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86f6a31e 1% \begin{meta-comment} <general public licence>
2%%
3%% mdwmath package -- various nicer mathematical things
8bc5bdd2 4%% Copyright (c) 2003, 2020 Mark Wooding
86f6a31e 5%%
3d509049 6%% This file is part of the `mdwtools' LaTeX package collection.
86f6a31e 7%%
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8%% `mdwtools' is free software: you can redistribute it and/or modify it
9%% under the terms of the GNU General Public License as published by the
10%% Free Software Foundation; either version 2 of the License, or (at your
11%% option) any later version.
12%%
13%% `mdwtools' is distributed in the hope that it will be useful, but
14%% WITHOUT ANY WARRANTY; without even the implied warranty of
15%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16%% General Public License for more details.
86f6a31e 17%%
18%% You should have received a copy of the GNU General Public License
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19%% along with `mdwtools'. If not, write to the Free Software Foundation,
20%% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
86f6a31e 21%%
22% \end{meta-comment}
23%
24% \begin{meta-comment} <Package preamble>
25%<+package>\NeedsTeXFormat{LaTeX2e}
26%<+package>\ProvidesPackage{mdwmath}
af8af7eb 27%<+package> [2020/09/06 1.14.0 Nice mathematical things]
86f6a31e 28%<+oldeqnarray>\NeedsTeXFormat{LaTeX2e}
29%<+oldeqnarray>\ProvidesPackage{eqnarray}
af8af7eb 30%<+oldeqnarray> [2020/09/06 1.14.0 Old enhanced eqnarray]
86f6a31e 31% \end{meta-comment}
32%
3ba7380e 33% \CheckSum{740}
86f6a31e 34%% \CharacterTable
35%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
36%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
37%% Digits \0\1\2\3\4\5\6\7\8\9
38%% Exclamation \! Double quote \" Hash (number) \#
39%% Dollar \$ Percent \% Ampersand \&
40%% Acute accent \' Left paren \( Right paren \)
41%% Asterisk \* Plus \+ Comma \,
42%% Minus \- Point \. Solidus \/
43%% Colon \: Semicolon \; Less than \<
44%% Equals \= Greater than \> Question mark \?
45%% Commercial at \@ Left bracket \[ Backslash \\
46%% Right bracket \] Circumflex \^ Underscore \_
47%% Grave accent \` Left brace \{ Vertical bar \|
48%% Right brace \} Tilde \~}
49%%
50%
51% \begin{meta-comment}
52%
53%<*driver>
54\input{mdwtools}
55\let\opmod\pmod
56\usepackage{amssymb}
57\describespackage{mdwmath}
4a655c6f 58%\describespackage{eqnarray}
86f6a31e 59\ignoreenv{old-eqnarray}
4a655c6f 60%\unignoreenv{old-eqnarray}
86f6a31e 61\mdwdoc
62%</driver>
63%
64% \end{meta-comment}
65%
66% \section{User guide}
67%
68% \subsection{Square root typesetting}
69%
70% \DescribeMacro{\sqrt}
71% The package supplies a star variant of the |\sqrt| command which omits the
72% vinculum over the operand (the line over the top). While this is most
73% useful in simple cases like $\sqrt*{2}$ it works for any size of operand.
74% The package also re-implements the standard square root command so that it
75% positions the root number rather better.
76%
77% \begin{figure}
78% \begin{demo}[w]{Examples of the new square root command}
79%\[ \sqrt*{2} \quad \mbox{rather than} \quad \sqrt{2} \]
80%\[ \sqrt*[3]{2} \quad \mbox{ rather than } \quad \sqrt[3]{2} \]
81%\[ \sqrt{x^3 + \sqrt*[y]{\alpha}} - \sqrt*[n+1]{a} \]
82%\[ x = \sqrt*[3]{\frac{3y}{7}} \]
83%\[ q = \frac{2\sqrt*{2}}{5}+\sqrt[\frac{n+1}{2}]{2x^2+3xy-y^2} \]
84% \end{demo}
85% \end{figure}
86%
87% [Note that omission of the vinculum was originally a cost-cutting exercise
88% because the radical symbol can just fit in next to its operand and
89% everything ends up being laid out along a line. However, I find that the
90% square root without vinculum is less cluttered, so I tend to use it when
91% it doesn't cause ambiguity.]
92%
93% \subsection{Modular arithmetic}
94%
95% In standard maths mode, there's too much space before the parentheses in
96% the output of the |\pmod| command. Suppose that $x \equiv y^2 \opmod n$:
97% then the spacing looks awful. Go on, admit it.
98%
99% It looks OK in a display. For example, if
100% \[ c \equiv m^e \opmod n \]
101% then it's fine. The package redefines the |\pmod| command to do something
102% more sensible. So now $c^d \equiv m^{ed} \equiv m \pmod n$ and all looks
103% fine.
104%
105% \subsection{Some maths symbols you already have}
106%
107% \DescribeMacro\bitor
108% \DescribeMacro\bitand
109% \DescribeMacro\dblor
110% \DescribeMacro\dbland
111% Having just tried to do some simple things, I've found that there are maths
112% symbols missing. Here they are, in all their glory:
113% \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
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114% $\&$ & "\&" & $\bitor$ & "\bitor" & $\dbland$ & "\dbland" \\
115% $\bitand$ & "\bitand" & $\dblor$ & "\dblor" &
86f6a31e 116% \end{tabular} \end{center}
117%
118% \DescribeMacro\xor
119% \DescribeMacro\cat
120% I also set up the |\xor| command to typeset `$\xor$', which is commonly
121% used to represent the bitsize exclusive-or operation among cryptographers.
122% The command |\cat| typesets `$\cat$', which is a common operator indicating
123% concatenation of strings.
124%
125% \DescribeMacro\lsl
126% \DescribeMacro\lsr
127% \DescribeMacro\rol
128% \DescribeMacro\ror
129% The commands |\lsl| and |\lsr| typeset binary operators `$\lsl$' and
130% `$\lsr$' respectively, and |\rol| and |\ror| typeset `$\rol$' and `$\ror$'.
131% Note that these are spaced as binary operators, rather than relations.
132%
133% \DescribeMacro\compose
134% \DescribeMacro\implies
135% \DescribeMacro\vect
136% The |\compose| command typesets `$\compose$', which is usually used to
137% denote function composition. The |\implies| command is made to typeset
138% `$\implies$'. And \syntax{"\\vect{"<x>"}"} typesets `$\vect{x}$'.
139%
140% \DescribeMacro\statclose
141% \DescribeMacro\compind
142% The |\statclose| command typesets `$\statclose$', which indicates
143% `statistical closeness' of probability distributions; |\compind| typesets
144% `$\compind$', which indicates computational indistinguishability.
145%
4a655c6f 146% \subsection{Fractions}
147%
148% \DescribeMacro\fracdef
149% We provide a general fraction system, a little tiny bit like
150% \package{amsmath}'s |\genfrac|. Say
151% \syntax{"\\fracdef{"<name>"}{"<frac-params>"}"} to define a new
152% |\frac|-like operator. The \<frac-params> are a comma-separated list of
153% parameters:
154% \begin{description}
155% \item[\lit*{line}] Include a horizontal line between the top and bottom
156% (like |\frac|).
157% \item[\lit*{line=}\<length>] Include a horizontal line with width
158% \<length>.
159% \item[\lit*{noline}] Don't include a line (like |\binom|).
160% \item[\lit*{leftdelim=}\<delim>] Use \<delim> as the left-hand delimiter.
161% \item[\lit*{rightdelim=}\<delim>] Use \<delim> as the right-hand delimiter.
162% \item[\lit*{nodelims}] Don't include delimiters.
163% \item[\lit*{style=}\<style>] Typeset the fraction in \<style>, which is one
164% of |display|, |text|, |script| or |scriptscript|.
165% \item[\lit*{style}] Use the prevailing style for the fraction.
166% \item[\lit*{innerstyle=}\<style>] Typeset the \emph{components} of the
167% fraction in \<style>.
168% \item[\lit*{innerstyle}] Typeset the fraction components according to the
169% prevailing style.
170% \end{description}
171% The commands created by |\fracdef| have the following syntax:
172% \syntax{<name>"["<frac-params>"]{"<top>"}{"<bottom>"}"}. Thus, you can use
173% the optional argument to `tweak' the fraction if necessary. This isn't
174% such a good idea to do often.
175%
176% \DescribeMacro\frac
177% \DescribeMacro\binom
86f6a31e 178% \DescribeMacro\jacobi
4a655c6f 179% The macros |\frac|, |\binom| and |\jacobi| are defined using |\fracdef|.
180% They typset $\frac{x}{y}$, $\binom{n}{k}$ and $\jacobi{x}{n}$ respectively.
181% (The last may be of use to number theorists talking about Jacobi or
182% Lagrange symbols.)
183%
184% By way of example, these commands were defined using
185%\begin{verbatim}
186%\fracdef\frac{nodelims, line}
187%\fracdef\binom{leftdelim = (, rightdelim = ), noline}
188%\fracdef\jacobi{leftdelim = (, rightdelim = ), line}
189%\end{verbatim}
86f6a31e 190%
191% \subsection{Rant about derivatives}
192%
193% \DescribeMacro\d
194% There is a difference between UK and US typesetting of derivatives.
195% Americans typeset
196% \[ \frac{dy}{dx} \]
197% while the British want
198% \[ \frac{\d y}{\d x}. \]
4a655c6f 199% The command |\d| command is fixed to typeset a `$\d$'. (In text mode,
200% |\d{x}| still typesets `\d{x}'.)
86f6a31e 201%
202% \subsection{New operator names}
203%
204% \DescribeMacro\keys
205% \DescribeMacro\dom
206% \DescribeMacro\ran
207% \DescribeMacro\supp
208% \DescribeMacro\lcm
4a655c6f 209% \DescribeMacro\ord
210% \DescribeMacro\poly
211% \DescribeMacro\negl
86f6a31e 212% A few esoteric new operator names are supplied.
213% \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
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214% $\keys$ & "\keys" & $\dom$ & "\dom" & $\ran$ & "\ran" \\
215% $\supp$ & "\supp" & $\lcm$ & "\lcm" & $\ord$ & "\ord" \\
216% $\poly$ & "\poly" & $\negl$ & "\negl"
86f6a31e 217% \end{tabular} \end{center}
218% I think |\lcm| ought to be self-explanatory. The |\dom| and |\ran|
219% operators pick out the domain and range of a function, respectively; thus,
220% if $F\colon X \to Y$ is a function, then $\dom F = X$ and $\ran F = Y$.
221% The \emph{support} of a probability distribution $\mathcal{D}$ is the set
222% of objects with nonzero probability; i.e., $\supp{D} = \{\, x \in
4a655c6f 223% \dom\mathcal{D} \mid \mathcal{D}(x) > 0 \,\}$. If $g \in G$ is a group
224% element then $\ord g$ is the \emph{order} of $g$; i.e., the smallest
225% positive integer $i$ where $g^i$ is the identity element, or $0$ if there
226% is no such $i$. $\poly(n)$ is some polynomial function of $n$. A function
227% $\nu(\cdot)$ is \emph{negligible} if, for every polynomial function
228% $p(\cdot)$, there is an integer $N$ such that $\nu(n) < 1/p(n)$ for all $n
229% > N$; $\negl(n)$ is some negligible function of $n$.
86f6a31e 230%
231% \subsection{Standard set names}
232%
233% \DescribeMacro\Z
234% \DescribeMacro\Q
235% \DescribeMacro\R
236% \DescribeMacro\C
237% \DescribeMacro\N
238% \DescribeMacro\F
239% \DescribeMacro\powerset
4a655c6f 240% \DescribeMacro\gf
86f6a31e 241% If you have a |\mathbb| command defined, the following magic is revealed:
242% \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
243% $\Z$ & "\Z" & $\Q$ & "\Q" & $\R$ & "\R" \\
244% $\N$ & "\N" & $\F$ & "\F" & $\C$ & "\C"
245% \end{tabular} \end{center}
246% which are handy for various standard sets of things. Also the |\powerset|
4a655c6f 247% command typesets `$\powerset$', and \syntax{"\\gf{"<q>"}"}, which by default
248% typesets $\gf{\syntax{<q>}}$ but you might choose to have it set
249% $\mathrm{GF}(\syntax{<q>})$ intead.
250%
251% \subsection{Biggles}
252%
253% \DescribeMacro\bbigg
254% \DescribeMacro\bbiggl
255% \DescribeMacro\bbiggr
256% \DescribeMacro\bbiggm
257% The |\bbigg| commands generalizes the Plain \TeX\ |\bigg| family of
258% macros. |\bbigg| produces an `ordinary' symbol; |\bbiggl| and |\bbiggr|
259% produce left and right delimiters; and |\bbiggm| produces a relation. They
260% produce symbols whose size is related to the prevailing text size -- so
261% they adjust correctly in chapter headings, for example.
262%
263% The syntax is straightforward:
264% \syntax{"\\"<bigop>"["$a$"]{"$n$"}{"<delim>"}"}. Describing it is a bit
265% trickier. The size is based on the current |\strut| height. If |\strut|
266% has a height of $h$ and a depth of $d$, then the delimiter produced has a
267% height of $n \times (h + d + a)$.
268%
269% The old |\big| commands have been redefined in terms of |\bbigg|.
86f6a31e 270%
271% \subsection{The `QED' symbol}
272%
273% \DescribeMacro\qed
274% \DescribeMacro\qedrule
275% For use in proofs of theorems, we provide a `QED' symbol which behaves well
276% under bizarre line-splitting conditions. To use it, just say |\qed|. The
277% little `\qedrule' symbol is available on its own, by saying |\qedrule|.
278% This also sets |\qedsymbol| if it's not set already.
279% \qed
280%
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281% \subsection{Punctuation in displays}
282%
283% It's conventional to follow displayed equations with the necessary
284% punctuation for them to fit into the surrounding prose. This isn't
285% universal: Ian Stewart says in the preface to the third edition of his
286% \emph{Galois Theory}:\footnote{^^A
287% Chapman \& Hall/CRC Mathematics, 2004; ISBN 1-58488-393-6.} ^^A
288% \begin{quote}
289% Along the way I made once change that may raise a few eyebrows. I have
290% spent much of my career telling students that written mathematics should
291% have punctuation as well as symbols. If a symbol or a formula would be
292% followed by a comma if it were replaced by a word or phrase, then it
293% should be followed by a comma; however strange the formula then looks.
294%
295% I still think that punctuation is essential for formulas in the main body
296% of the text. If the formula is $t^2 + 1$, say, then it should have its
297% terminating comma. But I have come to the conclusion that eliminating
298% visual junk from the printed page is more important than punctuatory
299% pedantry, so that when the same formula is \emph{displayed}, for example
300% \[ t^2 + 1 \]
301% then it looks silly if the comma is included, like this,
302% \[ t^2 + 1 \mpunct{,} \]
303% and everything is much cleaner and less ambiguous without punctuation.
304%
305% Purists will hate this, though many of them would not have noticed had I
306% not pointed it out here. Until recently, I would have agreed. But I
307% think it is time we accepted that the act of displaying a formula equips
308% it with \emph{implicit} (invisible) punctuation. This is the 21st
309% century, and typography has moved on.
310% \end{quote}%
311%
312% \DescribeMacro\mpunct
313% I tended to agree with Prof.\ Stewart, even before I read his preface; but
314% now I'm not so sure, and it's clear that we're in the minority. Therefore,
315% the command |\mpunct| sets its argument as text, a little distance from
316% the preceding mathematics.
317%
86f6a31e 318% \begin{ignore}
319% There used to be an eqnarray here, but that's migrated its way into the
320% \package{mdwtab} package. Maybe the original version, without dependency
321% on \package{mdwtab} ought to be releasable separately. I'll keep it around
322% just in case.
323%
324% The following is the documentation for the original version. There's an
325% updated edition in \package{mdwtab}.
326% \end{ignore}
327%
328% \begin{old-eqnarray}
329%
330% \subsection{A new \env{eqnarray} environment}
331%
332% \LaTeX's built-in \env{eqnarray} is horrible -- it puts far too much space
333% between the items in the array. This environment is rather nearer to the
334% \env{amsmath} \env{align} environments, although rather less capable.
335%
336% \bigskip
337% \DescribeEnv{eqnarray}
338% {\synshorts
339% \setbox0\hbox{"\\begin{eqnarray}["<preamble>"]" \dots "\\end{eqnarray}"}
340% \leavevmode \hskip-\parindent \fbox{\box0}
341% }
342% \smallskip
343%
344% The new version of \env{eqnarray} tries to do everything which you really
345% want it to. The \synt{preamble} string allows you to define the column
346% types in a vaguely similar way to the wonderful \env{tabular} environment.
347% The types provided (and it's easy-ish to add more) are:
348%
349% \def\ch{\char`}
78cdb9cc 350% \begin{description} \setdescriptionlabel{\normalfont\ttfamily#1}
86f6a31e 351% \item [r] Right aligned equation
352% \item [c] Centre-aligned equation
353% \item [l] Left aligned equation
354% \item [\textrm{\texttt{Tr}, \texttt{Tc} and \texttt{Tl}}] Right, centre and
355% left aligned text (not maths)
356% \item [L] Left aligned zero-width equation
357% \item [x] Centred entire equation
358% \item [:] Big gap separating sets of equations
359% \item [q] Quad space
360% \item [>\ch\{\synt{text}\ch\}] Insert text before column
361% \item [<\ch\{\synt{text}\ch\}] Insert text after column
362% \end{description}
363%
364% Some others are also defined: don't use them because they do complicated
365% things which are hard to explain and they aren't much use anyway.
366%
367% The default preamble, if you don't supply one of your own, is \lit{rcl}.
368% Most of the time, \lit{rl} is sufficient, although compatibility is more
369% important to me.
370%
371% By default, there is no space between columns, which makes formul\ae\ in an
372% \env{eqnarray} environment look just like formul\ae\ typeset on their own,
373% except that things get aligned in columns. This is where the default
374% \env{eqnarray} falls down: it leaves |\arraycolsep| space between each
375% column making the thing look horrible.
376%
377% An example would be good here, I think. This one's from exercise 22.9 of
378% the \textit{\TeX book}.
379%
380% \begin{demo}[w]{Simultaneous equations}
381%\begin{eqnarray}[rcrcrcrl]
382% 10w & + & 3x & + & 3y & + & 18z & = 1 \\
383% 6w & - & 17x & & & - & 5z & = 2
384%\end{eqnarray}
385% \end{demo}
386%
387% Choosing a more up-to-date example, here's one demonstrating the \lit{:}
388% column specifier from the \textit{\LaTeX\ Companion}.
389%
390% \begin{demo}[w]{Lots of equations}
391%\begin{eqnarray}[rl:rl:l]
eafdddad 392% V_i &= v_i - q_i v_j, & X_i &= x_i - q_i x_j, &
86f6a31e 393% U_i = u_i, \qquad \mbox{for $i \ne j$} \label{eq:A} \\
394% V_j &= v_j, & X_j &= x_j &
395% U_j u_j + \sum_{i \ne j} q_i u_i.
396%\end{eqnarray}
397% \end{demo}
398%
399% We can make things more interesting by adding a plain text column. Here we
400% go:
401%
402% \begin{demo}[w]{Plain text column}
403%\begin{eqnarray}[rlqqTl]
404% x &= y & by (\ref{eq:A}) \\
405% x' &= y' & by definition \\
406% x + x' &= y + y' & by Axiom~1
407%\end{eqnarray}
408% \end{demo}
409%
410% The new features also mean that you don't need to mess about with
411% |\lefteqn| any more. This is handled by the \lit{L} column type:
412%
413% \begin{demo}{Splitting example}
414%\begin{eqnarray*}[Ll]
415% w+x+y+z = \\
4a655c6f 416% & a+b+c+d+e+{} \\
86f6a31e 417% & f+g+h+i+j
418%\end{eqnarray*}
419% \end{demo}
420%
421% Finally, just to prove that the spacing's right at last, here's another one
422% from the \textit{Companion}.
423%
424% \begin{demo}{Spacing demonstration}
425%\begin{equation}
426% x^2 + y^2 = z^2
427%\end{equation}
428%\begin{eqnarray}[rl]
429% x^2 + y^2 &= z^2 \\
430% y^2 &< z^2
431%\end{eqnarray}
432% \end{demo}
433%
434% Well, that was easy enough. Now on to numbering. As you've noticed, the
435% equations above are numbered. You can use the \env{eqnarray$*$}
436% environment to turn off the numbering in the whole environment, or say
437% |\nonumber| on a line to suppress numbering of that one in particular.
438% More excitingly, you can say \syntax{"\\nonumber["<text>"]"} to choose
439% what text to display.
440%
441% A note for cheats: you can use the sparkly new \env{eqnarray} for simple
442% equations simply by specifying \lit{x} as the column description. Who
443% needs \AmSTeX? |;-)|
444%
445% \end{old-eqnarray}
446%
447% \implementation
448%
449% \section{Implementation}
450%
451% This isn't really complicated (honest) although it is a lot hairier than I
452% think it ought to be.
453%
454% \begin{macrocode}
455%<*package>
4a655c6f 456\RequirePackage{amssymb}
457\RequirePackage{mdwkey}
86f6a31e 458% \end{macrocode}
459%
460% \subsection{Square roots}
461%
462% \subsubsection{Where is the square root sign?}
463%
464% \LaTeX\ hides the square root sign away somewhere without telling anyone
465% where it is. I extract it forcibly by peeking inside the |\sqrtsign| macro
466% and scrutinising the contents. Here we go: prepare for yukkiness.
467%
468% \begin{macrocode}
469\newcount\sq@sqrt \begingroup \catcode`\|0 \catcode`\\12
470|def|sq@readrad#1"#2\#3|relax{|global|sq@sqrt"#2|relax}
471|expandafter|sq@readrad|meaning|sqrtsign|relax |endgroup
472\def\sq@delim{\delimiter\sq@sqrt\relax}
473% \end{macrocode}
474%
475% \subsubsection{Drawing fake square root signs}
476%
477% \TeX\ absolutely insists on drawing square root signs with a vinculum over
478% the top. In order to get the same effect, we have to attempt to emulate
479% \TeX's behaviour.
480%
481% \begin{macro}{\sqrtdel}
482%
483% This does the main job of typesetting a vinculum-free radical.\footnote{^^A
484% Note for chemists: this is nothing to do with short-lived things which
485% don't have their normal numbers of electrons. And it won't reduce the
486% appearance of wrinkles either.}
487% It's more or less a duplicate of what \TeX\ does internally, so it might be
488% a good plan to have a copy of Appendix~G open while you examine this.
489%
490% We start off by using |\mathpalette| to help decide how big things should
491% be.
492%
493% \begin{macrocode}
494\def\sqrtdel{\mathpalette\sqrtdel@i}
495% \end{macrocode}
496%
497% Read the contents of the radical into a box, so we can measure it.
498%
499% \begin{macrocode}
500\def\sqrtdel@i#1#2{%
501 \setbox\z@\hbox{$\m@th#1#2$}% %%% Bzzzt -- uncramps the mathstyle
502% \end{macrocode}
503%
504% Now try and sort out the values needed in this calculation. We'll assume
505% that $\xi_8$ is 0.6\,pt, the way it usually is. Next try to work out the
506% value of $\varphi$.
507%
508% \begin{macrocode}
509 \ifx#1\displaystyle%
510 \@tempdima1ex%
511 \else%
512 \@tempdima.6\p@%
513 \fi%
514% \end{macrocode}
515%
516% That was easy. Now for $\psi$.
517%
518% \begin{macrocode}
519 \@tempdimb.6\p@%
520 \advance\@tempdimb.25\@tempdima%
521% \end{macrocode}
522%
523% Build the `delimiter' in a box of height $h(x)+d(x)+\psi+\xi_8$, as
524% requested. Box~2 will do well for this purpose.
525%
526% \begin{macrocode}
527 \dimen@.6\p@%
528 \advance\dimen@\@tempdimb%
529 \advance\dimen@\ht\z@%
530 \advance\dimen@\dp\z@%
531 \setbox\tw@\hbox{%
532 $\left\sq@delim\vcenter to\dimen@{}\right.\n@space$%
533 }%
534% \end{macrocode}
535%
536% Now we need to do some more calculating (don't you hate it?). As far as
537% Appendix~G is concerned, $\theta=h(y)=0$, because we want no rule over the
e8e9e5d8 538% top.
86f6a31e 539%
540% \begin{macrocode}
541 \@tempdima\ht\tw@%
542 \advance\@tempdima\dp\tw@%
543 \advance\@tempdima-\ht\z@%
544 \advance\@tempdima-\dp\z@%
545 \ifdim\@tempdima>\@tempdimb%
546 \advance\@tempdima\@tempdimb%
547 \@tempdimb.5\@tempdima%
548 \fi%
549% \end{macrocode}
550%
551% Work out how high to raise the radical symbol. Remember that Appendix~G
552% thinks that the box has a very small height, although this is untrue here.
553%
554% \begin{macrocode}
555 \@tempdima\ht\z@%
556 \advance\@tempdima\@tempdimb%
557 \advance\@tempdima-\ht\tw@%
558% \end{macrocode}
559%
560% Build the output (finally). The brace group is there to turn the output
561% into a mathord, one of the few times that this is actually desirable.
562%
563% \begin{macrocode}
564 {\raise\@tempdima\box\tw@\vbox{\kern\@tempdimb\box\z@}}%
565}
566% \end{macrocode}
567%
568% \end{macro}
569%
570% \subsubsection{The new square root command}
571%
572% This is where we reimplement all the square root stuff. Most of this stuff
573% comes from the \PlainTeX\ macros, although some is influenced by \AmSTeX\
574% and \LaTeXe, and some is original. I've tried to make the spacing vaguely
575% automatic, so although it's not configurable like \AmSTeX's version, the
576% output should look nice more of the time. Maybe.
577%
578% \begin{macro}{\sqrt}
579%
580% \LaTeX\ says this must be robust, so we make it robust. The first thing to
581% do is to see if there's a star and pass the appropriate squareroot-drawing
582% command on to the rest of the code.
583%
584% \begin{macrocode}
585\DeclareRobustCommand\sqrt{\@ifstar{\sqrt@i\sqrtdel}{\sqrt@i\sqrtsign}}
586% \end{macrocode}
587%
588% Now we can sort out an optional argument to be displayed on the root.
589%
590% \begin{macrocode}
591\def\sqrt@i#1{\@ifnextchar[{\sqrt@ii{#1}}{\sqrt@iv{#1}}}
592% \end{macrocode}
593%
594% Stages~2 and~3 below are essentially equivalents of \PlainTeX's
595% |\root|\dots|\of| and |\r@@t|. Here we also find the first wrinkle: the
596% |\rootbox| used to store the number is spaced out on the left if necessary.
597% There's a backspace after the end so that the root can slip underneath, and
598% everything works out nicely. Unfortunately size is fixed here, although
599% doesn't actually seem to matter.
600%
601% \begin{macrocode}
602\def\sqrt@ii#1[#2]{%
603 \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#2}$}%
604 \ifdim\wd\rootbox<6\p@%
605 \setbox\rootbox\hb@xt@6\p@{\hfil\unhbox\rootbox}%
606 \fi%
607 \mathpalette{\sqrt@iii{#1}}%
608}
609% \end{macrocode}
610%
611% Now we can actually build everything. Note that the root is raised by its
612% depth -- this prevents a common problem with letters with descenders.
613%
614% \begin{macrocode}
615\def\sqrt@iii#1#2#3{%
616 \setbox\z@\hbox{$\m@th#2#1{#3}$}%
617 \dimen@\ht\z@%
618 \advance\dimen@-\dp\z@%
619 \dimen@.6\dimen@%
620 \advance\dimen@\dp\rootbox%
621 \mkern-3mu%
622 \raise\dimen@\copy\rootbox%
623 \mkern-10mu%
624 \box\z@%
625}
626% \end{macrocode}
627%
628% Finally handle a non-numbered root. We read the rooted text in as an
629% argument, to stop problems when people omit the braces. (\AmSTeX\ does
630% this too.)
631%
632% \begin{macrocode}
633\def\sqrt@iv#1#2{#1{#2}}
634% \end{macrocode}
635%
636% \end{macro}
637%
638% \begin{macro}{\root}
639%
640% We also re-implement \PlainTeX's |\root| command, just in case someone uses
641% it, and supply a star-variant. This is all very trivial.
642%
643% \begin{macrocode}
644\def\root{\@ifstar{\root@i\sqrtdel}{\root@i\sqrtsign}}
645\def\root@i#1#2\of{\sqrt@ii{#1}[#2]}
646% \end{macrocode}
647%
648% \end{macro}
649%
650% \subsection{Modular programming}
651%
652% \begin{macro}{\pmod}
653%
654% Do some hacking if not |\ifouter|.
655%
656% \begin{macrocode}
657\def\pmod#1{%
658 \ifinner\;\else\allowbreak\mkern18mu\fi%
659 ({\operator@font mod}\,\,#1)%
660}
661% \end{macrocode}
662%
663% \end{macro}
664%
665% \subsection{Some magic new maths characters}
666%
667% \begin{macro}{\bitor}
668% \begin{macro}{\bitand}
669% \begin{macro}{\dblor}
670% \begin{macro}{\dbland}
671% \begin{macro}{\xor}
672% \begin{macro}{\lor}
673% \begin{macro}{\ror}
674% \begin{macro}{\lsl}
675% \begin{macro}{\lsr}
676%
677% The new boolean operators.
678%
679% \begin{macrocode}
680\DeclareMathSymbol{&}{\mathbin}{operators}{`\&}
681\DeclareMathSymbol{\bitand}{\mathbin}{operators}{`\&}
682\def\bitor{\mathbin\mid}
683\def\dblor{\mathbin{\mid\mid}}
684\def\dbland{\mathbin{\mathrel\bitand\mathrel\bitand}}
685\let\xor\oplus
686\def\lsl{\mathbin{<\!\!<}}
687\def\lsr{\mathbin{>\!\!>}}
688\def\rol{\mathbin{<\!\!<\!\!<}}
689\def\ror{\mathbin{>\!\!>\!\!>}}
690\AtBeginDocument{\ifx\lll\@@undefined\else
691 \def\lsl{\mathbin{\ll}}
692 \def\lsr{\mathbin{\gg}}
693 \def\rol{\mathbin{\lll}}
694 \def\ror{\mathbin{\ggg}}
695\fi}
696% \end{macrocode}
697%
698% \end{macro}
699% \end{macro}
700% \end{macro}
701% \end{macro}
702% \end{macro}
703% \end{macro}
704% \end{macro}
705% \end{macro}
706% \end{macro}
707%
708% \begin{macro}{\cat}
709% \begin{macro}{\compose}
710% \begin{macro}{\implies}
711% \begin{macro}{\vect}
712% \begin{macro}{\d}
713% \begin{macro}{\jacobi}
714%
715% A mixed bag of stuff.
716%
717% \begin{macrocode}
718\def\cat{\mathbin{\|}}
719\let\compose\circ
720\def\implies{\Rightarrow}
721\def\vect#1{\mathord{\mathbf{#1}}}
4a655c6f 722\def\d{%
723 \ifmmode\mathord{\operator@font d}%
724 \else\expandafter\a\expandafter d\fi%
725}
86f6a31e 726\def\jacobi#1#2{{{#1}\overwithdelims()#2}}
727% \end{macrocode}
728%
729% \end{macro}
730% \end{macro}
731% \end{macro}
732% \end{macro}
733% \end{macro}
734% \end{macro}
735%
736% \begin{macro}{\statclose}
737% \begin{macro}{\compind}
738%
739% Fancy new relations for probability distributions.
740%
741% \begin{macrocode}
742\def\statclose{\mathrel{\mathop{=}\limits^{\scriptscriptstyle s}}}
743\def\compind{\mathrel{\mathop{\approx}\limits^{\scriptscriptstyle c}}}
744% \end{macrocode}
745%
746% \end{macro}
747% \end{macro}
748%
749% \begin{macro}{\keys}
750% \begin{macro}{\dom}
751% \begin{macro}{\ran}
752% \begin{macro}{\supp}
753% \begin{macro}{\lcm}
4a655c6f 754% \begin{macro}{\poly}
755% \begin{macro}{\negl}
756% \begin{macro}{\ord}
86f6a31e 757%
758% And the new operator names.
759%
760% \begin{macrocode}
761\def\keys{\mathop{\operator@font keys}\nolimits}
762\def\dom{\mathop{\operator@font dom}\nolimits}
763\def\ran{\mathop{\operator@font ran}\nolimits}
764\def\supp{\mathop{\operator@font supp}\nolimits}
765\def\lcm{\mathop{\operator@font lcm}\nolimits}
4a655c6f 766\def\poly{\mathop{\operator@font poly}\nolimits}
767\def\negl{\mathop{\operator@font negl}\nolimits}
768\def\ord{\mathop{\operator@font ord}\nolimits}
86f6a31e 769% \end{macrocode}
770%
771% \end{macro}
772% \end{macro}
773% \end{macro}
774% \end{macro}
775% \end{macro}
4a655c6f 776% \end{macro}
777% \end{macro}
778% \end{macro}
779%
780% \subsection{Fractions}
781%
782% \begin{macro}{\@frac@parse}
783%
784% \syntax{"\\@frac@parse{"<stuff>"}{"<frac-params>"}"} -- run \<stuff>
785% passing it three arguments: an infix fraction-making command, the `outer'
786% style, and the `inner' style.
787%
788% This is rather tricky. We clear a load of parameters, parse the parameter
789% list, and then build a token list containing the right stuff. Without the
790% token list fiddling, we end up expanding things at the wrong times -- for
791% example, |\{| expands to something terribly unpleasant in a document
792% preamble.
793%
794% All of the nastiness is contained in a group.
795%
796% \begin{macrocode}
797\def\@frac@parse#1#2{%
798 \begingroup%
799 \let\@wd\@empty\def\@ldel{.}\def\@rdel{.}%
800 \def\@op{over}\let\@dim\@empty\@tempswafalse%
801 \let\@is\@empty\let\@os\@empty%
802 \mkparse{mdwmath:frac}{#2}%
803 \toks\tw@{\endgroup#1}%
804 \toks@\expandafter{\csname @@\@op\@wd\endcsname}%
805 \if@tempswa%
806 \toks@\expandafter{\the\expandafter\toks@\@ldel}%
807 \toks@\expandafter{\the\expandafter\toks@\@rdel}%
808 \fi%
809 \expandafter\toks@\expandafter{\the\expandafter\toks@\@dim}%
810 \toks@\expandafter{\the\toks\expandafter\tw@\expandafter{\the\toks@}}
811 \toks@\expandafter{\the\expandafter\toks@\expandafter{\@os}}
812 \toks@\expandafter{\the\expandafter\toks@\expandafter{\@is}}
813 \the\toks@%
814}
815% \end{macrocode}
816%
817% The keyword definitions are relatively straightforward now. The error
818% handling for \textsf{style} and \textsf{innerstyle} could do with
819% improvement.
820%
821% \begin{macrocode}
822\def\@frac@del#1#2{\def\@wd{withdelims}\@tempswatrue\def#1{#2}}
823\mkdef{mdwmath:frac}{leftdelim}{\@frac@del\@ldel{#1}}
824\mkdef{mdwmath:frac}{rightdelim}{\@frac@del\@rdel{#1}}
825\mkdef{mdwmath:frac}{nodelims}*{\let\@wd\@empty\@tempswafalse}
826\mkdef{mdwmath:frac}{line}{%
827 \def\@op{above}\setlength\dimen@{#1}\edef\@dim{\the\dimen@\space}%
828}
829\mkdef{mdwmath:frac}{line}*{\def\@op{over}\let\@dim\@empty}
830\mkdef{mdwmath:frac}{noline}*{\def\@op{atop}\let\@dim\@empty}
831\def\@frac@style#1#2{%
832 \ifx\q@delim#2\q@delim\let#1\@empty%
833 \else%
834 \expandafter\ifx\csname #2style\endcsname\relax%
835 \PackageError{mdwmath}{Bad maths style `#2'}\@ehc%
836 \else%
837 \edef#1{\csname#2style\endcsname}%
838 \fi%
839 \fi%
840}
841\mkdef{mdwmath:frac}{style}[]{\@frac@style\@os{#1}}
842\mkdef{mdwmath:frac}{innerstyle}[]{\@frac@style\@is{#1}}
843% \end{macrocode}
844%
845% \end{macro}
846%
847% \begin{macro}{\fracdef}
848%
849% Here's where the rest of the pain is. We do a preliminary parse of the
850% parameters and `compile' the result into the output macro. If there's no
851% optional argument, then we don't need to do any really tedious formatting
852% at the point of use.
853%
854% \begin{macrocode}
855\def\fracdef#1#2{\@frac@parse{\fracdef@i{#1}{#2}}{#2}}
856\def\fracdef@i#1#2#3#4#5{\def#1{\@frac@do{#2}{#3}{#4}{#5}}}
857\def\@frac@do#1#2#3#4{%
858 \@ifnextchar[{\@frac@complex{#1}}{\@frac@simple{#2}{#3}{#4}}%
859}
860\def\@frac@complex#1[#2]{\@frac@parse\@frac@simple{#1,#2}}
861\def\@frac@simple#1#2#3#4#5{{#2{{#3#4}#1{#3#5}}}}
862% \end{macrocode}
863%
864% \end{macro}
865%
866% \begin{macro}{\frac@fix}
867% \begin{macro}{\@@over}
868% \begin{macro}{\@@atop}
869% \begin{macro}{\@@above}
870% \begin{macro}{\@@overwithdelims}
871% \begin{macro}{\@@atopwithdelims}
872% \begin{macro}{\@@abovewithdelims}
873%
874% Finally, we need to fix up |\@@over| and friends. Maybe \package{amsmath}
875% has hidden the commands away somewhere unhelpful. If not, we make the
876% requisite copies.
877%
878% \begin{macrocode}
879\def\q@delim{\q@delim}
880\def\frac@fix#1{\expandafter\frac@fix@i\string#1\q@delim}
881\def\frac@fix@i#1#2\q@delim{\frac@fix@ii{#2}\frac@fix@ii{#2withdelims}}
882\def\frac@fix@ii#1{%
883 \expandafter\ifx\csname @@#1\endcsname\relax%
884 \expandafter\let\csname @@#1\expandafter\endcsname\csname#1\endcsname%
885 \fi%
886}
887\frac@fix\over \frac@fix\atop \frac@fix\above
888% \end{macrocode}
889%
890% \end{macro}
891% \end{macro}
892% \end{macro}
893% \end{macro}
894% \end{macro}
895% \end{macro}
896% \end{macro}
897%
898% \begin{macro}{\frac}
899% \begin{macro}{\binom}
900% \begin{macro}{\jacobi}
901%
902% And finally, we define the fraction-making commands.
903%
904% \begin{macrocode}
905\fracdef\frac{nodelims, line}
906\fracdef\binom{leftdelim = (, rightdelim = ), noline}
907\fracdef\jacobi{leftdelim = (, rightdelim = ), line}
908% \end{macrocode}
909%
910% \end{macro}
911% \end{macro}
912% \end{macro}
86f6a31e 913%
914% \subsection{Blackboard bold stuff}
915%
916% \begin{macro}{\Z}
917% \begin{macro}{\Q}
918% \begin{macro}{\R}
919% \begin{macro}{\C}
920% \begin{macro}{\N}
921% \begin{macro}{\F}
922% \begin{macro}{\powerset}
4a655c6f 923% \begin{macro}{\gf}
86f6a31e 924%
925% First of all, the signs.
926%
927% \begin{macrocode}
928\def\Z{\mathbb{Z}}
929\def\Q{\mathbb{Q}}
930\def\R{\mathbb{R}}
931\def\C{\mathbb{C}}
932\def\N{\mathbb{N}}
933\def\F{\mathbb{F}}
934\def\powerset{\mathbb{P}}
4a655c6f 935\def\gf#1{\F_{#1}}
936%\def\gf#1{\mathrm{GF}({#1})}
86f6a31e 937% \end{macrocode}
938%
939% \end{macro}
940% \end{macro}
941% \end{macro}
942% \end{macro}
943% \end{macro}
944% \end{macro}
945% \end{macro}
4a655c6f 946% \end{macro}
86f6a31e 947%
948% And now, define |\mathbb| if it's not there already.
949%
950% \begin{macrocode}
951\AtBeginDocument{\ifx\mathbb\@@undefined\let\mathbb\mathbf\fi}
952% \end{macrocode}
953%
954% \subsection{Biggles}
955%
956% Now for some user-controlled delimiter sizing. The standard bigness of
957% plain \TeX's delimiters are all right, but it's a little limiting.
958%
959% The biggness of delimiters is based on the size of the current |\strut|,
960% which \LaTeX\ keeps up to date all the time. This will make the various
961% delimiters grow in proportion when the text gets bigger. Actually, I'm
962% not sure that this is exactly right -- maybe it should be nonlinear,
963%
964% \begin{macro}{\bbigg}
965% \begin{macro}{\bbiggl}
966% \begin{macro}{\bbiggr}
967% \begin{macro}{\bbiggm}
968%
969% This is where the bigness is done. This is more similar to the plain \TeX\
970% big delimiter stuff than to the \package{amsmath} stuff, although there's
971% not really a lot of difference.
972%
973% The two arguments are a multiplier for the delimiter size, and a small
974% increment applied \emph{before} the multiplication (which is optional).
975%
976% This is actually a front for a low-level interface which can be called
977% directly for efficiency.
978%
979% \begin{macrocode}
980\def\bbigg{\@bbigg\mathord} \def\bbiggl{\@bbigg\mathopen}
981\def\bbiggr{\@bbigg\mathclose} \def\bbiggm{\@bbigg\mathrel}
982% \end{macrocode}
983%
984% \end{macro}
985% \end{macro}
986% \end{macro}
987% \end{macro}
988%
989% \begin{macro}{\@bbigg}
990%
991% This is an optional argument parser providing a front end for the main
992% macro |\bbigg@|.
993%
994% \begin{macrocode}
995\def\@bbigg#1{\@ifnextchar[{\@bigg@i{#1}}{\@bigg@i{#1}[\z@]}}
996\def\@bigg@i#1[#2]#3#4{#1{\bbigg@{#2}{#3}{#4}}}
997% \end{macrocode}
998%
999% \end{macro}
1000%
1001% \begin{macro}{\bbigg@}
1002%
1003% This is it, at last. The arguments are as described above: an addition
1004% to be made to the strut height, and a multiplier. Oh, and the delimiter,
1005% of course.
1006%
1007% This is a bit messy. The smallest `big' delimiter, |\big|, is the same
1008% height as the current strut box. Other delimiters are~$1\frac12$, $2$
1009% and~$2\frac12$ times this height. I'll set the height of the delimiter by
1010% putting in a |\vcenter| of the appropriate size.
1011%
1012% Given an extra height~$x$, a multiplication factor~$f$ and a strut
1013% height~$h$ and depth~$d$, I'll create a vcenter with total height
1014% $f(h+d+x)$. Easy, isn't it?
1015%
1016% \begin{macrocode}
1017\def\bbigg@#1#2#3{%
1018 {\hbox{$%
1019 \dimen@\ht\strutbox\advance\dimen@\dp\strutbox%
1020 \advance\dimen@#1%
1021 \dimen@#2\dimen@%
1022 \left#3\vcenter to\dimen@{}\right.\n@space%
1023 $}}%
1024}
1025% \end{macrocode}
1026%
1027% \end{macro}
1028%
1029% \begin{macro}{\big}
1030% \begin{macro}{\Big}
1031% \begin{macro}{\bigg}
1032% \begin{macro}{\Bigg}
1033%
1034% Now for the easy macros.
1035%
1036% \begin{macrocode}
1037\def\big{\bbigg@\z@\@ne}
1038\def\Big{\bbigg@\z@{1.5}}
1039\def\bigg{\bbigg@\z@\tw@}
1040\def\Bigg{\bbigg@\z@{2.5}}
1041% \end{macrocode}
1042%
1043% \end{macro}
1044% \end{macro}
1045% \end{macro}
1046% \end{macro}
1047%
1048% \subsection{The `QED' symbol}
1049%
1050% \begin{macro}{\qed}
1051% \begin{macro}{\qedrule}
1052% \begin{macro}{\qedsymbol}
1053%
1054% This is fairly simple. Just be careful will the glue and penalties. The
1055% size of the little box is based on the current font size.
1056%
1057% The horizontal list constructed by the macro is like this:
1058%
1059% \begin{itemize}
1060% \item A |\quad| of space. This might get eaten if there's a break here or
1061% before. That's OK, though.
1062% \item An empty box, to break a run of discardable items.
1063% \item A |\penalty 10000| to ensure that the spacing glue isn't discarded.
1064% \item |\hfill| glue to push the little rule to the end of the line.
1065% \item A little square rule `\qedrule', with some small kerns around it.
1066% \item A glue item to counter the effect of glue added at the paragraph
e8e9e5d8 1067% boundary.
86f6a31e 1068% \end{itemize}
1069%
4a655c6f 1070% The vertical mode case is simpler, but less universal. It copes with
1071% relatively simple cases only.
1072%
86f6a31e 1073% A |\qed| commend ends the paragraph.
1074%
1075% \begin{macrocode}
4a655c6f 1076\def\qed{%
1077 \ifvmode%
1078 \unskip%
1079 \setbox\z@\hb@xt@\linewidth{\hfil\strut\qedsymbol}%
1080 \prevdepth-\@m\p@%
1081 \ifdim\prevdepth>\dp\strutbox%
1082 \dimen@\prevdepth\advance\dimen@-\dp\strutbox%
1083 \kern-\dimen@%
1084 \fi%
1085 \penalty\@M\vskip-\baselineskip\box\z@%
1086 \else%
1087 \unskip%
1088 \penalty\@M\hfill%
1089 \hbox{}\penalty200\quad%
1090 \hbox{}\penalty\@M\hfill\qedsymbol\hskip-\parfillskip\par%
1091 \fi%
86f6a31e 1092}
1093\def\qedrule{{%
1094 \dimen@\ht\strutbox%
4a655c6f 1095 \advance\dimen@\dp\strutbox%
86f6a31e 1096 \dimen@ii1ex%
1097 \advance\dimen@-\dimen@ii%
1098 \divide\dimen@\tw@%
1099 \advance\dimen@-\dp\strutbox%
1100 \advance\dimen@\dimen@ii%
1101 \advance\dimen@ii-\dimen@%
1102 \kern\p@%
1103 \vrule\@width1ex\@height\dimen@\@depth\dimen@ii%
1104 \kern\p@%
1105}}
1106\providecommand\qedsymbol{\qedrule}
1107% \end{macrocode}
1108%
1109% \end{macro}
1110% \end{macro}
1111% \end{macro}
1112%
3ba7380e
MW
1113% \subsection{Punctuation in displays}
1114%
1115% \begin{macro}{\mpunct}
1116%
1117% This is actually a little more subtle than you'd expect. If the
1118% \package{amstext} package is loaded, or something else has defined the
1119% |\text| command, then we should use that; otherwise, just drop a box in and
1120% hope for the best.
1121%
1122% \begin{macrocode}
1123\def\mpunct#1{%
1124 \,%
1125 \ifx\text\@@undefined\hbox%
1126 \else\expandafter\text\fi%
1127 {#1}%
1128}
1129% \end{macrocode}
1130%
1131%\end{macro}
1132%
86f6a31e 1133% \begin{ignore}
1134% The following is the original definition of the enhanced eqnarray
1135% environment. It's not supported, although if you can figure out how to
1136% extract it, it's all yours.
1137% \end{ignore}
1138%
1139% \begin{old-eqnarray}
1140%
1141% \subsection{The sparkly new \env{eqnarray}}
1142%
1143% Start off by writing a different package.
1144%
1145% \begin{macrocode}
1146%</package>
1147%<*oldeqnarray>
1148% \end{macrocode}
1149%
1150% \subsubsection{Options handling}
1151%
1152% We need to be able to cope with \textsf{fleqn} and \textsf{leqno} options.
1153% This will adjust our magic modified \env{eqnarray} environment
1154% appropriately.
1155%
1156% \begin{macrocode}
1157\newif\if@fleqn
1158\newif\if@leqno
1159\DeclareOption{fleqn}{\@fleqntrue}
1160\DeclareOption{leqno}{\@leqnotrue}
1161\ProcessOptions
1162% \end{macrocode}
1163%
1164% This is all really different to the \LaTeX\ version. I've looked at the
1165% various \env{tabular} implementations, the original \env{eqnarray} and the
1166% \textit{\TeX book} to see how best to do this, and then went my own way.
1167% If it doesn't work it's all my fault.
1168%
1169% \subsubsection{Some useful registers}
1170%
1171% The old \LaTeX\ version puts the equation numbers in by keeping a count of
1172% where it is in the alignment. Since I don't know how may columns there are
1173% going to be, I'll just use a switch in the preamble to tell me to stop
1174% tabbing.
1175%
1176% \begin{macrocode}
1177\newif\if@eqalast
1178% \end{macrocode}
1179%
1180% Now define some useful length parameters. First allocate them:
1181%
1182% \begin{macrocode}
1183\newskip\eqaopenskip
1184\newskip\eqacloseskip
1185\newskip\eqacolskip
1186\newskip\eqainskip
1187% \end{macrocode}
1188%
1189% Now assign some default values. Users can play with these if they really
1190% want although I can't see the point myself.
1191%
1192% \begin{macrocode}
1193\if@fleqn
1194 \AtBeginDocument{\eqaopenskip\leftmargini}
1195\else
1196 \eqaopenskip\@centering
1197\fi
1198\eqacloseskip\@centering
1199\eqacolskip\@centering
1200\eqainskip\z@
1201% \end{macrocode}
1202%
1203% We allow the user to play with the style if this is really wanted. I dunno
1204% why, really. Maybe someone wants very small alignments.
1205%
1206% \begin{macrocode}
1207\let\eqa@style\displaystyle
1208% \end{macrocode}
1209%
1210% \subsubsection{The main environments}
1211%
1212% We define the toplevel commands here. They just add in default arguments
1213% and then call |\@eqnarray| with a preamble string. The only difference is
1214% the last column they add in -- \env{eqnarray$*$} throws away the last
1215% column by sticking it in box~0. (I used to |\@gobble| it but that caused
1216% the |\cr| to be lost.)
1217%
1218% \begin{macrocode}
1219\def\eqnarray{\@ifnextchar[\eqnarray@i{\eqnarray@i[rcl]}}
1220\def\eqnarray@i[#1]{%
1221 \@eqnarray{#1!{\hb@xt@\z@{\hss##}\tabskip\z@}}
1222}
1223\@namedef{eqnarray*}{\@ifnextchar[\eqnarray@s@i{\eqnarray@s@i[rcl]}}
1224\def\eqnarray@s@i[#1]{%
1225 \@eqnarray{#1!{\nonumber\setbox\z@\hbox{##}\tabskip\z@}}%
1226}
1227% \end{macrocode}
1228%
1229% \subsubsection{Set up the initial display}
1230%
1231% \begin{macro}{\@eqnarray}
1232%
1233% The |\@eqnarray| command does most of the initial work. It sets up some
1234% flags and things, builds the |\halign| preamble, and returns.
1235%
1236% \begin{macrocode}
1237\def\@eqnarray#1{%
1238% \end{macrocode}
1239%
1240% Start playing with the counter here. The original does some icky internal
1241% playing, which isn't necessary. The |\if@eqnsw| switch is |true| if the
1242% user hasn't supplied an equation number. The |\if@eqalast| switch is
1243% |true| in the final equation-number column.
1244%
1245% \begin{macrocode}
1246 \refstepcounter{equation}%
1247 \@eqalastfalse%
1248 \global\@eqnswtrue%
1249 \m@th%
1250% \end{macrocode}
1251%
1252% Set things up for the |\halign| which is coming up.
1253%
1254% \begin{macrocode}
1255 \openup\jot%
1256 \tabskip\eqaopenskip%
1257 \let\\\@eqncr%
1258 \everycr{}%
1259 $$%
1260% \end{macrocode}
1261%
1262% We'll build the real |\halign| and preamble in a token register. All we
1263% need to do is stuff the header in the token register, clear a switch
1264% (that'll be explained later), parse the preamble and then expand the
1265% tokens we collected. Easy, no?
1266%
1267% \begin{macrocode}
1268 \toks@{\halign to\displaywidth\bgroup}%
1269 \@tempswafalse%
1270 \eqa@preamble#1\end%
1271 \the\toks@\cr%
1272}
1273% \end{macrocode}
1274%
1275% \end{macro}
1276%
1277% \subsubsection{Parsing the preamble}
1278%
1279% All this actually involves is reading the next character and building a
1280% command from it. That can pull off an argument if it needs it. Just make
1281% sure we don't fall off the end and we'll be OK.
1282%
1283% \begin{macrocode}
1284\def\eqa@preamble#1{%
1285 \ifx\end#1\else\csname eqa@char@#1\expandafter\endcsname\fi%
1286}
1287% \end{macrocode}
1288%
1289% Adding stuff to the preamble tokens is a simple matter of using
1290% |\expandafter| in the correct way.\footnote{^^A
1291% I have no idea why \LaTeX\ uses \cmd\edef\ for building its preamble. It
1292% seems utterly insane to me -- the amount of bodgery that \env{tabular}
1293% has to go through to make everything expand at the appropriate times is
1294% scary. Maybe Messrs~Lamport and Mittelbach just forgot about token
1295% registers when they were writing the code. Maybe I ought to rewrite the
1296% thing properly some time. Sigh.
1297%
1298% As a sort of postscript to the above, I \emph{have} rewritten the
1299% \env{tabular} environment, and made a damned fine job of it, in my
1300% oh-so-humble opinion. All this \env{eqnarray} stuff has been remoulded
1301% in terms of the generic column-defining things in \package{mdwtab}.
1302% You're reading the documentation of the old version, which isn't
1303% supported any more, so any bugs here are your own problem.}
1304%
1305% \begin{macrocode}
1306\def\eqa@addraw#1{\expandafter\toks@\expandafter{\the\toks@#1}}
1307% \end{macrocode}
1308%
1309% Now for some cleverness again. In order to put all the right bits of
1310% |\tabskip| glue in the right places we must \emph{not} terminate each
1311% column until we know what the next one is. We set |\if@tempswa| to be
1312% |true| if there's a column waiting to be closed (so it's initially
1313% |false|). The following macro adds a column correctly, assuming we're in
1314% a formula. Other column types make their own arrangements.
1315%
1316% \begin{macrocode}
1317\def\eqa@add#1{%
1318 \if@tempswa%
1319 \eqa@addraw{\tabskip\eqainskip&#1}%
1320 \else%
1321 \eqa@addraw{#1}%
1322 \fi%
1323 \@tempswatrue%
1324}
1325% \end{macrocode}
1326%
1327% Now to defining column types. Let's define a macro which allows us to
1328% define column types:
1329%
1330% \begin{macrocode}
1331\def\eqa@def#1{\expandafter\def\csname eqa@char@#1\endcsname}
1332% \end{macrocode}
1333%
1334% Now we can define the column types. Each column type must loop back to
1335% |\eqa@preamble| once it's finished, to read the rest of the preamble
1336% string. Note the positioning of ord atoms in the stuff below. This will
1337% space out relations and binops correctly when they occur at the edges of
1338% columns, and won't affect ord atoms at the edges, because ords pack
1339% closely.
1340%
1341% First the easy onces. Just stick |\hfil| in the right places and
1342% everything will be all right.
1343%
1344% \begin{macrocode}
1345\eqa@def r{\eqa@add{\hfil$\eqa@style##{}$}\eqa@preamble}
1346\eqa@def c{\eqa@add{\hfil$\eqa@style{}##{}$\hfil}\eqa@preamble}
1347\eqa@def l{\eqa@add{$\eqa@style{}##$\hfil}\eqa@preamble}
1348\eqa@def x{\eqa@add{\hfil$\eqa@style##$\hfil}\eqa@preamble}
1349% \end{macrocode}
1350%
1351% Now for the textual ones. This is also fairly easy.
1352%
1353% \begin{macrocode}
1354\eqa@def T#1{%
1355 \eqa@add{}%
1356 \if#1l\else\eqa@addraw{\hfil}\fi%
1357 \eqa@addraw{##}%
1358 \if#1r\else\eqa@addraw{\hfil}\fi%
1359 \eqa@preamble%
1360}
1361% \end{macrocode}
1362%
1363% Sort of split types of equations. I mustn't use |\rlap| here, or
1364% everything goes wrong -- |\\| doesn't get noticed by \TeX\ in the same way
1365% as |\cr| does.
1366%
1367% \begin{macrocode}
1368\eqa@def L{\eqa@add{\hb@xt@\z@{$\eqa@style##$\hss}\qquad}\eqa@preamble}
1369% \end{macrocode}
1370%
1371% The \lit{:} column type is fairly simple. We set |\tabskip| up to make
1372% lots of space and close the current column, because there must be one.^^A
1373% \footnote{This is an assumption.}
1374%
1375% \begin{macrocode}
1376\eqa@def :{%
1377 \eqa@addraw{\tabskip\eqacolskip&}\@tempswafalse\eqa@preamble%
1378}
1379\eqa@def q{\eqa@add{\quad}\@tempswafalse\eqa@preamble}
1380% \end{macrocode}
1381%
1382% The other column types just insert given text in an appropriate way.
1383%
1384% \begin{macrocode}
1385\eqa@def >#1{\eqa@add{#1}\@tempswafalse\eqa@preamble}
1386\eqa@def <#1{\eqa@addraw{#1}\eqa@preamble}
1387% \end{macrocode}
1388%
1389% Finally, the magical \lit{!} column type, which sets the equation number.
1390% We set up the |\tabskip| glue properly, tab on, and set the flag which
1391% marks the final column.
1392%
1393% \begin{macrocode}
1394\eqa@def !#1{%
1395 \eqa@addraw{\tabskip\eqacloseskip&\@eqalasttrue#1}\eqa@preamble%
1396}
1397% \end{macrocode}
1398%
1399% \subsubsection{Newline codes}
1400%
1401% Newline sequences (|\\|) get turned into calls of |\@eqncr|. The job is
1402% fairly simple, really. However, to avoid reading `|&|' characters
1403% prematurely, we set up a magic brace (from the \package{array} package --
1404% this avoids creating ord atoms and other nastyness).
1405%
1406% \begin{macrocode}
1407\def\@eqncr{%
1408 \iffalse{\fi\ifnum0=`}\fi%
1409 \@ifstar{\eqacr@i{\@M}}{\eqacr@i{\interdisplaylinepenalty}}%
1410}
1411\def\eqacr@i#1{\@ifnextchar[{\eqacr@ii{#1}}{\eqacr@ii{#1}[\z@]}}
1412\def\eqacr@ii#1[#2]{%
1413 \ifnum0=`{}\fi%
1414 \eqa@eqnum%
1415 \noalign{\penalty#1\vskip#2\relax}%
1416}
1417% \end{macrocode}
1418%
1419% \subsubsection{Setting equation numbers}
1420%
1421% Before we start, we need to generalise the flush-left number handling bits.
1422% The macro |\eqa@eqpos| will put its argument in the right place.
1423%
1424% \begin{macrocode}
1425\if@leqno
1426 \def\eqa@eqpos#1{%
1427 \hb@xt@.01\p@{}\rlap{\normalfont\normalcolor\hskip-\displaywidth#1}%
1428 }
1429\else
1430 \def\eqa@eqpos#1{\normalfont\normalcolor#1}
1431\fi
1432% \end{macrocode}
1433%
1434% First we need to move into the right column. Then we just set the equation
1435% number appropriately. There is some subtlety here, ish. The |\relax| is
1436% important, to delay expansion of the |\if|\dots\ until the new column has
1437% been started. The two helper macros are important too, to hide `|&|'s and
1438% `|\cr|'s from \TeX's scanner until the right time.
1439%
1440% \begin{macrocode}
1441\def\eqa@eqnum{%
1442 \relax%
1443 \if@eqalast\expandafter\eqa@eqnum@i\else\expandafter\eqa@eqnum@ii\fi%
1444}
1445\def\eqa@eqnum@i{%
1446 \if@eqnsw%
1447 \eqa@eqpos{(\theequation)}\stepcounter{equation}%
1448 \else%
1449 \eqa@eqpos\eqa@number%
1450 \fi%
1451 \global\@eqnswtrue%
1452 \cr%
1453}
1454\def\eqa@eqnum@ii{&\eqa@eqnum}
1455% \end{macrocode}
1456%
1457% \subsubsection{Numbering control}
1458%
1459% This is trivial. We set the |\if@eqnsw| flag to be |false| and store the
1460% text in a macro.
1461%
1462% \begin{macrocode}
1463\let\nonumber\relax
1464\newcommand\nonumber[1][]{\global\@eqnswfalse\global\def\eqa@number{#1}}
1465% \end{macrocode}
1466%
1467% \subsubsection{Closing the environments off}
1468%
1469% This is really easy. Set the final equation number, close the |\halign|,
1470% tidy up the equation counter (it's been stepped once too many times) and
1471% close the display.
1472%
1473% \begin{macrocode}
1474\def\endeqnarray{%
1475 \eqa@eqnum%
1476 \egroup%
1477 \global\advance\c@equation\m@ne%
1478 $$%
1479 \global\@ignoretrue%
1480}
1481\expandafter\let\csname endeqnarray*\endcsname\endeqnarray
1482% \end{macrocode}
1483%
1484% Now start up the other package again.
1485%
1486% \begin{macrocode}
1487%</oldeqnarray>
1488%<*package>
1489% \end{macrocode}
1490%
1491% \end{old-eqnarray}
1492%
1493% That's all there is. Byebye.
1494%
1495% \begin{macrocode}
1496%</package>
1497% \end{macrocode}
1498%
1499% \hfill Mark Wooding, \today
1500%
1501% \Finale
1502\endinput