From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- usergrps/uktug/baskervi/5_2/bailey.tex | 920 +++++++++++++++++++++++++++++++++ 1 file changed, 920 insertions(+) create mode 100644 usergrps/uktug/baskervi/5_2/bailey.tex (limited to 'usergrps/uktug/baskervi/5_2/bailey.tex') diff --git a/usergrps/uktug/baskervi/5_2/bailey.tex b/usergrps/uktug/baskervi/5_2/bailey.tex new file mode 100644 index 0000000000..cd5c9b2444 --- /dev/null +++ b/usergrps/uktug/baskervi/5_2/bailey.tex @@ -0,0 +1,920 @@ +\title{Maths in \LaTeX: Part~4, Numbered and Unnumbered Things} +\author[R.~A.~Bailey]{R.~A.~Bailey\\ +Queen Mary and Westfield College, \\University of London} +\newenvironment{oneoff}[1]{\equation% + \addtocounter{equation}{-1}% + \renewcommand{\theequation}{\mbox{#1}}}% + {\endequation} +%%% +\newcommand{\writer}[1]{{\sc #1}:} +\newcommand{\book}[1]{{\it #1},} +\newcommand{\publish}[2]{{\rm #1, #2,}} +\newcommand{\byear}[1]{{\rm (#1).}} +\newtheorem{preqn}{Exercise} +\newenvironment{qn}{\begin{preqn}\normalfont\rm}{\end{preqn}} +\newcommand{\latexword}[1]{{\normalfont\tt #1}} +%%% and the above should be in typewriter-ordinary IRRESPECTIVE of the +%%% surrounding fonts +%%% +%%% +%%% editor: I have been as generic as I can, but of course you can't +%%% put \verb inside a \newcommand. I have consistently used + as the +%%% delimiter for \verb, except when I needed the + in Maths! +%%% +\newcommand{\lamport}{{\it \LaTeX: A Document Preparation System\/} by Leslie +Lamport} +\newcommand{\shortlamp}{{\it The Manual}} +%%% +\let\torl\AllTeX +%%% editor, can you do a better macro for the above? +%%% +\newcommand{\littlehead}[1]{\textit{#1}} +\begin{Article} +\section*{Recall} +This is the fourth in a sequence of tutorials on typesetting Mathematics in +\LaTeX. The first three appeared in issues~4.4, 4.5 and~5.1 of \BV. The series +includes some things which can be found in \cite{leslie}, but I am +working in more things which, while straightforward and necessary for +Mathematical work, are not in \cite{leslie} or \cite{newleslie}. In this +tutorial I concentrate not on Mathematical formulae but on things like +equations and theorems which Mathematicians like to display in special ways and +to number (or not). + +In case you missed the first three +tutorials, I remind you that +I expect you, the reader, to do some work. Every so +often comes a group of exercises, which you are supposed to do. Use \LaTeX\ to +typeset everything in the exercise except sentences in italics, which are +instructions. If you are not satisfied that you can do the exercise, then tell +me. Either write +to me +at +\begin{verse} +School of Mathematical Sciences\\ +Queen Mary and Westfield College\\ +Mile End Road\\ +London E1 4NS +\end{verse} +with hard copy of your input and output, +or email me at \mbox{\tt r.a.bailey@qmw.ac.uk} +with a copy of the +smallest possible piece of \LaTeX\ input file that contains your +attempt at the answer. +In either case +I will include a solution in the following issue of \BV: you will remain +anonymous if you wish. + + +\section*{Answers} +I promised to answer all questions arising from this series of articles (as far +as I can). + +\subsection*{Size of parentheses} +Charles M.~Goldie asks why I put $(t^{g^{-1}})v$ in Exercise~26 instead of +using \verb+\bigl(+ and \verb+\bigr)+ to make the parentheses larger than +what they enclose. +%\[\bigl(t^{g^{-1}}\bigr)\] +%\[\Bigl(t^{g^{-1}}\Bigr)\] +The answer is that you would need \verb+\Bigl(+ and \verb+\Bigr)+ to make them +large enough in this case: I should have used +\verb+\left+ and \verb+\right+ (see +Part~2 of this series) but I was lazy. + +Both he and Charles Leedham-Green have asked why I permit, or +even encourage, deeply nested parentheses, as in +\begin{equation} +u(P((1 - \varepsilon)z)), +\label{goldie} +\end{equation} +without using commands like \verb+\bigl(+ to make some of the outer +parentheses somewhat larger. In Chapter~17 of \cite{dek}, Knuth +advises that authors should use \verb+\bigl+ and its relatives to +specify the size of parentheses and other expandable fences, to +improve the readability of their formulae. However, I have +deliberately avoided telling people about these commands. + +I have two reasons for ignoring Knuth's advice. The first is that I +regard \LaTeX\ primarily as a system for {\em authors}, not for +typesetters. Authors should not be stopping to worry about the size of +parentheses, particularly if the level of nesting may change in a +later version of the document. Conventions on size of fence should be +a matter for the style designer, not the author. If someone can write +a style file that automatically detects the level of nesting and +adjusts the size accordingly, well and good. I have no objection to +using such a style file; I do object to interrupting my Mathematical +thoughts to fret over niceties of sizing. + +My second reason is related to the first. Journal editors and +executive editors tend to have policies about the size of fences, and +they will impose these policies whatever we as authors do. So it is +generally a {\em complete waste of time\/} for authors to use +\verb+\Bigr+ and the like, or for referees to insist on them. + +This is not to say that I disapprove of \verb+\left+ and +\verb+\right+. These commands automatically adjust the size of the +fence to fit what is inside it. Adding, say, an extra item inside a +\verb+\left( ... \right)+ does not cause the author to rethink the +size of the parentheses. In fact, in my \mbox{basic} style file I have +macros such as \verb+\probab+, \verb+\setof+ and \verb+\card+ which +use \verb+\left+ and \verb+\right+ precisely so that I can type as I +think, {\em the set of \ldots\/} rather than {\em squiggly brackets, + now what size and how much space?} (Oh, all right: +\begin{verbatim} + \newcommand{\card}[1]{\left|#1\right|} +\end{verbatim} +---you can guess the others.) +In fact, \verb+\left+ and \verb+\right+ make no difference to the formula +in~(\ref{goldie}), so neither of my questioners will be satisfied by my answer. + +\subsection*{Interchangeability of parentheses, brackets and braces} +Charles M.~Goldie also asks if I have an opinion about whether nested +parentheses should be routinely replaced so that one uses the sequence +$\{[( \ldots )]\}$, which is demanded by some journals. I do have an +opinion, quite a strong one, probably because one of the journals in +which I publish most frequently insists on the sequence $[\{( \ldots +)\}]$ and shows surprise (or the executive editor does) each time that +I explain that I am using $\{ \ldots \}$ to denote a {\em set}. My +opinion has been admirably expressed by Ellen Swanson in her bible of +Mathematical typesetting~\cite{swan}: +\begin{quote} + Often, however, the author of research mathematics attaches a + special meaning to different types of enclosures, and this author + believes that they {\it should be left in whatever order and variety + the author has indicated in the manuscript.} +\end{quote} +(her italics). + +\addtocounter{section}{4} +\section{Numbered and Unnumbered Displays} +\subsection{Unnumbered Maths displays} +Use \verb+\[+ and \verb+\]+ for an unnumbered single line of displayed +Maths: see Part~1. If you have two or more lines of displayed Maths +that must be vertically aligned then you need one of the +\latexword{array} environments. I shall deal with them in the final +tutorial in this series. + +\subsection{Unnumbered word displays} +Sometimes what you want to display is not simply a formula but a +verbal condition that may or may not involve short pieces of notation. +For example: +\begin{quote} +each basis vector~$f$ in~$V_{T,B}$ is orthogonal to every basis vector +in~$V_{B,T}$ except $f\psi$. +\end{quote} +If this will fit on a single line then you can use +\verb+\[\mbox{...}\]+, but this is not very satisfactory because you +have to stop and think how long it is and it is subject to changes in +the line width. I find that the \latexword{quote} environment works +well for such displays. + +\subsection{Numbered Maths displays} +Use the \latexword{equation} environment for a numbered single line of +displayed Maths such as (\ref{goldie}) in the `Answers' section above. +If you have two or more consecutive equations or formulae that do not +need to be vertically aligned, simply use one \latexword{equation} +environment per line. For vertical alignment, wait until the tutorial +on arrays. + +If you put a \verb+\label+ within an \latexword{equation} you can painlessly +refer back (or forward) to that equation. +\begin{verbatim} + For contrasts, we put + \begin{equation} + W_T = V_T \cap V_0^\perp + \label{contrasts} + \end{equation} + The space~$W_T$ was defined + in Equation~(\ref{contrasts}). +\end{verbatim} +\begin{quote} + For contrasts, we put +\begin{equation} +W_T = V_T \cap V_0^\perp +\label{contrasts} +\end{equation} +The space~$W_T$ was defined in Equation~(\ref{contrasts}). +\end{quote} + +\subsection{Numbered word displays} +Sometimes word displays also need to be numbered for reference. +\LaTeX\ does not directly provide an environment for this, but I find +that the following works quite well. +\begin{verbatim} + There is a bijection ... + \begin{equation} + \begin{minipage}[t]{0.8\linewidth} + each basis vector~$f$ ... + \end{minipage} + \end{equation} + Using ... +\end{verbatim} +\begin{quote} + There is a bijection~$\psi$ between the bases which satisfies: + \begin{equation} + \begin{minipage}[t]{0.8\linewidth} + each basis vector~$f$ in~$V_{T,B}$ is orthogonal to every basis vector + in~$V_{B,T}$ except $f\psi$. + \end{minipage} + \end{equation} + Using~$\psi$, we can show that \ldots +\end{quote} +These displays are numbered in the same sequence as the +\latexword{equation}s, and can be labelled and referred to in just the +same way. Note that I have made no attempt to make the indentation +the same as that in \latexword{quote}. + +You can suppress the \verb+[t]+ if you want the number to be +vertically centred on the display. You can replace 0.8 by any +reasonable fraction. There is a catch, however: if you have numbered +word displays labelled (9) and~(10) you may find that the second one +comes out shifted to the left, to allow space for the wider label. +Whether or not this happens depends on the settings of other +parameters, such as \verb+\linewidth+. With the default width for A4 +paper in 10pt in \LaTeXe, I found that I had to decrease 0.8 to 0.75 +in order to have satisfactory word displays numbered (9) and~(10). + +Of course, if you have two or more such displays you should make an +environment for them. I do it as follows. +\begin{verbatim} + \newenvironment{condition}% + {\equation% + \begin{minipage}[t]{0.8\linewidth}}% + {\end{minipage}\endequation} +\end{verbatim} +You may wonder why I have used \verb+\equation+ and +\verb+\endequation+ in the definition instead of +\verb+\begin{equation}+ and \verb+\end{equation}+. This is because of +the clever things that \LaTeX\ does with spaces before and after +displayed material. When you type the line +\begin{verbatim} + \end{equation} +\end{verbatim} +\LaTeX\ ignores the spaces on the rest of the line; if you type the line +\begin{verbatim} + \end{condition} +\end{verbatim} +and the final part of the \latexword{condition} environment is +\verb+\end{equation}+ then this forgetfulness about spaces is not +passed through to \verb+\end{condition}+. Use of the more primitive +\verb+\equation+ and \verb+\endequation+ does pass on the +forgetfulness. + +\subsection{Numbering equations within sections} +By default, \latexword{equation}s are numbered~1, 2, \ldots\ right +through the document in the \latexword{article} class. To make them +numbered within sections you need +\begin{verbatim} + \renewcommand{\theequation}% + {\thesection.\arabic{equation}} +\end{verbatim} +Then the first equation in Section~1 will be numbered~1.1, the +next~1.2, and so on. However, if there are four equations in +Section~1, then the first equation in Section~2 will be numbered~2.5 +because the \latexword{equation} counter has not been reset at the +start of the new section. To correct this, you also need +\begin{verbatim} + \@addtoreset{equation}{section} +\end{verbatim} +Because of the \verb+@+~sign in this command, you must either place it +in a style file or make sure that it comes between the commands +\verb+\makeatletter+ and \verb+\makeatother+ in the preamble to the +document. + +\subsection{One-off numbering of equations} +Occasionally you want to number an equation not in the main sequence +but by a particular symbol, such as ($*$) or (1.1$'$). Use the +following \latexword{oneoff} environment in place of +\latexword{equation}, putting the desired symbol as the single +parameter. +\begin{verbatim} +\newenvironment{oneoff}[1]{\equation% + \addtocounter{equation}{-1}% + \renewcommand{\theequation}{\mbox{#1}}}% + {\endequation} +\end{verbatim} +For example, +\begin{verbatim} + \begin{oneoff}{$*$} + a(p_i,q) - a(p_j,q) = 0 \bmod s + \end{oneoff} +\end{verbatim} +\begin{quote} + \begin{oneoff}{$*$} + a(p_i,q) - a(p_j,q) = 0 \bmod s + \end{oneoff} +\end{quote} +(See \cite[page~92]{leslie} or \cite[pages~98--99]{newleslie} for how these +counter commands work.) +Note that automatic cross-referencing does not work for such equations. + +If you want a one-off equation numbered~1.1$'$ related to +Equation~(1.1) then give the latter a label (say, \latexword{rowsum}) +and then do +\begin{verbatim} + \begin{oneoff}{\ref{rowsum}$'$} ... +\end{verbatim} + +\subsection{Subsequences of equations} +Suppose that between Equations~(5) and~(7) you want a sequence of +equations numbered~(6a), (6b) etc. Put the following in the preamble +to the document (or in the style file). +\begin{verbatim} +\newsavebox{\saveeqn} +\newcounter{subeqnno} +\renewcommand{\thesubeqnno}{\alph{subeqnno}} +\newenvironment{subequations}% + {\refstepcounter{equation}% + \savebox{\saveeqn}{\theequation}% + \setcounter{subeqnno}{0}}% + {} +\newenvironment{subeqn}% + {\refstepcounter{subeqnno}% + \oneoff{\usebox{\saveeqn}\thesubeqnno}}% + {\endoneoff} +\end{verbatim} +(See \cite[page~101]{leslie} or \cite[pages107--108]{newleslie} for +details of \verb+\savebox+.) Then use \latexword{subeqn} in place of +\latexword{equation} for each of the equations~(6a), (6b) etc., and +place the whole sub\-sequence in the \latexword{subequations} +environment. + +Automatic cross-referencing doesn't work for these either. The reason +is that in constructing \latexword{oneoff} and \latexword{subeqn} I +have {\em used\/} the \latexword{equation} environment rather than +{\em mimicking\/} it, with the result that any \verb+\label+ picks up +the \latexword{equation} counter. To do this properly you would have +to copy out the \latexword{equation} part of \latexword{latex.tex} +(which is well documented) and hack it (for 2.09ers; of course, +\LaTeXe\ persons would have to hack part of \latexword{ltmath.dtx} and +\latexword{classes.dtx}, which some would argue are even better +documented). I have never needed this construct often enough to bother +to do it properly, but I am sure that it could be done. + +\section*{Exercises} +\addtocounter{preqn}{47} +\begin{qn} +\it Make a numbered displayed equation saying +\[ +t\left(vP_g\right) = \left(t^{g^{-1}}\right)v +\] +and a sentence which refers to it. +\end{qn} + + +\begin{qn} +\it Make an unnumbered word display saying +\begin{quote} +\rm There is a natural surjective homomorphism $\phi\colon G \to G/N$ with +$\ker(\phi) \simeq \mathop{\rm Im}(\phi)$. +\end{quote} +\end{qn} + +\begin{qn} +\it +Make a displayed numbered verbal condition saying +\begin{quote} +\rm +for all $A$, $B$, $C$ in $\cal P$: if $A\prec B$ and $B\prec C$ then $A\prec +C$; and if $A \preceq B$ and $B\preceq A$ then $A=B$. +\end{quote} +Then add a sentence which refers to it. +\end{qn} + +\section{Theorems and their friends} +\subsection{Basics} +To make a new environment called \latexword{thm} for theorems, do +\begin{verbatim} + \newtheorem{thm}{Theorem} +\end{verbatim} + \newtheorem{thm}{Theorem} This sets up the environment, which is + then used as follows. +\begin{verbatim} + \begin{thm} + The kernel of a homomorphism + is a congruence. + \label{basic} + \end{thm} + In Theorem~\ref{basic} we ... +\end{verbatim} +\begin{quote} + \begin{thm} + The kernel of a homomorphism is a congruence. + \label{basic} + \end{thm} + In Theorem~\ref{basic} we \ldots +\end{quote} +The theorems are all given the heading `Theorem'. They are numbered +automatically, and may be cross-referred to in the usual way. + +For clarity in the rest of this section, I shall call the item like +\latexword{thm} the {\em theorem environment}, the item like +\latexword{Theorem} the {\em theorem name}, the text like `Theorem~1' +the {\em theorem head}, and the text like `The kernel of \ldots' the +{\em theorem body}. + +Note that there is nothing to prevent two different theorem +environments having the same theorem name. Indeed, the theorem name +can be empty. + +By default, the theorem head is in bold and the theorem body is in +italics. The theorems are numbered in arabic numbers, in a single +sequence throughout the document (in the \latexword{article} class). +All of these defaults can be changed, as I show below. + +It may not be obvious to the novice user, but there is more to an +environment created with \verb+\newtheorem+ than special layout and +automatic numbering. The spacing before and after each theorem +environment is controlled, and penalties are set so that no page break +will come after the first line of a theorem environment unless there +is a natural break-point in the text. + +Unfortunately, there is a bug (oops, feature) in \LaTeX\ which means +that if you put \verb+\label{...}+ immediately after +\verb+\begin{thm}+ you spoil this page-breaking penalty. But the +\verb+\label+ should be somewhere easy to find, so I always play safe +and put it immediately before \verb+\end{thm}+. + +\subsection{Named theorems} +If you have a theorem environment \latexword{thm} then you can use an optional +argument to \latexword{thm} to obtain a named theorem. For example, +\begin{verbatim} + \begin{thm}[The Central Limit Theorem] + If $X_1$, ... +\end{verbatim} +\begin{quote} + \begin{thm}[The Central Limit Theorem] + If $X_1$, $X_2$, \ldots, $X_n$ are independent \ldots + \end{thm} +\end{quote} +or +\begin{verbatim} + \begin{thm}[Galois, 1832] +\end{verbatim} +\begin{quote} + \begin{thm}[Galois, 1832] + If $L:K$ is a finite normal \ldots + \end{thm} +\end{quote} + +\subsection{Sequences of numbering} +Two optional arguments to \verb+\newtheorem+ give you control of which +theorem environments are numbered in which sequences. Although it is +logical to number theorems, lemmas, corollaries etc.\ all in their own +sequences, it is much easier to find your way around a long document +if they are all in a single sequence. To get a theorem environment +\latexword{lem} numbered in the same sequence as \latexword{thm}, do +\begin{verbatim} + \newtheorem{lem}[thm]{Lemma} +\end{verbatim} + \newtheorem{lem}[thm]{Lemma} +After the theorems we have had so far, if we now do +\begin{verbatim} + \begin{lem} + With the above notation ... + \end{lem} +\end{verbatim} +we get +\begin{quote} + \begin{lem} + With the above notation \ldots + \end{lem} +\end{quote} + + +The other optional argument numbers the theorem environment inside something +else. If you want the second example in Section~3 to be numbered~3.2 +irrespective of how many examples there were in previous sections, then do +\begin{verbatim} + \newtheorem{eg}{Example}[section] +\end{verbatim} +You can use at most one optional argument with each \verb+\newtheorem+ +command. + +You can even number one theorem environment inside another: for +example +\begin{verbatim} + \newtheorem{cor}{Corollary}[thm] +\end{verbatim} +if you want the corollaries after Theorem~10 to be Corollary~10.1, +Corollary~10.2, etc. Be careful not to create a circle of environments numbered +within each other. + +\subsection{Unnumbered environments} +There are several items, such as definitions, remarks and notation, +that clearly should be theorem-like environments except that they +should not be numbered. It would be possible to set them all up and +then separately adjust the counter on each one so that it is not +numbered. However, it is easier to take advantage of the +number-in-the-same-sequence option. Set up a single unnumbered counter +with +\begin{verbatim} + \newcounter{unnumber} + \renewcommand{\theunnumber}{} +\end{verbatim} +and then put the other unnumbered theorem environments in the same sequence +with +\begin{verbatim} + \newtheorem{rem}[unnumber]{Remark} + \newtheorem{def}[unnumber]{Definition} +\end{verbatim} + + +\subsection{Other systems of numbering} +Many Mathematicians want the possibility of having Theorem~A, Theorem~B etc.\ +as well as Theorem~1 etc. This is no problem. Use the commands given in +\cite[page~92]{leslie} or \cite[page~98]{newleslie} to alter the way a theorem +environment is numbered. Thus +\begin{verbatim} + \newtheorem{thma}{Theorem} + \renewcommand{\thethma}{\Alph{thma}} + \begin{thma} The subgroups ... + ... + \begin{thma} The irreducible ... + \label{char} + ... + The result of Theorem~\ref{char} \ldots +\end{verbatim} + \newtheorem{thma}{Theorem} + \renewcommand{\thethma}{\Alph{thma}} +\begin{quote} + \begin{thma} The subgroups \ldots + \end{thma} + \begin{thma} The irreducible \ldots + \label{char} + \end{thma} +The result of Theorem~\ref{char} \ldots +\end{quote} + +Other possibilities for numbering are +\[ +\begin{tabular}{ll} +\verb+\alph{thma}+ & Theorem~b\\ +\verb+\roman{thma}+ & Theorem~ii\\ +\verb+\Roman{thma}+ & Theorem~II +\end{tabular} +\] + + + +\subsection{Changing the fonts} +Fonts are handled differently in \LaTeX\ 2.09, +in NFSS, and in the new standard \LaTeX, \LaTeXe. +All the suggestions that I give in this section work in both \LaTeX\ 2.09 and +\LaTeXe. They do not work at all if you run NFSS without \LaTeXe. If you are +using \LaTeXe, you {\em must\/} use the forms like \verb+\sc+ given here: the +commands like \verb+\textsc+ will not do the right thing, because they +{\em add\/} small capitals (say) to the default fonts instead of +{\em replacing\/} the default fonts. + +The \verb+\newtheorem+ command in \LaTeX\ is the most wonderful thing +to happen to Mathematical writers in a long time, because so many of +our constructs fit it. However, one of the worst things to happen to +Mathematical writers is the hard-wiring of the fonts for the theorem +heads and the theorem bodies. Ordinary \LaTeX\ simply does not give +you the flexibility to change these easily. Yet the defaults are not +always appropriate, and different journals demand different fonts for +these purposes. I suspect that this hard-wiring is one reason that +some Mathematicians have been reluctant to use \LaTeX. What can the +ordinary user do about this problem? + +I shall give four answers, because different solutions are appropriate +in different circumstances. + +(i)~\littlehead{Bare hands} Sometimes (for example, when sending an +article to \BV) you cannot submit your favourite style files along +with your main file. So you need a `bare hands' way of changing the +fonts, without losing too much genericity. Here's how. + +To make a theorem environment \latexword{prop} whose theorem head is +set in small capitals, do +\begin{verbatim} + \newtheorem{prop}{\sc Proposition} +\end{verbatim} +For a small document, this will do. To be more generic, you could do +\begin{verbatim} + \newcommand{\headfont}{\sc} + \newtheorem{prop}{\headfont Proposition} +\end{verbatim} +so that only one line has to be changed if you decide to change the +font of all the theorem heads. + +To make a theorem environment \latexword{qn} whose theorem body font +is set in roman, use a two-stage process. The exercises in this +sequence of tutorials are defined by +\begin{verbatim} + \newtheorem{preqn}{Exercise} + \newenvironment{qn}{\preqn\rm}% + {\endpreqn} +\end{verbatim} +(The exercises in this particular tutorial are bad examples, because +they all have italic instructions.) + +(ii)~\littlehead{Mittelbach's style file} Frank Mittelbach wrote the +style file \latexword{theorem.sty}, which should be available from all +good CTAN hosts. It is described in \cite[pages~251--255]{companion}. +It enables you to change the fonts and the layout of theorem +environments. However, it does not do exactly what I need. + +(iii)~\littlehead{My style file} When I first started to use \LaTeX\ +it was obvious to me that a flexible means of changing the fonts for +theorem heads and theorem bodies had to be provided. I hacked +\verb+@begintheorem+ from \latexword{latex.tex} to produce a style +file which lets me give a single command to set the font for theorem +heads, another to set the font for (most) theorem bodies, and another +to say that all subsequently declared theorem environments will have +their bodies set in `ordinary' type: not necessarily in roman, but in +{\em whatever font the surrounding text is in}. However, like many +others, I deplore the proliferation of personal style files because +they inhibit portability of documents, so I haven't made this style +file generally available. + +(iv)~\littlehead{American Mathematical Society} The old version of +\latexword{amstex.sty} (see \cite{amslatex}) gives the user the +possibility of declaring theorem environments in three classes---plain +theorems, definitions and remarks. However, it does not give the user +any control over the fonts used in those environments. I do not know +if the forthcoming package \latexword{amsthm.sty} will give any more +freedom. + +\subsection{Proofs} +We all need a proof environment, so everyone invents her own, some +more successfully than others. I think that the proof environment +should be made with \verb+\newtheorem+, so that all the benefits of +spacing, of page-break penalties and of consistent head fonts can be +retained. Of course, proofs should be unnumbered and (usually) set in +the same font as the surrounding text. So I simply use the foregoing +methods to create an environment \latexword{pf} with name +\latexword{Proof} which is unnumbered and has its body +set either in the surrounding text font or in roman. +%\begin{verbatim} +% \plaintheorems +% \newtheorem{pf}[unnumber]{Proof} +%\end{verbatim} + +What should you do about the end-of-proof symbol? Some people want it put in +automatically. In principle this could be done with something like +\begin{verbatim} + \newenvironment{proof}{\pf}% + {\eop\endpf} +\end{verbatim} +where \verb+\eop+ is your favourite end-of-proof symbol, for example +\begin{verbatim} +\unskip\protect\nolinebreak\mbox{\quad$\Box$} +\end{verbatim} +This is not really satisfactory if you have any proofs that end in +displayed Maths (or any other sort of display). Traditionally the +end-of-proof sign goes in the display, not on a new line; but if you +have a display inside an environment then \LaTeX\ finishes off the +display and gets ready for a new line before it reads the instructions +for the end of the environment. So my advice is to have an \verb+\eop+ +macro and put it in by hand at the end of every proof, either just +inside the final display (if this is the last thing in the proof) or +just before the \verb+\end{pf}+. + + +\subsection{Questions and Exercises} + +A theorem environment is ideal for questions on exam papers and +coursework sheets, and exercises in text books. It is usually better +than \latexword{enumerate} because it retains the normal text\-width, +paragraph indentation and paragraph separation. If you want the +questions to be headed simply `1', `2', etc. then do +\begin{verbatim} + \newtheorem{question}{} +\end{verbatim} + +If the questions have parts and subparts, it is sensible to use +\latexword{enumerate} for them. In that case you probably need to change the +default numbering of the \latexword{enumerate} environments so that, say, parts +are labelled~`(a)' etc.\ and subparts~`(ii)' etc. The next section shows how +to do this. + +\section*{Exercises} +\begin{qn} +\it +Create a short document with two sections. +In the first section put one theorem, +a lemma subtitled `Burnside', another theorem, and a remark. The remark should +be neither numbered nor in italic. In the second section put another lemma, +another theorem, a corollary numbered in the same sequence as the theorems, and +finally a theorem in a roman-numbered sequence. +Include cross-references to all the numbered items. +\label{thmdoc} +\end{qn} + +\begin{qn} +\it +Redo the previous question, in such a way that lemmas and equations are +numbered within sections. +\end{qn} + +\section{Other numbered things} +\subsection{Numbered lists} +If you use \latexword{enumerate} within a theorem environment then you will +probably have to change the way that the different levels of enumerated list +are numbered. This is controlled by commands containing the strings +\latexword{enumi}, \latexword{enumii}, \latexword{enumiii} and +\latexword{enumiv}. Thus the $N$th level of nesting is controlled by +\latexword{enumN}. + +The counter for \latexword{enumN} is called simply \latexword{enumN}. To alter +whether the counter is displayed as an arabic numeral, a letter etc., you +change \verb+\theenumN+ (see \cite[pages~91--92]{leslie} or +\cite[pages~97--99]{newleslie}.) To alter the printed labels which are +put on the items in the +list, change \verb+\labelenumN+ to be a suitable text containing +\verb+\theenumN+. + +I find that two levels of nesting are quite sufficient within exam questions +and homework problems. My style files for exams and homeworks contain the lines +\begin{verbatim} + \renewcommand{\theenumi}{\alph{enumi}} + \renewcommand{\labelenumi}{(\theenumi)} + \renewcommand{\theenumii}{\roman{enumii}} + \renewcommand{\labelenumii}{(\theenumii)} +\end{verbatim} +In a book, you might need to put something similar in the start of an +\latexword{exercises} environment. + +If you are lazy then you might try to alter just \verb+\labelenumN+. The +list items will have the correct printed labels but your printed +cross-references will not match. +The cross-reference generated by a \verb+\ref+ call to a \verb+\label+ in the +$N$th level of nested \latexword{enumerate}s has the form +\begin{verbatim} + \p@enumN\theenumN +\end{verbatim} +where \verb+\p@enumN+ usually picks up the \verb+\theenumM+ +from higher levels ($M < N$), and +possibly some punctuation. If you don't like the settings of \verb+\p@enumN+ +that \LaTeX\ gives you by default, you will have to change them in a style file. + +\subsection{Footnotes} +Mathematicians usually don't use footnotes, because the footnote marks would be +interpreted as superscripts or operators. However, we do sometimes like to put +information at the bottom of the first page of a document, under a horizontal +line: perhaps an address for correspondence, or a list of AMS subject +categories. You can do this with a \verb+\footnote+ early in the document, so +long as you have first done +\begin{verbatim} + \renewcommand{\thefootnote}{} +\end{verbatim} +It is best to put this command in a small group around the use of +\verb+\footnote+. + +\section*{Exercises} +\begin{qn} +\textit{Modify the document in Exercise~\ref{thmdoc} so that one of the theorems +has parts and subparts. The parts should be labelled} +\begin{quote} +[A], [B], \ldots +\end{quote} +\textit{and the subparts} +\begin{quote} +1/, 2/, \ldots . +\end{quote} +\label{enumex} +\end{qn} + +\begin{qn} +\textit{Modify the document in Exercise~\ref{enumex} so that the foot of the +first page carries the text} +\begin{quote} +Key words: construction of designs; neighbour balance; optimality; +randomization; software. +\end{quote} + +\end{qn} + +\begin{thebibliography}{9} +\bibitem{amslatex} +\writer{American Mathematical Society} +\book{\AMS-\LaTeX\ Version~1.0 User's Guide} +\publish{American Mathematical Society}{Providence, Rhode Island} +\byear{1990} + +\bibitem{companion} +\writer{Goossens,~M., Mittelbach,~F. \& Samarin,~A.} +\book{The \LaTeX\ Companion} +\publish{Addison-Wesley}{Reading, Mass.} +\byear{1994} + +\bibitem{dek} +\writer{Knuth,~D.~E.} +\book{The \TeX book} +\publish{Addison-Wesley}{Reading, Mass.} +\byear{1984} + +\bibitem{leslie} +\writer{Lamport,~L.} +\book{\LaTeX: A Document Preparation System} +first edition, +\publish{Addison-Wesley}{Reading, Mass.} +\byear{1986} + +\bibitem{newleslie} +\writer{Lamport,~L.} +\book{\LaTeX: A Document Preparation System} +second edition, +\publish{Addison-Wesley}{Reading, Mass.} +\byear{1994} + +\bibitem{swan} +\writer{Swanson, E.} +\book{Mathematics into Type} +revised edition, +\publish{American Mathematical Society}{Providence, Rhode Island} +\byear{1979} +\end{thebibliography} +\end{Article} +\endinput + +leslie +newleslie +\bibitem{hart} +%\writer{Oxford University Press} +\book{Hart's Rules for Compositors and Readers} +\publish{Oxford University Press}{Oxford} +\byear{1967} +\bibitem{chamb} +\book{The Chambers Dictionary} +\publish{Chambers Harrap}{Edinburgh} +\byear{1993} +\bibitem{chicago} +\book{The Chicago Manual of Style} +\publish{The University of Chicago Press}{Chicago} +\byear{1982} + +Like many others, I deplore the proliferation of personal style files +because they inhibit portability of documents. Yet when I first +started to use \LaTeX\ it was obvious to me that a flexible means of +changing the fonts for theorem heads and theorem bodies had to be +provided. I hacked \verb+@begintheorem+ from \latexword{latex.tex} to +produce the code in Figure~\ref{rabcode}. My only excuse for +reproducing it here is that none of the widely available styles gives +the necessary flexibility. +\begin{figure*} +\begin{verbatim} +%commands to change the type face in theorems +%default is heading in small caps, content in roman +\newif\ifplaintheorems +\def\plaintheorems{\plaintheoremstrue} +\def\fancytheorems{\plaintheoremsfalse} + +\let\thmheadfont\sc +\let\thmcontfont\rm +\def\theoremheadfontis#1{\def\thmheadfont{#1}} +\def\theoremcontfontis#1{\def\thmcontfont{#1}} + +\def\@xnthm#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname +{\@definecounter{#1}\@addtoreset{#1}{#3}% +\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% + \ifplaintheorems \global\@namedef{#1}{\@thm{#1}{#2}}% + \else \global\@namedef{#1}{\thmcontfont\@thm{#1}{#2}}\fi% +\global\@namedef{end#1}{\@endtheorem}}} + +\def\@ynthm#1#2{\expandafter\@ifdefinable\csname #1\endcsname +{\@definecounter{#1}% +\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \ifplaintheorems \global\@namedef{#1}{\@thm{#1}{#2}}% + \else \global\@namedef{#1}{\thmcontfont\@thm{#1}{#2}}\fi% +\global\@namedef{end#1}{\@endtheorem}}} + +\def\@othm#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}}% +\ifplaintheorems \global\@namedef{#1}{\@thm{#2}{#3}}% +\else \global\@namedef{#1}{\thmcontfont\@thm{#2}{#3}}\fi% +\global\@namedef{end#1}{\@endtheorem}}} + +\def\@begintheorem#1#2% + {\trivlist\item[\hskip\labelsep + \thmheadfont #1\ #2\unskip]} +\def\@opargbegintheorem#1#2#3 + {\trivlist\item[\hskip\labelsep + \thmheadfont #1\ #2\unskip\ (#3)]} +\end{verbatim} +\caption{Revised code to give flexible changes to fonts in theorems} +\label{rabcode} +\end{figure*} +If you put this code into your style file then you can make all your theorem +heads come out in italic by doing +\begin{verbatim} + \theoremheadfontis{\it} +\end{verbatim} +To put all the theorem bodies in slanted type do +\begin{verbatim} + \theoremcontfontis{\sl} +\end{verbatim} +Each of these commands should be used at most once in the document. However, +you can also use the command +\begin{verbatim} + \plaintheorems +\end{verbatim} +After this command has been issued, any theorem environments declared +subsequently will have their bodies set in `ordinary' type: not necessarily in +roman, but in {\em whatever font the surrounding text is in}. This seems to me +most suitable for remarks, definitions and so on. The command +\verb+\fancytheorems+ nullifies \verb+\plaintheorems+. + +\end{Article} -- cgit v1.2.3