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diff --git a/Master/texmf-dist/doc/plain/gentle/gentle.pdf b/Master/texmf-dist/doc/plain/gentle/gentle.pdf Binary files differnew file mode 100644 index 00000000000..83c3f5f0a21 --- /dev/null +++ b/Master/texmf-dist/doc/plain/gentle/gentle.pdf diff --git a/Master/texmf-dist/doc/plain/gentle/gentle.tex b/Master/texmf-dist/doc/plain/gentle/gentle.tex new file mode 100644 index 00000000000..a03678d4bf5 --- /dev/null +++ b/Master/texmf-dist/doc/plain/gentle/gentle.tex @@ -0,0 +1,5397 @@ + + +%% 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 +${a+b\over c}\quad {a\over b+c}\quad {1\over a+b+c} \not= {1\over a}+ +{1\over b}+{1\over c}$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +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 ${\partial \over \partial x} f(x,y) = {\partial \over +\partial y} f(x,y) = 0$? +\vskip \baselineskip \hrule + + +\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 +$\nabla^2 f(x,y) = {\partial^2 f \over\partial x^2}+ {\partial^2 f \over +\partial y^2}$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +$\lim_{x\to 0} (1+x)^{1\over x}=e$. +@endliteral +$\lim_{x\to 0} (1+x)^{1\over x}=e$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +The cardinality of $(-\infty, \infty)$ is $\aleph_1$. +@endliteral +The cardinality of $(-\infty, \infty)$ is $\aleph_1$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +$\lim_{x\to {0^+}} x^x = 1$. +@endliteral +$\lim_{x\to {0^+}} x^x = 1$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +$\int_0^1 3x^2\,dx = 1$. +@endliteral +$\int_0^1 3x^2\,dx = 1$. +\vskip \baselineskip \hrule + + +\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 $e^{\sqrt x}$. +\vskip \baselineskip \hrule + + +\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 +$\underline x \quad \overline y \quad \underline{\overline{x+y}}$. +@endliteral +$\underline x \quad \overline y \quad \underline{\overline{x+y}}$. +\vskip \baselineskip \hrule + + +\goodbreak \vskip 2pt \hrule +\beginliteral +$\bigl \lceil \lfloor x \rfloor \bigr \rceil \leq \bigl \lfloor \lceil x \rceil +\bigr \rfloor$. +@endliteral +$\bigl \lceil \lfloor x \rfloor \bigr \rceil \leq \bigl \lfloor \lceil x \rceil +\bigr \rfloor$. +\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 +\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 +\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 +\beginliteral +\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 +} +@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 +\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 +} +\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 + }% +} +\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} +} +\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 + + |