each line is handled individually,
-according to set tab columns, but with greater flexibility than
-that provided by a typewriter. The second is the horizontal
-alignment environment which typesets the whole table at once
-using a prescribed pattern.
-
-\subsection{Picking up the tab}
-
-To align material using the tabbing environment, you must first
-set the tab positions using the {\tt \\settabs} control word.
-Having done this, a line to use these tabs starts with the
-control symbol {\tt \\+ } and ends with {\tt \\cr } (remember
-that the actual spacing on lines in the input file in
-unimportant). \toindex{settabs}
-
-The easiest way to use the {\tt \\settabs} control word is to put
-the text into equal columns.
-\TeXref{231}
-Using {\tt \\settabs 4 \\columns} will set the tabs that will
-produce four equal columns. The tabbing is then done by using
-the alignment character {\tt \&} to move to the next tab stop.
-So, for example, \toindex{columns}
-
-\beginliteral
-\settabs 4 \columns
-\+ British Columbia & Alberta & Saskatchewan & Manitoba \cr
-\+ Ontario & Quebec & New Brunswick & Nova Scotia \cr
-\+ & Prince Edward Island & Newfoundland \cr
-@endliteral
-
-
-\noindent
-will produce the table
-\vskip\baselineskip
-
-\settabs 4 \columns
-\+ British Columbia & Alberta & Saskatchewan & Manitoba \cr
-\+ Ontario & Quebec & New Brunswick & Nova Scotia \cr
-\+ & Prince Edward Island & Newfoundland \cr
-
-Notice that it is possible to skip over some tab positions, and
-it is not necessary to use all of the tabs in a given line. To
-make the same table using five columns, it is only necessary to
-use {\tt \\settabs 5 \\columns} to reset the tab stops; then the
-same three lines from the last example will produce:
-\vskip\baselineskip
-
-\settabs 5 \columns
-\+ British Columbia & Alberta & Saskatchewan & Manitoba \cr
-\+ Ontario & Quebec & New Brunswick & Nova Scotia \cr
-\+ & Prince Edward Island & Newfoundland \cr
-
-In this example, the columns are smaller, of course. In fact
-there are two overlapping entries in the last row. This is
-because \TeX{} will tab to the next tab position even if (unlike
-a typewriter) it means going backward on the page.
-
-There is an interesting relationship between grouping and
-tabbing. The {\tt \\settabs} values are only applicable to the
-group in which it is defined, as would be expected. Thus it is
-possible to temporarily change the tab settings by grouping
-within braces. In addition, each table entry is in a group of
-its own. Hence we may make a single entry boldface, for example,
-by using {\tt \\bf} without braces. In addition, for any column
-but the last one it is possible to \centre{} the entry or to
-align it either on the left or on the right, or to fill a column
-with a line or dots. Each entry has an implicit {\tt \\hfil} at
-the end so that it will be at the left of the column by default.
-Adding {\tt \\hfil} at the beginning of the entry will then cause
-it to be \centred{}, just as with the {\tt \\line} control word.
-Adding {\tt \\hfill} to the beginning will cause the entries to
-be pushed to the right ({\tt \\hfill} acts just like {\tt \\hfil}
-in that it absorbs excess space; when both {\tt \\hfil} and {\tt
-\\hfill} appear, the {\tt \\hfill} takes precedence).
-\toindex{hfill}
-
-\beginliteral
-\settabs 4 \columns
-\+ \hfil British Columbia & \hfill Alberta \qquad & \bf Saskatchewan
-@hskip 2.5in & Manitoba \cr
-\+ \hfil Ontario & \hfill Quebec \qquad & \bf New Brunswick
-@hskip 2.5in & Nova Scotia \cr
-\+ \hfil --- & \hfill * \qquad & \bf Newfoundland
-@hskip 2.5in & Prince Edward Island \cr
-\+ \dotfill && \hrulefill & \cr
-@endliteral
-
-\noindent
-will produce a table with the first column \centred{}, the second
-column flush right with a {\tt \\qquad} of padding, and the third
-column boldface. The control words {\tt \\dotfill} and {\tt \\hrulefill}
-give alternative column entries.
-\toindex{dotfill}
-\toindex{hrulefill}
-\vskip\baselineskip
-
-\settabs 4 \columns
-\+ \hfil British Columbia & \hfill Alberta \qquad & \bf Saskatchewan
- & Manitoba \cr
-\+ \hfil Ontario & \hfill Quebec \qquad & \bf New Brunswick
- & Nova Scotia \cr
-\+ \hfil --- & \hfill * \qquad & \bf Newfoundland &
- Prince Edward Island \cr
-\+ \dotfill && \hrulefill & \cr
-
-\exercise Take the table of Canadian provinces above and \centre{} each
-entry within its column.
-
-The tab positions can be set with much more flexibility than just
-in equal columns. The general pattern is to use a sample line of
-the form {\tt \\settabs \\+ $\ldots$ \& $\ldots$ \& $\ldots$ \\cr}.
-The spacing between the alignment characters {\tt \&}
-determines the position of the tabs. For example, {\tt \\settabs
-\\+ \\hskip 1 in \& \\hskip 2 in \& \\hskip 1.5 in \& \\cr} would
-set the first tab one inch from the left margin, the next another
-two inches further in, and the third 1.5 inches more. It's also
-possible to use text to determine the distance between tabs. So,
-for example, another possible sample line is
-{\tt \\settabs \\+ \\quad Province \\quad \& \\quad Population \\quad
-\& \\quad Area \\quad \& \\cr}.
-The tab column would then be just wide enough to accept the headings
-with a quad of space on each side. Here's a more complete example:
-
-\beginuser \obeyspaces
-\\settabs \\+ \\quad Year \\quad \& \\quad Price \\quad
- \& \\quad Dividend \& \\cr
-\\+ \\hfill Year \\quad \& \\quad Price \\quad \& \\quad Dividend \\cr
-\\+ \\hfill 1971 \\quad \& \\quad 41--54 \\quad \& \\qquad \\\$2.60 \\cr
-\\+ \\hfill 2 \\quad \& \\quad 41--54 \\quad \& \\qquad \\\$2.70 \\cr
-\\+ \\hfill 3 \\quad \& \\quad 46--55 \\quad \& \\qquad \\\$2.87 \\cr
-\\+ \\hfill 4 \\quad \& \\quad 40--53 \\quad \& \\qquad \\\$3.24 \\cr
-\\+ \\hfill 5 \\quad \& \\quad 45--52 \\quad \& \\qquad \\\$3.40 \\cr
-\enduser
-
-\noindent
-gives \TeXref{247}
-\vskip\baselineskip
-
-\settabs \+ \quad Year \quad & \quad Price \quad & \quad
-Dividend \quad & \cr
-\+ \hfill Year \quad & \quad Price \quad & \quad Dividend \cr
-\+ \hfill 1971 \quad & \quad 41--54 \quad & \qquad \$2.60 \cr
-\+ \hfill 2 \quad & \quad 41--54 \quad & \qquad \$2.70 \cr
-\+ \hfill 3 \quad & \quad 46--55 \quad & \qquad \$2.87 \cr
-\+ \hfill 4 \quad & \quad 40--53 \quad & \qquad \$3.24 \cr
-\+ \hfill 5 \quad & \quad 45--52 \quad & \qquad \$3.40 \cr
-
-\exercise Take the table given above and move it closer to the
-\centre{} of the page.
-
-\exercise One way to \centre{} a block of text, possibly several
-lines long, is to use: {\tt \$\$\\vbox\lb$\ldots$\rb\$\$}. Use
-this to \centre{} the table given above. Does the
-{\tt \\settabs} line need to be included in the {\tt \\vbox}?
-
-\exercise Improve your last result by putting a line under the
-column heads. The control word {\tt \\hrule} will insert a
-horizontal line if introduced between two rows of a table. Now
-repeat with the control word {\tt \\strut} after the {\tt \\+ }
-of the line containing the column heads. (A {\tt \\strut}
-effectively makes the spacing between lines a little greater. The
-size can be altered from the default.)\TeXref{82} Note the extra
-space that results.
-\toindex{strut}
-
-\exercise Make the following table with decimal alignment, that
-is, with the decimal points above each other (think of the dollar
-figure as being right aligned and the cents figure as being left
-aligned against the decimal point):
-\medskip
-\settabs \+ \hskip 2 in & \hskip .75in & \hskip 1cm& \cr
-\+ &Plums &\hfill\$1&.22 \cr
-\+ &Coffee &\hfill1&.78 \cr
-\+ &Granola &\hfill1&.98 \cr
-\+ &Mushrooms & &.63 \cr
-\+ &{Kiwi fruit} & &.39 \cr
-\+ &{Orange juice} &\hfill1&.09 \cr
-\+ &Tuna &\hfill1&.29 \cr
-\+ &Zucchini & &.64 \cr
-\+ &Grapes &\hfill1&.69 \cr
-\+ &{Smoked beef} & &.75 \cr
-\+ &Broccoli &\hfill\underbar{\ \ 1}&\underbar{.09} \cr
-\+ &Total &\hfill \$12&.55 \cr
-
-
-\exercise Devise a method to make a rough table of contents by using
-{\tt \\settabs} and having entries looking something like:\hfil\break
-\leftline{\tt Getting Started \\dotfill \& \\hfill 1}
-\leftline{\tt All Characters Great and Small \\dotfill \& \\hfill 9.}
-
-\subsection{Horizontal alignment with more sophisticated patterns}
-
-The {\tt \\settabs} environment is not difficult to use, and once
-the pattern is set, it can be used repeatedly in different
-portions of the text that follows. It does have some drawbacks,
-however. For one, the column size must be set before the entries
-are known. Also, even though in one case we wanted the third
-column to be boldface, it had to be specified in each line.
-These problems can be handled more easily by using the {\tt
-\\halign} environment.
-\TeXref{235--238}
-\toindex{halign}
-
-
-The general pattern in the {\tt \\halign} is as follows:
-\beginuser
-\\halign\lb{} <template line> \\cr
-<first display line> \\cr
-<second display line> \\cr
-$\vdots$
-<last display line> \\cr
-\rb
-\enduser
-
-Both the template line and the display lines are divided into
-sections by the alignment symbol {\tt \&}\null. In the template
-line each section uses control words in the same manner as does
-{\tt \\line\lb\rb}\null. The control word {\tt \\hfil}, for
-example, can be used to display flush left, flush right, or \centred.
-Fonts can be changed using {\tt \\bf}, {\tt \\it}, etc.
-Text may also be entered in the template line. In addition the
-special symbol {\tt \#} must appear once in each section. Each
-display line is then set by substituting each section of the
-display line into its corresponding section of the template line
-at the occurrence of the {\tt \#}\null.
-
-Consider the following example:
-
-\beginuser
-\\halign\lb\\hskip 2 in \$\#\$\& \\hfil \\quad \# \\hfil \& \\qquad \$\#\$
- \hskip 3in \& \\hfil \\quad \# \\hfil \\cr
-\\alpha \& alpha \& \\beta \& beta \\cr
-\\gamma \& gamma \& \\delta \& delta \\cr
-\\epsilon \& epsilon \& \\zeta \& zeta \\cr
-\rb
-\enduser
-
-\noindent The template line indicates that the first section of
-the typeset text will always be set two inches in from the left
-and also be set as mathematics. The second section will be \centred{}
-after adding a quad of space on the left. The third
-and fourth sections are handled similarly. Here is the result:
-\vskip\baselineskip
-
-\halign{\hskip 2in $#$& \hfil\quad # \hfil & \qquad $#$
- & \hfil\quad # \hfil\cr
-\alpha & alpha & \beta & beta \cr
-\gamma & gamma & \delta & delta \cr
-\epsilon & epsilon & \zeta & zeta \cr
-}
-
-In this case the first display line is formed by substituting {\tt
-\\alpha} for the first {\tt \#} in the template line, {\tt alpha} for
-the second {\tt \#}, {\tt \\beta} for the third and {\tt beta} for
-the fourth. The whole line is then saved for setting. This
-continues until all the lines are accumulated, and then they are set
-with each column being as wide as necessary to accept all of its
-entries (an implication of this accumulation process is that a table
-with too many entries could cause \TeX{} to run out of memory; it's
-better not to set tables that are more than a page or so long).
-
-Hence the template line establishes the pattern for the table entries
-and the display lines insert the individual entries.
-
-Sometimes horizontal and vertical lines are used to delimit
-entries in a table. To put in horizontal lines, we use {\tt \\hrule},
-just as we did in the {\tt \\settabs} environment.
-However, we don't want the rule to be aligned according to the
-template, so we use the control word {\tt \\noalign}. Hence
-horizontal lines are inserted by putting {\tt \\noalign\lb\\hrule\rb};
-vertical lines are inserted by putting {\tt \\vrule}
-in either the template or the display line. But still all is not
-completely straightforward. Suppose we take our last example and
-change the template to get vertical lines and also insert
-horizontal lines.
-\toindex{noalign}
-
-\beginuser
-\\halign\lb\\hskip 2in\\vrule\\quad \$\#\$\\quad \& \\vrule \\hfil\\quad %
-\# \\hfil
-\hskip 2 in \& \\quad \\vrule \\quad \$\#\$\\quad
-\hskip 2 in \& \\vrule\\hfil \\quad \# \\quad \\hfil \\vrule \\cr
-\\noalign\lb\\hrule\rb
-\\alpha \& alpha \& \\beta \& beta \\cr
-\\noalign\lb\\hrule\rb
-\\gamma \& gamma \& \\delta \& delta \\cr
-\\noalign\lb\\hrule\rb
-\\epsilon \& epsilon \& \\zeta \& zeta \\cr
-\\noalign\lb\\hrule\rb
-\rb
-\enduser
-
-\noindent
-doesn't give exactly what we want.
-
-\vskip\baselineskip
-
-\halign{\hskip 2in\vrule\quad $#$\quad & \vrule \hfil\quad # \hfil
-& \quad \vrule \quad $#$\quad & \vrule \hfil\quad # \quad \hfil
-\vrule \cr
-\noalign{\hrule}
-\alpha & alpha & \beta & beta \cr
-\noalign{\hrule}
-\gamma & gamma & \delta & delta \cr
-\noalign{\hrule}
-\epsilon & epsilon & \zeta & zeta \cr
-\noalign{\hrule}
-}
-
-There are several deficiencies: the most obvious is the extended
-horizontal lines, but also the text looks somewhat squashed into
-the boxes. In addition, the text has a little extra space on the
-right rather than being perfectly \centred. As in the {\tt \\settabs}
-environment, lines can be made taller by including the control
-word {\tt \\strut} in the template.\TeXref{82} A further problem
-can occur when the page is set since \TeX{} may spread lines
-apart slightly to improve the appearance of the page. This would
-leave a gap between the vertical lines, so we use the control
-word {\tt \\offinterlineskip} within the {\tt \\halign} to avoid
-this. Finally we can get rid of the lines sticking out on the
-left by deleting the {\tt \\hskip 2 in} from the template line.
-To move the table to the same position we use {\tt \\moveright}.
-Finally, we can see how to \centre{} the text by noting that the
-extra space occurs in the template line after the {\tt \#} where
-the text is inserted.
-Hence we can improve our result by using
-\toindex{offinterlineskip}
-\toindex{moveright}
-
-\beginuser
-\\moveright 2 in
-\\vbox\lb\\offinterlineskip
-
-\\halign\lb\\strut \\vrule \\quad \$\#\$\\quad \&\\vrule \\hfil \\quad %
-\#\\quad \\hfil
-\&\\vrule \\quad \$\#\$\\quad \&\\vrule \\hfil \\quad \#\\quad \\hfil %
-\\vrule \\cr
-\\noalign\lb\\hrule\rb
-\\alpha \& alpha \& \\beta \& beta \\cr
-\\noalign\lb\\hrule\rb
-\\gamma \& gamma \& \\delta \& delta \\cr
-\\noalign\lb\\hrule\rb
-\\epsilon \& epsilon \& \\zeta \& zeta \\cr
-\\noalign\lb\\hrule\rb
-\rb\rb
-\enduser
-
-\noindent
-to get
-\vskip\baselineskip
-
-\moveright 2 in
-\vbox{\offinterlineskip
-\halign{\strut \vrule \quad $#$\quad &\vrule \hfil \quad #\quad \hfil
-&\vrule \quad $#$\quad &\vrule \hfil \quad #\quad \hfil
-\vrule \cr
-\noalign{\hrule}
-\alpha & alpha & \beta & beta \cr
-\noalign{\hrule}
-\gamma & gamma & \delta & delta \cr
-\noalign{\hrule}
-\epsilon & epsilon & \zeta & zeta \cr
-\noalign{\hrule}
-}
-}
-
-
-
-In general, if we want to construct a table with boxed entries
-that is \centred{} on the page, we can do so by putting the {\tt
-\\vbox} within a {\tt \\centerline\lb\rb}\null. But here is a
-trick that will produce a nicer result. If the {\tt \\vbox} is
-put in between double dollar signs, it will be typeset as
-displayed mathematics. Of course, there is no actual
-mathematics being displayed, but \TeX{} will put in a little
-extra space above and below the table as is appropriate for a
-display. Hence a \centred{} table with this nice spacing may be
-formed using the following four steps:
-(1) put a {\tt \\vbox} between double dollar signs,
-(2) put an {\tt \\offinterlineskip} and an {\tt \\halign} within
-the {\tt \\vbox},
-(3) in the {\tt \\halign} put a template line with a {\tt \\strut}
-in the beginning, and a {\tt \\vrule} surrounding each entry,
-(4) each row of the table should be preceded and followed by
-{\tt \\noalign\lb\\hrule\rb}.
-
-Here is the pattern to be followed:
-
-\beginuser
-\$\$\\vbox\lb
-\\offinterlineskip
-\\halign\lb
-\\strut \\vrule \# \& \\vrule \# \& \dots \& \\vrule \# \\vrule \\cr
-\\noalign\lb\\hrule\rb
-<first column entry> \& <second column entry> \& \dots %
-\& <last column entry> \\cr
-\\noalign\lb\\hrule\rb
-\dots
-\\noalign\lb\\hrule\rb
-<first column entry> \& <second column entry> \& \dots %
-\& <last column entry> \\cr
-\\noalign\lb\\hrule\rb
-\rb
-\rb\$\$
-\enduser
-
-
-
-\section{Rolling your own}
-
-In this section we'll create new control words. The making of
-these new definitions, also called macros, is one of the most
-powerful techniques available in \TeX\null. For the first
-application of this facility, we'll see how a new definition can
-save a lot of typing by substituting short strings for long ones.
-
-\subsection{The long and short of it}
-
-The control word {\tt \\def} is used to define new control words.
-The simplest form for doing this is {\tt \\def\\newname\lb$\ldots$\rb}.
-Then whenever {\tt \\newname} appears in your
-input file, it will be replaced by whatever is between the braces
-in the definition. Of course {\tt \\newname} must satisfy the
-convention for naming control sequences, that is, it must be a
-control word (all letters) or a control symbol (exactly one
-nonletter). So, for example, suppose you write a document that
-contains the phrase ``University of Manitoba'' many times. Then
-{\tt \\def\\um\lb University of Manitoba\rb} defines a new
-control sequence {\tt \\um} which can then be used at any time.
-The sentence {\tt I take courses at the \\um.}\ then makes
-sense. If the control word exists, your new definition will
-replace it (this includes the control words defined by \TeX{}, so
-a little care must be taken in the choice of name). Any
-definition is, however, local to the group in which it is
-defined. For example, \toindex{def}
-
-\beginuser
-\\def\\um\lb University of Manitoba\rb
-I took my first course at the \\um.
-\lb
-\\def\\um\lb Universit\\'e de Montr\\'eal\rb
-Then I took my next course at the \\um.
-\rb
-Finally I took my last course at the \\um.
-\enduser
-
-\noindent gives \medskip
-
-\def\um{University of Manitoba}
-I took my first course at the \um.
-{
-\def\um{Universit\'e de Montr\'eal}
-Then I took my next course at the \um.
-}
-Finally I took my last course at the \um.
-
-Remember that all spaces after a control word are absorbed; this
-includes the control words that you define. In the previous
-example, any space after {\tt \\um} would be ignored. However,
-the space after the first period and the space after the first
-opening brace are different; if you look closely at the end of
-the first sentence typeset using the example, you'll see some
-extra space. This can be eliminated by putting a {\tt \%} after
-the opening brace to make the rest of the line a comment. The
-same holds for the line with the last closing brace. Careful
-control of spaces often calls for the ``commenting out'' of the
-end of lines in this manner.
-
-Once a new control sequence has been defined, it may be used in
-new definitions. This is one way of making simple form letters.
-First let's define a simple letter.
-
-\beginuser
-\\def\\letter\lb
-\\par \\noindent
-Dear \\name,
-\
-This is a little note to let you know that your name is \\name.
-\
-\\hskip 2 in Sincerely yours,
-\\vskip 2\\baselineskip
-\\hskip 2 in The NameNoter
-\\smallskip \\hrule
-\rb
-\enduser
-
-\def\letter{
-\par \noindent
-Dear \name,
-
-This is a little note to let you know that your name is \name.
-
-\hskip 2 in Sincerely yours,
-\vskip 2\baselineskip\nobreak
-\hskip 2 in The NameNoter
-\smallskip \hrule
-}
-
-Now this letter uses the control word {\tt \\name}, which is
-undefined at this point. When {\tt \\letter} is used, the
-current value of {\tt \\name} will appear in the body of the
-letter. Hence
-
-\beginuser
-\\def\\name\lb Michael Bishop\rb
-\\letter
-\\def\\name\lb Michelle L\\'ev\\\^{}eque\rb
-\\letter
-\enduser
-
-\noindent will produce two copies of the letter, each with the
-correct name, followed by a horizontal rule:
-
-\def\name{Michael Bishop}
-\letter
-\goodbreak
-\def\name{Michelle L\'ev\^eque}
-\letter
-
-We could have put anything between the braces in
-{\tt \\def\\name\lb$\ldots$\rb}; it could be several paragraphs
-long and use other control sequences (although in this context it
-would be a little strange). Of course it is possible to use {\tt
-\\vfill \\eject} as part of the definition of {\tt \\letter} to
-eject the page when the letter is completed.
-
-\exercise Make a form letter that uses the control words {\tt \\name},
-{\tt \\address}, {\tt \\city}, {\tt \\\province}, and {\tt
-\\\postcode}.
-
-\exercise An unnumbered list of items is often made
-using {\tt \\item\lb\$\\bullet\$\rb}. Define a macro {\tt \\bitem}
-that does this, and use it for several paragraphs. Now change
-each bullet to a dash (note that a simple change in the macro
-propagates all the necessary changes in all of the paragraphs).
-
-\exercise Suppose that you are going to have to format several
-paragraphs in a paper using {\tt \\hangindent = 30 pt}, {\tt \\hangafter
-= 4}, and {\tt \\filbreak} (don't worry about what
-these control sequences actually do; the only important thing
-for now is that once they are set, they remain in effect for only
-one paragraph). Define a single control sequence {\tt \\setpar}
-which can then be put in front of each paragraph that needs to be
-so formatted.
-
-
-\subsection{Filling in with parameters}
-
-It's possible to use macros in much greater generality by
-allowing parameters to be passed. The idea is somewhat similar
-to the template line in the {\tt \\halign} environment. First,
-let's look at the case where there is one parameter. In this
-case a control sequence is defined by {\tt \\def\\newword\#1\lb
-$\ldots$\rb}\null. The symbol {\tt \#1} may appear between the
-braces (several times) in the definition of {\tt \\newword}. The
-material between the braces acts like a template. When {\tt
-\\newword\lb$\ldots$\rb} appears in the text, it will use the
-definition of {\tt \\newword} with the material between the
-braces inserted into the template at every occurrence of {\tt
-\#1} in the original definition. {\bf The spacing in the original
-definition is crucial here; there must be no spaces before the
-opening brace}.
-
-As an example, we could use the form letter of the last section in
-the following way:
-
-
-\beginuser
-\\def\\letter\#1\lb
-\\par \\noindent
-Dear \#1,
-\vskip\baselineskip
-This is a little note to let you know that your name is \#1.
-\vskip\baselineskip
-\\hskip 2 in Sincerely yours,
-\\vskip 2\\baselineskip
-\\hskip 2 in The NameNoter
-\\smallskip \\hrule
-\rb
-\enduser
-
-\def\letter#1{
-\par \noindent
-Dear #1,
-
-This is a little note to let you know that your name is #1.
-
-\hskip 2 in Sincerely yours,
-\vskip 2\baselineskip
-\hskip 2 in The NameNoter
-\smallskip \hrule
-}
-
-Now we can use
-
-\beginuser
-\\letter\lb Michael Bishop\rb
-\\letter\lb Michelle L\\'ev\\\^{}eque\rb
-\enduser
-
-\noindent to get \medskip
-\letter{Michael Bishop}
-\goodbreak
-\letter{Michelle L\'ev\^eque}
-
-\def\displaytext#1{$$\vbox{\hsize=12cm #1}$$}
-\bigskip
-\displaytext{
-Now let's define
-{\tt\\def\\displaytext\#1\lb \$\$\\vbox\lb\\hsize = 12 cm \#1\rb\$\$\rb}
-as a new macro to display text.
-Then {\tt \\displaytext\lb$\ldots$\rb} will cause the material
-between the braces to be put in a paragraph with width 12 \centimetre
-s and then \centred{} with some space added above and
-below as is appropriate for a display. This paragraph was set
-using this {\tt \\displaytext} macro.
-}
-
-The parameter of a macro can be no more than one paragraph long.
-If a new paragraph is encountered as part of a parameter, an
-error will be generated. This is a safety feature, for
-otherwise the accidental omission of a closing brace would cause
-\TeX{} to eat up the rest of the file as the parameter.
-
-\exercise Define a macro {\tt \\yourgrade} so that {\tt
-\\yourgrade\lb89\rb} will cause the following sentence to be
-typeset: The grade you received is 89\%\null. It should be able
-to work with any other percentage, of course.
-\medbreak
-
-It's not really any harder to use more than one parameter. The form
-used to define a new control word with two parameters is
-{\tt \\def\\newword\#1\#2\lb$\ldots$\rb}. The definition between the
-braces may have {\tt \#1} and {\tt \#2} occurring in it, perhaps
-several times. When {\tt \\newword\lb$\ldots$\rb\lb$\ldots$\rb}
-appears in the text, the material between the first set of braces
-replaces {\tt \#1} in the definition and the material between the
-second set of braces replaces {\tt \#2} in the definition. Here is
-an example followed by its result:
-
-\beginuser
-\\def\\talks\#1\#2\lb \#1 talks to \#2.\rb
-\\talks\lb John\rb\lb Jane\rb
-\\talks\lb Jane\rb\lb John\rb
-\\talks\lb John\rb\lb me\rb
-\\talks\lb She\rb\lb Jane\rb
-\enduser
-
-\def\talks#1#2{#1 talks to #2.}
-\talks{John}{Jane}
-\talks{Jane}{John}
-\talks{John}{me}
-\talks{She}{Jane}
-
-\exercise In a manner similar to the previous exercise, define a
-macro {\tt \\yourgrade} so that {\tt \\yourgrade\lb89\rb\lb85\rb}
-causes the following sentence to be typeset: You received a grade
-of 89\% on your first exam and a grade of 85\% on your second
-exam.
-
-\exercise Write a macro {\tt \\frac} so that {\tt \\frac\lb
-a\rb\lb b\rb} will typeset the fraction ${a\over b}$.
-
-\bigskip
-It's important not to put any spaces before the first brace in
-the definition. If you do, \TeX{} will interpret the definition
-differently from the way described here. For more than two
-parameters, the method of definition is similar. To define a
-control word with three parameters, start with
-{\tt \\def\\newword\#1\#2\#3\lb$\ldots$\rb}. Then {\tt \#1},
-{\tt \#2} and {\tt \#3} may occur between the braces. When
-{\tt \\newword\lb$\ldots$\rb\lb$\ldots$\rb\lb$\ldots$\rb}
-appears in the text, the material between each set of braces
-replaces its corresponding symbol in the definition of the
-control word. The parameters may go up to {\tt \#9}.
-
-\subsection{By any other name}
-
-Sometimes it's convenient to be able to give a control word an
-alternative name. For example, if you prefer a different spelling,
-you might want to call the control word {\tt \\centerline} by the
-name of {\tt \\centreline}. This can be done by using the {\tt
-\\let} control word. The use of {\tt \\let \\centreline =
-\\centerline} now makes a new (as well as the old) control word
-available. This can also be used with mathematical names as with
-{\tt \\let \\tensor = \\otimes}. It is then possible to use
-\TeXref{206--207}
-
-\toindex{let}
-\toindex{centreline}
-\toindex{tensor}
-
-\let\tensor=\otimes
-\beginuser
-\$\$ (A \\tensor B) (C \\tensor D) = AC \\tensor BD. \$\$
-\enduser
-
-\noindent to get
-
-$$ (A \tensor B) (C \tensor D) = AC \tensor BD. $$
-
-
-
-\exercise Define control sequences {\tt \\ll}, {\tt \\cl}, and
-{\tt \\rl} that are equivalent to {\tt \\leftline}, {\tt \\centerline},
-and {\tt \\rightline}.
-
-The {\tt \\let} control word allows users to name their own
-control sequences. This allows a personalized set of control
-sequences that may be used in place of the ones provided by \TeX{}
-when desired.
-
-\section{To err is human}
-
-In some ways \TeX{} is not completely divine. \TeX{} will respond
-to invalid input by giving an error message to the screen if you
-are using it interactively and also to the log file. Because
-\TeX{} is very complicated, the actual point where the error is
-detected may be deep within the program, so a full report of the
-error may be rather long and involved. Not only that, \TeX{}
-will try to recover from errors, and will report what was done in
-that process. For this reason the reading of error messages may
-be a little difficult for the uninitiated. The key is to know
-what is important from your perspective and what can be safely
-ignored. So let's look at some typical errors and the messages
-that they generate.
-
-\subsection{The forgotten bye}
-
-The first mistake that we'll look at is one that everyone makes
-at some time, namely, the omission of {\tt \\bye} at the end of
-the file. If you're using \TeX{} interactively, an asterisk \hfil
-\break
-\leftline{\tt *}
-will be printed on the screen and nothing will happen since,
-having not been told to finish up, \TeX{} is waiting for input
-(from your keyboard). Whatever you type in will be appended to
-whatever has been input from your files. The usual response is
-to type {\tt \\bye<CR>}\fnote{{\tt <CR>} is the key
-used to end a line of input. It might be called the carriage
-return, enter, or simply the return key on your terminal.
-Sometimes it is indicated by a large left arrow.} since that will
-finish things up.
-
-\subsection{The misspelled or unknown control sequence}
-
-Using a misspelled or other control sequence unknown to \TeX{} is
-a common error. If \TeX{} is being run as a batch job, an error
-message is printed and the job goes on ignoring the control
-sequence. When using \TeX{} interactively, it is possible to
-repair errors (of course this does not change the original input
-file, so that must be done when the \TeX{} job is completed).
-Suppose we have a \TeX{} input file consisting of the following
-two lines:
-\beginuser
-\\line\lb The left side \\hfli the right side\rb
-\\bye
-\enduser
-
-The control word should be {\tt \\hfil}, of course. Here is the
-message that would be sent to your terminal:
-
-\beginuser
-\obeyspaces
-! Undefined control sequence.
-l.1 \\line\lb The left side \\hfli
-\ the right side\rb
-?
-\enduser
-
-The first line starts with {\tt !} and gives the error message.
-Next comes the line number on which the error occurred and the
-part of the line that was read successfully. The next line gives
-the continuation of the line after the error. At this point the
-question mark means that \TeX{} is waiting for a response. There
-are several legal ones:
-\nobreak
-\maketable [Responses to \TeX{} error messages]
-\halign{
-\strut \hfil # \hfil & \quad \hfil \tt # \hfil & # \hfil\cr
- \bf Desired response & \bf Input to \TeX{} & \bf \hfil Result\cr
- \noalign{\hrule} \noalign{\smallskip}
- Help & h<CR>& Reason for stopping listed on terminal.\cr
- Insert & i<CR>& Next line inserted into \TeX{} input file.\cr
- Exit & x<CR>& Exit from \TeX\null. Completed pages to DVI file.\cr
- Scroll & s<CR>& List message and continue after minor errors.\cr
- Run & r<CR>& List message and continue after any errors.\cr
- Quiet & q<CR>& All terminal listings suppressed.\cr
- Carry on &<CR> & \TeX{} continues as best it can.\cr
- }
-
-In our last example a reasonable response might be to enter {\tt
-h<CR>} to get a help message, then {\tt i<CR>} to insert more
-text, (at which point \TeX{} responds with {\tt insert> } and
-finally {\tt \\hfil} as the correct control word. Here is the
-result:
-
-
-\beginuser
-? h <CR>
-The control sequence at the end of the top line
-of your error message was never \\def'ed. If you have
-misspelled it (e.g., `\\hobx'), type `I' and the correct
-spelling (e.g., `I\\hbox'). Otherwise just continue,
-and I'll forget about whatever was undefined.
-
-? i <CR>
-insert>\\hfil
-[1]
-\enduser
-
-The final {\tt [1]} means that the first (and only) page has
-been completed and sent to the DVI file. The original input file
-still needs to be fixed, of course.
-
-\subsection{The misnamed font}
-
-A misspelled font name is an error similar to the misspelled
-control sequence. The error message is different and a little
-confusing at first. Suppose for example the following appears in
-your input file:
-
-\leftline{\tt \\font\\sf = cmss01}
-
-It should be {\tt cmss10}, that is, the numbers have been
-transposed. Here are the error and help messages:
-
-\beginuser \obeyspaces
-! Font \\sf=cmss01 not loadable: Metric (TFM) file not found.
-<to be read again>
-\ \\par
-\\bye ->\\par
-\ \\vfill \\supereject \\end
-l.2 \\bye
-
-? h <CR>
-I wasn't able to read the size data for this font,
-so I will ignore the font specification.
-[Wizards can fix TFM files using TFtoPL/PLtoTF.]
-You might try inserting a different font spec;
-e.g., type `I\\font<same font id>=<substitute font name>'.
-\enduser
-
-The TFM (\TeX{} font metric) file is an auxiliary file that is
-used by \TeX\null. So this strange message is just telling you
-that the font you defined doesn't exist on your computer system.
-
-\subsection{Mismatched mathematics}
-
-Another common error is to use {\tt \$} or {\tt \$\$} to start a
-mathematical expression and then to forget the second {\tt \$}
-or {\tt \$\$} when finished. The text that follows is then
-treated as mathematics, and to make matters worse, if more
-mathematics is started by a new {\tt \$} or {\tt \$\$}, it will
-then be treated as ordinary text. Needless to say, error
-messages galore may be generated. \TeX{} will attempt to correct
-the problem by inserting a new {\tt \$} or {\tt \$\$}; in any
-case, the problem is corrected by the end of the paragraph since
-a new paragraph will automatically start as ordinary text.
-
-Consider the following correct input and its output:
-\beginuser
-Since \$f(x) > 0\$, \$a<b\$, and \$f(x)\$ is continuous, we know that
-\$\\int\_{}a\^{}b f(x)\\,dx >0\$.
-\enduser
-
-Since $f(x) > 0$, $a<b$, and $f(x)$ is continuous, we know that
-$\int_a^b f(x)\,dx >0$.
-
-If we now leave out the second dollar sign in {\tt \$f(x)\$} we
-then get the following error and help messages:
-
-\beginuser \obeyspaces
-! Missing \$ inserted.
-<inserted text>
-\ \$
-<to be read again>
-\ \\intop
-\\int ->\\intop
-\ \\nolimits
-l.2 \$\\int
-\ \_{}a\^{}b f(x)\\,dx >0\$.
-? h <CR>
-I've inserted a begin-math/end-math symbol since I think
-you left one out. Proceed, with fingers crossed.
-
-?
-\enduser
-
-The line starting with {\tt !} tells us what has been done. The
-line starting with {\tt l.2} shows us where we were in the input
-file when the error occurred. As in our other examples, the part
-of the line successfully read, that is, through {\tt \\int},
-appears on one line, and the continuation appears on the next
-line. The remaining material may seem somewhat obscure. These
-intermediate messages show what was happening further in the guts
-of the \TeX{} program when the error occurred. The newer user
-may ignore them.
-
-Here is what you get as output after \TeX{} tries to recover from
-the error.
-
-Since $f(x) > 0$, $a<b$, and $f(x) is continuous, we know that
-\int_a^b f(x)\,dx >0$.
-
-There is a stretch of text that is italic with no spacing. This
-is typical for normal text being processed as mathematics; if you
-see this in your output, you have almost certainly left out a
-{\tt \$} or {\tt \$\$}.
-
-\subsection{Mismatched braces}
-
-It's easy to forget or mismatch the closing braces when making
-groups. The result may be a relatively benign error, or it may
-be catastrophic. Suppose, for example, you have {\tt \lb\\bf A
-bold title } in your text with the closing right brace omitted.
-The result will be the same as if no opening brace were there;
-that is, the rest of the paper will be boldface if no other font
-changes are made. You will get the following message at the end
-of the file:
-
-{\tt (\\end occurred inside a group at level 1)}
-
-If you had made the same mistake twice, then there would be two
-more opening braces than closing braces, and you would get the
-message:
-
-{\tt (\\end occurred inside a group at level 2)}
-
-\TeX{} doesn't know that the closing brace is missing until it
-reaches the end of the input file. Hence the message doesn't
-tell you where you went wrong. If the location of the missing
-brace isn't obvious, it's always possible to insert {\tt \\bye}
-halfway through your document. Running \TeX{} again will cause
-only the first half to be processed, and if the error message
-persists, you will know that the error is in the first half of
-the document. By moving the {\tt \\bye} to different places, the
-error can be localized. Also, looking at the output often
-reveals what has gone wrong.
-
-Missing opening braces are much easier to spot. Here is a two
-line input file and the resulting error and help messages:
-
-\beginuser
-\\bf Here is the start\rb, but there is the finish.
-\\bye
-\enduser
-
-\beginuser \obeyspaces
-! Too many \rb's.
-l.1 \\bf Here is the start\rb
-\ , but there is the finish.
-
-? h <CR>
-You've closed more groups than you opened.
-Such booboos are generally harmless, so keep going.
-\enduser
-
-It's quite possible, of course, that the line that is supposed to
-have the missing left brace will not be on the line where \TeX{}
-catches the error.
-
-A mismatched brace in the definition of a new control sequence
-can cause a major error. Since such a definition may include
-several paragraphs, it may not be caught by the end of a
-paragraph, but, rather will just keep piling more and more text
-into the unfinished definition. It's even possible for \TeX{} to
-run out of memory as it keeps eating up more text! This is called
-a ``runaway definition''.
-\TeXref{206}
-Here is a two line input file with a runaway definition:
-
-\vbox{
-\beginuser
-\\def\\newword\lb the def
-\\newword
-\\bye
-\enduser
-}
-
-Here are the resulting error and help messages:
-
-\beginuser \obeyspaces
-Runaway definition?
-->the def
-! Forbidden control sequence found while scanning definition of \\newword.
-<inserted text>
-\ \rb
-<to be read again>
-\ \\bye
-l.3 \\bye
-
-? h <CR>
-I suspect you have forgotten a `\rb', causing me
-to read past where you wanted me to stop.
-I'll try to recover; but if the error is serious,
-you'd better type `E' or `X' now and fix your file.
-
-? <CR>
-No pages of output.
-\enduser
-
-This is obviously a serious error. If it occurs at the beginning
-of a file (as in the previous example), there will be no output
-at all!
-
-If a closing brace is left out while using a macro with
-parameters, the runaway definition will be terminated at the end
-of the paragraph. So if {\tt \\def\\newword\#1\lb$\ldots$\rb} has
-been defined and you use {\tt \\newword\lb$\dots$ } without the
-closing brace, then at most one paragraph will be ruined.
-\TeXref{205}
-
-In short, when an error occurs, make a note of the line number to
-see how much of the input file has been read, and also the line
-starting with an exclamation point to get a short description of
-the error. If the error is still not clear, ask \TeX{} for more
-information by typing {\tt h<CR>}. For small errors, \TeX{} can
-carry on quite a way if you just keep hitting the {\tt <CR>}.
-
-
-
-
-\section{Digging a little deeper}
-
-In this section we look at a few topics that allow \TeX{} to be
-used with greater flexibility or efficiency. As the documents
-being produced get longer, different techniques can help make
-their creation easier.
-
-\subsection{Big files, little files}
-
-\TeX{} can read and write files as it runs. This makes it
-possible to use files that are smaller and more convenient to
-handle by creating a master file that reads the smaller files in
-the proper order. This document, for example, consists of ten
-sections plus an introduction. In addition, there are macros
-that are used for all sections. The macros can be put in a file
-called, say, {\tt macros.tex}, the introduction can be put in {\tt
-intro.tex}, and each section put in its own file. The control
-word {\tt \\input} is then used to read in a file. In general,
-{\tt \\input filename} will cause the file called {\tt
-filename.tex} to be read in and processed immediately, just as if
-the text of {\tt filename.tex} had been part of the file that
-read it in. This file may input other files. In fact it's often
-convenient to make a single file that reads in smaller pieces,
-perhaps as follows:
-\toindex{input}
-
-\beginuser
-\\input macros
-\\input intro
-\\input sec1
-\\input sec2
-\\input sec3
-\\input sec4
-\\input sec5
-\\input sec6
-\\input sec7
-\\input sec8
-\\input sec9
-\\input sec10
-\enduser
-
-While the text is still being heavily edited, it's possible to
-process only some of the files by putting a {\tt \%} at the
-beginning of each line that contains a file to be skipped (this
-is sometimes called ``commenting out'' the unwanted files).
-
-The {\tt \\input} control word also allows the use of
-predesigned macros. The macros for a memorandum, for example,
-might be put in a file called {\tt memo.tex}. These macros might
-set up the right {\tt \\hsize}, {\tt \\vsize} and other
-parameters, and might stamp the time and date. Once this has
-been set up, all memoranda may be started with {\tt \\input memo}
-to make them come out with a common format.
-
-Be sure that you don't have the control word {\tt \\bye} in your
-input file or the \TeX{} program will stop at that point.
-
-\exercise Make a \TeX{} input file that reads in a second file.
-Try reading in the second file twice using the {\tt \\input}
-control word twice.
-
-\subsection{Larger macro packages}
-
-Designing macros that can be used with many types of documents
-is obviously useful. Most universities, for example, have
-specific and often complicated format requirements for theses. A
-collection of macros, that is, a macro package that meets all
-these specifications could be somewhat time consuming to design
-and could be quite long. It is possible to use the {\tt \\input}
-command to use such a macro package, just as it is possible to
-use it with your own macros. But \TeX{} has a better facility
-for larger packages.
-
-A macro package can be put in a special form that can be quickly
-read by \TeX\null. This is called a {\sl format file}, and
-the exact form is of technical interest only. The important
-thing is it allows \TeX{} to be run with many new control
-sequences predefined. Certain commands called {\sl primitives\/}
-are part of the definition of \TeX\null.
-
-What we have described in this manual is sometimes called {\sl
-plain \TeX\/}, and consists of the \TeX{} primitives plus a set
-of macros in a format file (that is usually included in \TeX{}
-automatically) called {\tt plain.fmt}. For the curious, any
-control word can be viewed using {\tt \\show}. The command {\tt
-\\show\\centerline} will display
-\beginliteral
-> \centerline=macro:
-#1->\line {\hss #1\hss }.
-@endliteral
-\noindent
-on the screen and in the log file. You can use {\tt \\show} with
-your own macros, too. If you end up using several macro
-packages, you can use the {\tt \\show} command to see if a
-particular macro is defined.
-
-Many computer \centre{}s have the \LaTeX{} macro package. This
-package allows the user to create an index, a table of contents,
-and a bibliography automatically. It also has the ability to
-insert some elementary graphic figures such as circles, ovals,
-lines, and arrows. \LaTeX{} also uses special predefined files
-called {\sl style files\/} to set up
-specific page parameters. Many different style files are
-available; some journals will accept papers on a magnetic medium
-for direct processing if they are prepared using \LaTeX{} and a
-designated style file. It is not difficult to shift from \TeX{}
-to \LaTeX\null. A user's guide by the author of the macro
-package, Leslie Lamport, is available:
-{\bf \LaTeX{}: A document preparation system}%
-\fnote{Addison-Wesley, Reading, Massachusetts, 1986,
-ISBN 0-201-15790-X.}.
-
-The American Mathematical Society uses the \AMSTeX{} macro
-package for its journals. It is readily available from that
-Society, and papers may be submitted to their journals on a
-magnetic medium using \AMSTeX\null. A manual by Michael Spivak,
-{\bf The Joy of \TeX{}}\fnote{American Mathematical
-Society, 1986, ISBN 0-8218-2999-8}, is available from the
-American Mathematical Society.
-
-Other macro packages exist, and undoubtedly more will be
-developed. They are usually of modest cost and can be very
-effective in some circumstances. The \TeX{} Users Group
-announces the existence of new macro packages in its
-publications.
-
-\subsection{Horizontal and vertical lines}
-
-Making horizontal and vertical lines is easy using \TeX\null.
-When typing in text, {\tt \\hrule } will cause the current
-paragraph to end, will draw a horizontal line whose width is the
-current value of {\tt \\hsize}, and then will continue on with a
-new paragraph. It's possible to specify the width of the hrule
-as, for example, with {\tt \\hrule width 5 cm}; also you can use
-{\tt \\vskip} or {\tt \\bigskip} to put some space above or below
-the hrule. Here is an example:
-
-\beginuser
-\\parindent = 0 pt \\parskip = 12 pt
-Here is the text before the hrule.
-\\bigskip
-\\hrule width 3 in
-And here is some text after the hrule.
-\enduser
-
-\noindent that produces
-\vfill\eject
-
-{
-\parindent = 0 pt
-Here is the text before the hrule.
-\bigskip
-\hrule width 3 in
-And here is some text after the hrule.
-}
-
-In fact this hrule not only has width of three inches, but also
-by default has a height (the amount by which the hrule extends
-above the baseline on which the type is being set) of 0.4 points
-and a depth (the amount by which the hrule extends below the
-baseline on which the type is being set) of 0 points. Each of
-these parameters can be individually set. Thus if we change the
-last example to say
-
-{\tt \\hrule width 3 in height 2 pt depth 3 pt } we get
-
-{
-\parindent = 0 pt
-Here is the text before the hrule.
-\bigskip
-\hrule width 3 in height 2 pt depth 3 pt
-And here is some text after the hrule.
-}
-
-The three parameters {\tt width}, {\tt height}, and {\tt depth} may
-be given in any order.
-\toindex{hrule}
-\TeXref{221--222}
-
-A vrule may be defined analogously to an hrule by specifying the
-{\tt width}, {\tt height}, and {\tt depth} if desired.
-\TeXref{221--222}
-But, unlike the hrule, the vrule will not automatically start a
-new paragraph when it appears. By default the vrule will be 0.4
-points wide, and will be as high as the line on which it is being
-set. Hence
-
-\toindex{vrule}
-
-\beginuser
-Here is some text before the vrule
-\\vrule\\
-and this follows the vrule.
-\enduser
-
-\noindent will give
-
-Here is some text before the vrule
-\vrule\
-and this follows the vrule.
-
-\exercise Make three horizontal lines that are 15 points apart,
-3 inches in length, and one inch in from the left margin.
-
-Although we usually think of hrules and vrules as horizontal and
-vertical lines, they need not necessarily be used that way. For
-example:
-
-\beginuser
-\\noindent
-Name: \\vrule height 0 pt depth 0.4 pt width 3 in
-\enduser
-
-\noindent will give
-
-\noindent
-Name: \vrule height 0 pt depth 0.4 pt width 3 in
-
-\exercise Make the following grid (each box is 1 \centimetre{} square):
-\medskip
-\settabs \+ \hskip 1cm&\hskip 1 cm&\hskip 1 cm& \cr
-\moveright 2 in
-\vbox{
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-}
-
-
-\subsection{Boxes within boxes}
-
-We have already seen (in our discussion of line shapes) that
-vboxes and hboxes are objects that may be overfull or underfull.
-In this section we will look at these boxes in a bit more detail.
-They may be stacked or lined up to allow a variety of positions
-for text on the page.
-
-An hbox is formed by using {\tt \\hbox\lb $\ldots$\rb}\null.
-Once the material between the braces has been put into an hbox,
-it is set and can not be further split (this means that material
-that must go on one line can be put into an hbox, and it will
-then remain as one unit). It's possible to specify the size of
-an hbox.\TeXref{64--66} Thus {\tt \\hbox to 5 cm\lb contents of
-the box\rb } will produce an hbox exactly five \centimetre{}s
-wide containing the typeset text ``contents of the box''.
-It's easy to get an underfull or overfull box in this way. An
-underfull box can be avoided by using {\tt \\hfil} to absorb the
-extra space. When no dimension is given, an hbox is formed that
-is just wide enough to hold the enclosed text.
-\toindex{hbox}
-
-Similarly, vboxes are formed using {\tt \\vbox\lb $\ldots$\rb}.
-What makes these boxes interesting is that when a vbox contains
-hboxes, these hboxes are stacked one above the other and set as a
-unit. Similarly, an hbox can contain vboxes, which will be set in
-a row. Suppose we take three hboxes and put them in a vbox:
-\toindex{vbox}
-
-\beginuser \obeyspaces
-\\vbox\lb
-\ \\hbox\lb{}Contents of box 1\rb
-\ \\hbox\lb{}Contents of box 2\rb
-\ \\hbox\lb{}Contents of box 3\rb
-\ \rb
-\enduser
-
-\noindent gives
-\vskip \baselineskip
-\vbox{
- \hbox{Contents of box 1}
- \hbox{Contents of box 2}
- \hbox{Contents of box 3}
- }
-
-Now suppose we take another vbox:
-
-\beginuser \obeyspaces
-\\vbox\lb
-\ \\hbox\lb{}Contents of box 4\rb
-\ \\hbox\lb{}Contents of box 5\rb
-\ \rb
-\enduser
-
-These two vboxes can be put into an hbox; this will cause them to
-be placed side by side. In other words
-
-\beginuser \obeyspaces
-\\hbox\lb
-\ \\vbox\lb
-\ \\hbox\lb{}Contents of box 1\rb
-\ \\hbox\lb{}Contents of box 2\rb
-\ \\hbox\lb{}Contents of box 3\rb
-\ \rb
-\ \\vbox\lb
-\ \\hbox\lb{}Contents of box 4\rb
-\ \\hbox\lb{}Contents of box 5\rb
-\ \rb
-\ \rb
-\enduser
-
-\noindent gives
-\vskip \baselineskip
-\hbox{
- \vbox{
- \hbox{Contents of box 1}
- \hbox{Contents of box 2}
- \hbox{Contents of box 3}
- }
- \vbox{
- \hbox{Contents of box 4}
- \hbox{Contents of box 5}
- }
- }
-
-
-Notice that the two vboxes are aligned so that the bottoms are
-level; also there is a little space at the beginning of each line
-and also between the vboxes. Actually, the reason these spaces
-appear is rather subtle. Unless a line ends in a control word,
-there is always a space between the last entry in one line and
-the first one in the next line. For this reason the space between
-the vboxes comes from the end of the line containing the closing
-brace of the first vbox. Similarly, the space at the beginning
-of the line is caused by the space after the opening brace of the
-hbox. These spaces can be avoided by ``commenting out'' the end of
-the line, that is, by putting a {\tt \%} immediately after the
-closing brace of the first vbox or the opening brace of the hbox.
-If you try to put some vboxes together and accidentally get extra
-space by forgetting to comment out the end of the line, you're in
-good company. Some very able and experienced \TeX{} users have
-done the same thing!
-
-Extra space, say one \centimetre, can be added by putting an
-{\tt \\hskip 1 cm } between the vboxes. They can be aligned so
-that the tops are level by using {\tt \\vtop } instead of
-{\tt \\vbox}. Making these two changes results in:
-
-\toindex{vtop}
-\vskip \baselineskip
-\hbox{
- \vtop{
- \hbox{Contents of box 1}
- \hbox{Contents of box 2}
- \hbox{Contents of box 3}
- }
- \hskip 1 cm
- \vtop{
- \hbox{Contents of box 4}
- \hbox{Contents of box 5}
- }
- }
-
-
-We can combine vboxes, hboxes, vrules, and hrules to get boxed
-text. How might we construct such a box? One way is to take the
-material to be boxed and put it in an hbox preceded and followed
-by a vrule. Then put this in a vbox with hrules above and below
-it. This gives us:
-
-\beginuser \obeyspaces
-\\vbox\lb
-\ \\hrule
-\ \\hbox\lb\\vrule\lb\rb The text to be boxed \\vrule\rb
-\ \\hrule
-\ \rb
-\enduser
-
-\noindent which results in
-\vskip \baselineskip
-\vbox{
- \hrule
- \hbox{\vrule{} The text to be boxed \vrule}
- \hrule
- }
-
-This produces boxed material, but there is no margin around it
-and so it looks very cramped (of course \TeX{} is just giving us
-what we asked for). We can improve the spacing by putting a {\tt
-\\strut} at the beginning of the hbox to make it a little taller
-and deeper. This gives us:
-\vskip \baselineskip
-\vbox{
- \hrule
- \hbox{\strut \vrule{} The text to be boxed \vrule}
- \hrule
- }
-
-\def\boxtext#1{%
-\vbox{%
- \hrule
- \hbox{\strut \vrule{} #1 \vrule}%
- \hrule
- }%
-}
-
-\exercise Why is it that we were forced to add extra space above
-and below the text but not before and after it?
-
-
-\exercise Use the method of boxing material to put text \centred{}
-in a box which extends from the left to the right margin.
-
-\exercise By stacking nine little boxes, make the following magic square:
-\vskip\baselineskip
-
-\moveright 2 in \vbox{\offinterlineskip
-\hbox{\boxtext 6\boxtext 1\boxtext 8}
-\hbox{\boxtext 7\boxtext 5\boxtext 3}
-\hbox{\boxtext 2\boxtext 9\boxtext 4}
-}
-
-\exercise Notice that the magic square in the previous exercise
-has internal lines that are twice as thick as the outside ones.
-Also, there is a tiny space at the intersection of the internal
-lines. Fix up the magic square so this doesn't happen.
-
-\def\boxtext#1 {%
-\vbox{%
- \hrule
- \hbox{\strut \vrule #1\vrule}%
- \hrule
- }
-}
-
-\exercise Write a macro { \tt \\boxtext\#1\lb$\ldots$\rb } which
-will take the text between the braces and put a box around it. Test
-your macro by making up a sentence with every other word boxed.
-I'm \boxtext not quite \boxtext sure why \boxtext someone
-would \boxtext do this \boxtext since the \boxtext result is \boxtext
-pretty strange. Note how the baseline and the bottom of
-the surrounding boxes align.
-
-\def\boxtext#1 {%
-\lower 3.5pt \hbox{%
- \vbox{%
- \hrule
- \hbox{\strut \vrule #1\vrule}%
- \hrule
- }
- }%
-}
-
-It's easy to move boxes up, down, left, or right on the page. A
-{\tt \\vbox} can be moved to the right one inch by using {\tt
-\\moveright 1 in \\vbox\lb\dots\rb}. To move it to the left,
-use {\tt \\moveleft}. Similarly, an {\tt \\hbox} can be moved up
-or down using {\tt \\raise} or {\tt \\lower}.
-\toindex{moveright}
-\toindex{moveleft}
-\toindex{raise}
-\toindex{lower}
-
-\exercise Rewrite the {\tt \\boxtext} macro from the previous
-exercise so that all of the text is aligned (hint: by default the
-depth of a strut is 3.5 points). This would give a sentence like
-the following: I'm \boxtext not quite \boxtext sure why \boxtext
-someone would \boxtext do this \boxtext since the \boxtext result
-is \boxtext pretty strange.
-
-It's possible to fill a box with either an hrule or with dots.
-The idea is to use {\tt \\hrulefill } or {\tt \\dotfill } in the
-hbox.
-
-\beginuser
-\\hbox to 5 in\lb Getting Started\\hrulefill 1\rb
-\\hbox to 5 in\lb All Characters Great and Small\\hrulefill 9\rb
-\\hbox to 5 in\lb The Shape of Things to come\\hrulefill 17\rb
-\\hbox to 5 in\lb No Math Anxiety Here!\\hrulefill 30\rb
-\enduser
-
-\noindent gives
-\vskip \baselineskip
-
-\hbox to 5 in{Getting Started\hrulefill 1}
-\hbox to 5 in{All Characters Great and Small\hrulefill 9}
-\hbox to 5 in{The Shape of Things to come\hrulefill 17}
-\hbox to 5 in{No Math Anxiety Here!\hrulefill 30}
-
-If {\tt \\hrulefill} is replaced by {\tt \\dotfill} we get
-\vskip \baselineskip
-
-\hbox to 5 in{Getting Started\dotfill 1}
-\hbox to 5 in{All Characters Great and Small\dotfill 9}
-\hbox to 5 in{The Shape of Things to come\dotfill 17}
-\hbox to 5 in{No Math Anxiety Here!\dotfill 30}
-
-\exercise Make a boxed headline appear at the top of the page
-that is like the one used in this manual.
-
-
-
-\section{Control word list}
-
-Here is a list of the control words given in this manual.
-If you want more detail about these words than is given here,
-check the index of {\bf The \TeX book}.
-
-\vskip 2\baselineskip
-\centerline{Control symbols}
-\vskip\baselineskip
-
-\settabs \+ \hskip 1.5 in & \hskip 1.65in & \hskip 1.3in & \cr
-{\tt
-\+ \\\sp{} 4 & \\!\ 34 & \\" 11 & \\' 11 \cr
-\+ \\, 34 & \\.\ 11 & \\/ 16 & \\; 34 \cr
-\+ \\= 11 & \\> 34 & \\\# 10& \\\$ 6 \cr
-\+ \\\% 6 & \\\& 10 & \\\char '173{} 10 & \\\char '175{} 10 \cr
-\+ \\\underbar{ } 10 & \\` 11 & \\{\accent "7E } 10 & \\{\accent 94 } 10 \cr
-\+ \\| 40 \cr
-}
-
-\vskip 2\baselineskip
-\centerline{Control words}
-\vskip\baselineskip
-
-{\tt
-\+ \\AA 12 & \\aa 12 & \\acute 36 & \\AE 12 \cr
-\+ \\ae 12 & \\aleph 37 & \\alpha 35 & \\angle 37 \cr
-\+ \\approx 37 & \\arccos 41 & \\arcsin 41 & \\arctan 41 \cr
-\+ \\arg 41 & \\ast 36 & \\b 12 & \\backslash 37 \cr
-\+ \\bar 36 & \\baselineskip 22 & \\beta 35 & \\bf 16 \cr
-\+ \\biggl 40 & \\Biggl 40 & \\biggr 40 & \\Biggr 40 \cr
-\+ \\bigl 40 & \\Bigl 40 & \\bigr 40 & \\Bigr 40 \cr
-\+ \\bigskip 26 & \\break 26 & \\breve 36 & \\bullet 36 \cr
-\+ \\bye 4 & \\c 12 & \\cap 36 & \\cdot 36 \cr
-\+ \\centerline 26 & \\centreline 60 & \\check 36 & \\chi 35 \cr
-\+ \\circ 35 & \\columns 48 & \\cos 41 & \\cosh 41 \cr
-\+ \\cot 41 & \\coth 41 & \\csc 41& \\cup 36 \cr
-\+ \\d 12 & \\ddag 27 & \\ddot 36 & \\def 55 \cr
-\+ \\deg 41 & \\delta 35 & \\Delta 35 & \\det 41 \cr
-\+ \\diamond 36 & \\dim 41 & \\div 36 & \\dot 36 \cr
-\+ \\dotfill 49 & \\dots 14 & \\downarrow 41 & \\Downarrow 41 \cr
-\+ \\eject 20 & \\ell 37 & \\endinsert 26 & \\epsilon 35 \cr
-\+ \\eqalign 45 & \\eqalignno 46 & \\eqno 46 & \\equiv 37 \cr
-\+ \\eta 35 & \\exists 37 & \\exp 41 & \\flat 37 \cr
-\+ \\folio 28 & \\font 16 & \\footline 28 & \\footnote 27 \cr
-\+ \\forall 37 & \\gamma 35 & \\Gamma 35 & \\gcd 41 \cr
-\+ \\geq 37 & \\grave 36 & \\H 12 & \\halign 51 \cr
-\+ \\hang 23 & \\hangafter 23 & \\hangindent 23 & \\hat 36 \cr
-\+ \\hbadness 29 & \\hbox 72 & \\headline 28 & \\hfil 27 \cr
-\+ \\hfill 26 & \\hfuzz 29 & \\hoffset 20 & \\hom 41 \cr
-\+ \\hrule 71 & \\hrulefill 49 & \\hsize 20 & \\hskip 27 \cr
-\+ \\hyphenation 30 & \\i 11 & \\Im 37 & \\in 37 \cr
-\+ \\inf 41 & \\infty 37 & \\input 68 & \\int 38 \cr
-\+ \\iota 35 & \\it 16 & \\item 24 & \\itemitem 24 \cr
-\+ \\j 11 & \\kappa 35 & \\ker 41 & \\L 12 \cr
-\+ \\l 12 & \\lambda 35 & \\Lambda 35 & \\langle 41 \cr
-\+ \\lceil 41 & \\left 44 & \\leftline 26 & \\leftskip 23 \cr
-\+ \\leq 37 & \\leqalignno 46 & \\leqno 46 & \\let 61 \cr
-\+ \\lfloor 41 & \\lg 41 & \\lim 38 & \\liminf 41 \cr
-\+ \\limsup 41 & \\line 26 & \\ln 41 & \\log 41 \cr
-\+ \\lower 75 & \\magnification 21 & \\magstep 16 & \\matrix 44 \cr
-\+ \\max 41 & \\medskip 26 & \\min 41 & \\moveleft 75 \cr
-\+ \\moveright 75 & \\mu 35 & \\nabla 37 & \\narrower 23 \cr
-\+ \\natural 37 & \\neg 37 & \\ni 37 & \\noalign 52 \cr
-\+ \\noindent 22 & \\nopagenumbers 5 & \\not 36 & \\nu 35 \cr
-\+ \\O 12 & \\o 12 & \\odot 36 & \\OE 12 \cr
-\+ \\oe 12 & \\offinterlineskip 53 & \\omega 35 & \\Omega 35 \cr
-\+ \\ominus 36 & \\oplus 36 & \\otimes 36 & \\over 37 \cr
-\+ \\overfullrule 29 & \\overline 39 & \\P 27 & \\pageno 28 \cr
-\+ \\par 7 & \\parallel 37 & \\parindent 23 & \\parshape 24 \cr
-\+ \\parskip 22 & \\partial 37 & \\perp 37 & \\phi 35 \cr
-\+ \\Phi 35 & \\pi 35 & \\Pi 35 & \\pmatrix 43 \cr
-\+ \\Pr 41 & \\proclaim 42 & \\psi 35 & \\Psi 35 \cr
-\+ \\qquad 34 & \\quad 34 & \\raggedright 27 & \\raise 75 \cr
-\+ \\rangle 41 & \\rceil 41 & \\Re 37 & \\rfloor 41 \cr
-\+ \\rho 35 & \\right 44 & \\rightline 26 & \\rightskip 23 \cr
-\+ \\rm 16 & \\root 39 & \\S 27 & scaled 16 \cr
-\+ \\sec 41 & \\settabs 48 & \\sharp 37 & \\sigma 35 \cr
-\+ \\Sigma 35 & \\sim 37 & \\simeq 37 & \\sin 41 \cr
-\+ \\sinh 41 & \\sl 16 & \\smallskip 26 & \\sqroot 39 \cr
-\+ \\ss 12 & \\star 36 & \\strut 50 & \\subset 37 \cr
-\+ \\subseteq 37 & \\sum 38 & \\sup 41 & \\supset 37 \cr
-\+ \\supseteq 37 & \\surd 39 & \\t 12 & \\tan 41 \cr
-\+ \\tanh 41 & \\tau 35 & \\tensor 60 & \\TeX{} 5 \cr
-\+ \\tensor 60 & \\the 28 & \\theta 35 & \\Theta 35 \cr
-\+ \\tilde 36 & \\times 36 & \\tolerance 29 & \\topinsert 26 \cr
-\+ \\tt 16 & \\u 12 & \\underbar 39 & \\underline 39 \cr
-\+ \\uparrow 41 & \\Uparrow 41 & \\updownarrow 41 & \\Updownarrow 41 \cr
-\+ \\upsilon 35 & \\Upsilon 35 & \\v 12 & \\varepsilon 35 \cr
-\+ \\varphi 35 & \\varrho 35 & \\varsigma 35 & \\vartheta 35 \cr
-\+ \\vbadness 30 & \\vbox 71 & \\vec 36 & \\vee 36 \cr
-\+ \\vfill 20 & \\vglue 25 & \\voffset 20 & \\vrule 71 \cr
-\+ \\vsize 20 & \\vtop 74 & \\wedge 36 & \\widehat 36 \cr
-\+ \\widetilde 36 & \\xi 35 & \\Xi 35 & \\zeta 35 \cr
-}
-
-\ifwritinganswers
- \let\next=\relax
-\else
- \let\next=\endinput
- \datestamp
-\fi
-
-\next
-
-\def\beginliteral{
-\vskip\baselineskip
-\begingroup
-\obeylines
-\tt
-\catcode`\@=0\catcode`\~=12
-\catcode`\$=12\catcode`\&=12\catcode`\^=12\catcode`\#=12
-\catcode`\_=12\catcode`\=12
-\def\par{\leavevmode\endgraf}
-\catcode`\{=12\catcode`\}=12\catcode`\%=12\catcode`\\=12
-
-}
-\def\endliteral{\nobreak \vskip 6pt \endgroup}
-
-
-\section{I get by with a little help}
-Many of the exercises can be answered in several ways. If you
-like your way better than the way given below, by all means use
-it!
-\vskip 2\baselineskip
-
-\parskip=0pt \parindent=0pt
-\raggedright
-\hbadness=10000
-
-\hrule
-\beginliteral
-I like \TeX!
-Once you get the hang of it, \TeX\ is really easy to use.
-You just have to master the \TeX nical aspects.
-@endliteral
-I like \TeX! Once you get the hang of it, \TeX\ is really easy
-to use. You just have to master the \TeX nical aspects.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-Does \AE schylus understand \OE dipus?
-@endliteral
-Does \AE schylus understand \OE dipus?
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-The smallest internal unit of \TeX{} is about 53.63\AA.
-@endliteral
-The smallest internal unit of \TeX{} is about 53.63\AA.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- They took some honey and plenty of money wrapped up in a {\it \$}5 note.
-@endliteral
- They took some honey and plenty of money wrapped up in a {\it \$}5 note.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- \'El\`eves, refusez vos le\c cons! Jetez vos cha\^\i nes!
-@endliteral
- \'El\`eves, refusez vos le\c cons! Jetez vos cha\^\i nes!
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Za\v sto tako polako pijete \v caj?
-@endliteral
- Za\v sto tako polako pijete \v caj?
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Mein Tee ist hei\ss.
-@endliteral
- Mein Tee ist hei\ss.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Peut-\^etre qu'il pr\'ef\`ere le caf\'e glac\'e.
-@endliteral
- Peut-\^etre qu'il pr\'ef\`ere le caf\'e glac\'e.
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\def\`{\relax\lq}
-\beginliteral
-?@`Por qu\'e no bebes vino blanco? !@`Porque est\'a avinagrado!
-@endliteral
-?`Por qu\'e no bebes vino blanco? !`Porque est\'a avinagrado!
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- M\'\i\'\j n idee\"en worden niet be\"\i nvloed.
-@endliteral
- M\'\i\'\j n idee\"en worden niet be\"\i nvloed.
-\vskip \baselineskip \hrule
-
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Can you take a ferry from \"Oland to \AA land?
-@endliteral
- Can you take a ferry from \"Oland to \AA land?
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- T\"urk\c ce konu\c san ye\u genler nasillar?
-@endliteral
- T\"urk\c ce konu\c san ye\u genler nasillar?
-\vskip \baselineskip \hrule
-
-
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- I entered the room and---horrors---I saw both my father-in-law and my
-mother-in-law.
-@endliteral
- I entered the room and---horrors---I saw both my father-in-law and my
-mother-in-law.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-The winter of 1484--1485 was one of discontent.
-@endliteral
-The winter of 1484--1485 was one of discontent.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-His ``thoughtfulness'' was impressive.
-@endliteral
-His ``thoughtfulness'' was impressive.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Frank wondered, ``Is this a girl that can't say `No!'?''
-@endliteral
- Frank wondered, ``Is this a girl that can't say `No!'?''
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- He thought, ``\dots and this goes on forever, perhaps to the last recorded
-syllable.''
-@endliteral
- He thought, ``\dots and this goes on forever, perhaps to the last recorded
-syllable.''
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
- Have you seen Ms.~Jones?
-@endliteral
- Have you seen Ms.~Jones?
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-Prof.~Smith and Dr.~Gold flew from
-Halifax N.~S. to Montr\'eal, P.~Q. via Moncton, N.~B.
-@endliteral
-Prof.~Smith and Dr.~Gold flew from
-Halifax N.~S. to Montr\'eal, P.~Q. via Moncton, N.~B.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\line{left end \hfil left tackle \hfil left guard \hfil @centre \hfil
-right guard \hfil right tackle \hfil right end}
-@endliteral
-\line{left end \hfil left tackle \hfil left guard \hfil \centre{} \hfil
-right guard \hfil right tackle \hfil right end}
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\line{left \hfil \hfil right-@centre \hfil right}
-@endliteral
-\line{left \hfil \hfil right-\centre{} \hfil right}
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\line{\hskip 1 in ONE \hfil TWO \hfil THREE}
-@endliteral
-\line{\hskip 1 in ONE \hfil TWO \hfil THREE}
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-i{f}f if{}f if{f}
-@endliteral
-i{f}f if{}f if{f}
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-I started with roman type {\it switched to italic type}, and
-returned to roman type.
-@endliteral
-I started with roman type {\it switched to italic type}, and
-returned to roman type.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$C(n,r) = n!/(r!\,(n-r)!)$
-@endliteral
-$C(n,r) = n!/(r!\,(n-r)!)$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$a+b=c-d=xy=w/z$
-$$a+b=c-d=xy=w/z$$
-@endliteral
-$a+b=c-d=xy=w/z$
-$$a+b=c-d=xy=w/z$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$(fg)' = f'g + fg'$
-$$(fg)' = f'g + fg'$$
-@endliteral
-$(fg)' = f'g + fg'$
-$$(fg)' = f'g + fg'$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\alpha\beta=\gamma+\delta$
-$$\alpha\beta=\gamma+\delta$$
-@endliteral
-$\alpha\beta=\gamma+\delta$
-$$\alpha\beta=\gamma+\delta$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\Gamma(n) = (n-1)!$
-$$\Gamma(n) = (n-1)!$$
-@endliteral
-$\Gamma(n) = (n-1)!$
-$$\Gamma(n) = (n-1)!$$
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$x\wedge (y\vee z) = (x\wedge y) \vee (x\wedge z)$
-@endliteral
-$x\wedge (y\vee z) = (x\wedge y) \vee (x\wedge z)$
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$2+4+6+\cdots +2n = n(n+1)$
-@endliteral
-$2+4+6+\cdots +2n = n(n+1)$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\vec x\cdot \vec y = 0$ if and only if $\vec x \perp \vec y$.
-@endliteral
-$\vec x\cdot \vec y = 0$ if and only if $\vec x \perp \vec y$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\vec x\cdot \vec y \not= 0$ if and only if $\vec x \not\perp \vec y$.
-@endliteral
-$\vec x\cdot \vec y \not= 0$ if and only if $\vec x \not\perp \vec y$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$(\forall x\in \Re)(\exists y\in\Re)$ $y>x$.
-@endliteral
-$(\forall x\in \Re)(\exists y\in\Re)$ $y>x$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-${a+b\over c}\quad {a\over b+c}\quad {1\over a+b+c} \not= {1\over a}+
-{1\over b}+{1\over c}$.
-@endliteral
-${a+b\over c}\quad {a\over b+c}\quad {1\over a+b+c} \not= {1\over a}+
-{1\over b}+{1\over c}$.
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-
-
-\goodbreak \vskip 2pt \hrule
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-What are the points where ${\partial \over \partial x} f(x,y) = {\partial \over
-\partial y} f(x,y) = 0$?
-@endliteral
-What are the points where ${\partial \over \partial x} f(x,y) = {\partial \over
-\partial y} f(x,y) = 0$?
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$e^x \quad e^{-x} \quad e^{i\pi}+1=0 \quad x_0 \quad x_0^2
-\quad {x_0}^2 \quad 2^{x^x}$.
-@endliteral
-$e^x \quad e^{-x} \quad e^{i\pi}+1=0 \quad x_0 \quad x_0^2
-\quad {x_0}^2 \quad 2^{x^x}$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\nabla^2 f(x,y) = {\partial^2 f \over\partial x^2}+ {\partial^2 f \over
-\partial y^2}$.
-@endliteral
-$\nabla^2 f(x,y) = {\partial^2 f \over\partial x^2}+ {\partial^2 f \over
-\partial y^2}$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\lim_{x\to 0} (1+x)^{1\over x}=e$.
-@endliteral
-$\lim_{x\to 0} (1+x)^{1\over x}=e$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
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-The cardinality of $(-\infty, \infty)$ is $\aleph_1$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\lim_{x\to {0^+}} x^x = 1$.
-@endliteral
-$\lim_{x\to {0^+}} x^x = 1$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\int_0^1 3x^2\,dx = 1$.
-@endliteral
-$\int_0^1 3x^2\,dx = 1$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\sqrt2 \quad \sqrt {x+y\over x-y} \quad \root 3 \of {10}$ \quad $e^{\sqrt x}$.
-@endliteral
-$\sqrt2 \quad \sqrt {x+y\over x-y} \quad \root 3 \of {10}$ \quad $e^{\sqrt x}$.
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-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\|x\| = \sqrt{x\cdot x}$.
-@endliteral
-$\|x\| = \sqrt{x\cdot x}$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\phi(t) = {1 \over \sqrt{2\pi}} \int_0^t e^{-x^2/2}\,dx$.
-@endliteral
-$\phi(t) = {1 \over \sqrt{2\pi}} \int_0^t e^{-x^2/2}\,dx$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\underline x \quad \overline y \quad \underline{\overline{x+y}}$.
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-$\underline x \quad \overline y \quad \underline{\overline{x+y}}$.
-\vskip \baselineskip \hrule
-
-
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-\beginliteral
-$\bigl \lceil \lfloor x \rfloor \bigr \rceil \leq \bigl \lfloor \lceil x \rceil
-\bigr \rfloor$.
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-\bigr \rfloor$.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$\sin(2\theta) = 2\sin\theta\cos\theta
-\quad \cos(2\theta) = 2\cos^2\theta - 1 $.
-@endliteral
-$\sin(2\theta) = 2\sin\theta\cos\theta
-\quad \cos(2\theta) = 2\cos^2\theta - 1 $.
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$$\int \csc^2x\, dx = -\cot x+ C
-\qquad \lim_{\alpha\to 0} {\sin\alpha \over \alpha} = 1
-\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0.$$
-@endliteral
-$$\int \csc^2x\, dx = -\cot x+ C
-\qquad \lim_{\alpha\to 0} {\sin\alpha \over \alpha} = 1
-\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0.$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$$\tan(2\theta) = {2\tan\theta \over 1-\tan^2\theta}.$$
-@endliteral
-$$\tan(2\theta) = {2\tan\theta \over 1-\tan^2\theta}.$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\proclaim Theorem (Euclid). There exist an infinite number of primes.
-@endliteral
-\proclaim Theorem (Euclid). There exist an infinite number of primes.
-
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\proclaim Proposition 1.
-$\root n \of {\prod_{i=1}^n X_i} \leq
-{1 \over n} \sum_{i=1}^n X_i$ with equality if and only if $X_1=\cdots=X_n$.
-@endliteral
-\proclaim Proposition 1.
-$\root n \of {\prod_{i=1}^n X_i} \leq
-{1 \over n} \sum_{i=1}^n X_i$ with equality if and only if $X_1=\cdots=X_n$.
-
-\vskip \baselineskip \hrule
-
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$$ I_4 = \pmatrix{
-1 &0 &0 &0 \cr
-0 &1 &0 &0 \cr
-0 &0 &1 &0 \cr
-0 &0 &0 &1 \cr}$$
-@endliteral
-$$ I_4 = \pmatrix{
-1 &0 &0 &0 \cr
-0 &1 &0 &0 \cr
-0 &0 &1 &0 \cr
-0 &0 &0 &1 \cr}$$
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-$$ |x| = \left\{ \matrix{
-x & x \ge 0 \cr
--x & x \le 0 \cr} \right.$$
-@endliteral
-$$ |x| = \left\{ \matrix{
-x & x \ge 0 \cr
--x & x \le 0 \cr} \right.$$
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\settabs \+ \hskip 2 in & \hskip .75in & \hskip 1cm& \cr
-\+ &Plums &\hfill\$1&.22 \cr
-\+ &Coffee &\hfill1&.78 \cr
-\+ &Granola &\hfill1&.98 \cr
-\+ &Mushrooms & &.63 \cr
-\+ &{Kiwi fruit} & &.39 \cr
-\+ &{Orange juice} &\hfill1&.09 \cr
-\+ &Tuna &\hfill1&.29 \cr
-\+ &Zucchini & &.64 \cr
-\+ &Grapes &\hfill1&.69 \cr
-\+ &{Smoked beef} & &.75 \cr
-\+ &Broccoli &\hfill\underbar{\ \ 1}&\underbar{.09} \cr
-\+ &Total &\hfill \$12&.55 \cr
-@endliteral
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-\+ &Plums &\hfill\$1&.22 \cr
-\+ &Coffee &\hfill1&.78 \cr
-\+ &Granola &\hfill1&.98 \cr
-\+ &Mushrooms & &.63 \cr
-\+ &{Kiwi fruit} & &.39 \cr
-\+ &{Orange juice} &\hfill1&.09 \cr
-\+ &Tuna &\hfill1&.29 \cr
-\+ &Zucchini & &.64 \cr
-\+ &Grapes &\hfill1&.69 \cr
-\+ &{Smoked beef} & &.75 \cr
-\+ &Broccoli &\hfill\underbar{\ \ 1}&\underbar{.09} \cr
-\+ &Total &\hfill \$12&.55 \cr
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\settabs \+ \hskip 4.5 in & \cr
-\+Getting Started \dotfill &1 \cr
-\+All Characters Great and Small \dotfill &9 \cr
-@endliteral
-\settabs \+ \hskip 4.5 in & \cr
-\+Getting Started \dotfill &1 \cr
-\+All Characters Great and Small \dotfill &9 \cr
-\vskip \baselineskip \hrule
-
-\goodbreak \vskip 2pt \hrule
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-\moveright 2 in
-\vbox{
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-}
-@endliteral
-\settabs \+ \hskip 1cm&\hskip 1 cm&\hskip 1 cm& \cr
-\moveright 2 in
-\vbox{
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
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-\+ \vrule height 1 cm & \vrule height 1 cm & \vrule height 1 cm
- & \vrule height 1 cm \cr
-\hrule width 3 cm
-}
-\vskip \baselineskip \hrule
-
-
-\goodbreak \vskip 2pt \hrule
-\beginliteral
-\def\boxtext#1{%
-\vbox{%
- \hrule
- \hbox{\strut \vrule{} #1 \vrule}%
- \hrule
- }%
-}
-\moveright 2 in \vbox{\offinterlineskip
-\hbox{\boxtext{6}\boxtext{1}\boxtext {8}}
-\hbox{\boxtext{7}\boxtext{5}\boxtext{3}}
-\hbox{\boxtext{2}\boxtext{9}\boxtext{4}}
-}
-@endliteral
-\def\boxtext#1{%
-\vbox{%
- \hrule
- \hbox{\strut \vrule{} #1 \vrule}%
- \hrule
- }%
-}
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-\hbox{\boxtext 6\boxtext 1\boxtext 8}
-\hbox{\boxtext 7\boxtext 5\boxtext 3}
-\hbox{\boxtext 2\boxtext 9\boxtext 4}
-}
-\vskip \baselineskip \hrule
-
-
-\vfill
-\datestamp
-\eject
-
-\parindent=20pt
-This introduction is available for {\tt ftp} transfer on CTAN (Combined
-\TeX{} Archive Network). Use an anonymous login to grab it from the
-server nearest to you.
-
-
-$$\vbox{
-\halign{#\quad &#\cr
-\bf Server & \bf file name \cr
-ftp.tex.ac.uk (134.151.79.32) &
-/tex-archive/documentation/gentle-introduction.tex\cr
-ftp.uni-stuttgart.de (129.69.8.13) &
-/tex-archive/documentation/gentle-introduction.tex\cr
-ftp.shsu.edu (192.92.115.10) &
-/tex-archive/documentation/gentle-introduction.tex\cr
-}}
-$$
-
-
-\newdimen\squaredimen
-\def\square#1{\setbox0=\hbox{#1}%
- \dp0=.4ex \squaredimen=\ht0
- \ifdim \wd0 > \ht0 \squaredimen=\wd0\fi
- \advance \squaredimen by \dp0
- \ht0=\squaredimen \advance \squaredimen by \dp0
- \leavevmode
- \lower .4ex \vbox{%
- \hsize=\squaredimen
- \hrule
- \hbox to \squaredimen{\vrule\hfil\box0\hfil\vrule}%
- \hrule height .4pt depth 0pt}}
-
-Also, a somewhat expanded version of this introduction is available as a book:\
-{\bf \TeX: Starting from \square1}. Springer-Verlag 1993
-(ISBN 3-540-56441-1 or 0-387-56441-1).
-
-
-
-
-\bye
-
-