1 % \begin{meta-comment} <general public licence>
3 %% mdwmath package -- various nicer mathematical things
4 %% Copyright (c) 2003, 2020 Mark Wooding
6 %% This file is part of the `mdwtools' LaTeX package collection.
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.
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.
18 %% You should have received a copy of the GNU General Public License
19 %% along with `mdwtools'. If not, write to the Free Software Foundation,
20 %% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
24 % \begin{meta-comment} <Package preamble>
25 %<+package>\NeedsTeXFormat{LaTeX2e}
26 %<+package>\ProvidesPackage{mdwmath}
27 %<+package> [2020/09/06 1.14.0 Nice mathematical things]
28 %<+oldeqnarray>\NeedsTeXFormat{LaTeX2e}
29 %<+oldeqnarray>\ProvidesPackage{eqnarray}
30 %<+oldeqnarray> [2020/09/06 1.14.0 Old enhanced eqnarray]
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 \~}
51 % \begin{meta-comment}
57 \describespackage{mdwmath}
58 %\describespackage{eqnarray}
59 \ignoreenv{old-eqnarray}
60 %\unignoreenv{old-eqnarray}
66 % \section{User guide}
68 % \subsection{Square root typesetting}
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.
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 %\[ q = \frac{2\sqrt*{2}}{5}+\sqrt[\frac{n+1}{2}]{2x^2+3xy-y^2} \]
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.]
93 % \subsection{Modular arithmetic}
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.
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
105 % \subsection{Some maths symbols you already have}
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}
114 % $\&$ & "\&" & $\bitor$ & "\bitor" & $\dbland$ & "\dbland" \\
115 % $\bitand$ & "\bitand" & $\dblor$ & "\dblor" &
116 % \end{tabular} \end{center}
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.
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.
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 `$\vect{x}$'.
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.
146 % \subsection{Fractions}
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
154 % \begin{description}
155 % \item[\lit*{line}] Include a horizontal line between the top and bottom
157 % \item[\lit*{line=}\<length>] Include a horizontal line with width
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
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.
176 % \DescribeMacro\frac
177 % \DescribeMacro\binom
178 % \DescribeMacro\jacobi
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
184 % By way of example, these commands were defined using
186 %\fracdef\frac{nodelims, line}
187 %\fracdef\binom{leftdelim = (, rightdelim = ), noline}
188 %\fracdef\jacobi{leftdelim = (, rightdelim = ), line}
191 % \subsection{Rant about derivatives}
194 % There is a difference between UK and US typesetting of derivatives.
196 % \[ \frac{dy}{dx} \]
197 % while the British want
198 % \[ \frac{\d y}{\d x}. \]
199 % The command |\d| command is fixed to typeset a `$\d$'. (In text mode,
200 % |\d{x}| still typesets `\d{x}'.)
202 % \subsection{New operator names}
204 % \DescribeMacro\keys
207 % \DescribeMacro\supp
210 % \DescribeMacro\poly
211 % \DescribeMacro\negl
212 % A few esoteric new operator names are supplied.
213 % \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
214 % $\keys$ & "\keys" & $\dom$ & "\dom" & $\ran$ & "\ran" \\
215 % $\supp$ & "\supp" & $\lcm$ & "\lcm" & $\ord$ & "\ord" \\
216 % $\poly$ & "\poly" & $\negl$ & "\negl"
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., $\supp{D} = \{\, x \in
223 % \dom\mathcal{D} \mid \mathcal{D}(x) > 0 \,\}$. 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 $n$.
231 % \subsection{Standard set names}
239 % \DescribeMacro\powerset
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|
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.
251 % \subsection{Biggles}
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.
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 $n \times (h + d + a)$.
269 % The old |\big| commands have been redefined in terms of |\bbigg|.
271 % \subsection{The `QED' symbol}
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.
281 % \subsection{Punctuation in displays}
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
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.
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
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.
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.
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.
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
324 % The following is the documentation for the original version. There's an
325 % updated edition in \package{mdwtab}.
328 % \begin{old-eqnarray}
330 % \subsection{A new \env{eqnarray} environment}
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.
337 % \DescribeEnv{eqnarray}
339 % \setbox0\hbox{"\\begin{eqnarray}["<preamble>"]" \dots "\\end{eqnarray}"}
340 % \leavevmode \hskip-\parindent \fbox{\box0}
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:
350 % \begin{description} \setdescriptionlabel{\normalfont\ttfamily#1}
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
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.
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
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.
377 % An example would be good here, I think. This one's from exercise 22.9 of
378 % the \textit{\TeX book}.
380 % \begin{demo}[w]{Simultaneous equations}
381 %\begin{eqnarray}[rcrcrcrl]
382 % 10w & + & 3x & + & 3y & + & 18z & = 1 \\
383 % 6w & - & 17x & & & - & 5z & = 2
387 % Choosing a more up-to-date example, here's one demonstrating the \lit{:}
388 % column specifier from the \textit{\LaTeX\ Companion}.
390 % \begin{demo}[w]{Lots of equations}
391 %\begin{eqnarray}[rl:rl:l]
392 % V_i &= v_i - q_i v_j, & X_i &= x_i - q_i x_j, &
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.
399 % We can make things more interesting by adding a plain text column. Here we
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
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:
413 % \begin{demo}{Splitting example}
414 %\begin{eqnarray*}[Ll]
421 % Finally, just to prove that the spacing's right at last, here's another one
422 % from the \textit{Companion}.
424 % \begin{demo}{Spacing demonstration}
428 %\begin{eqnarray}[rl]
429 % x^2 + y^2 &= z^2 \\
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.
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? |;-)|
449 % \section{Implementation}
451 % This isn't really complicated (honest) although it is a lot hairier than I
452 % think it ought to be.
456 \RequirePackage{amssymb}
457 \RequirePackage{mdwkey}
460 % \subsection{Square roots}
462 % \subsubsection{Where is the square root sign?}
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.
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}
475 % \subsubsection{Drawing fake square root signs}
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
481 % \begin{macro}{\sqrtdel}
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.
490 % We start off by using |\mathpalette| to help decide how big things should
494 \def\sqrtdel{\mathpalette\sqrtdel@i}
497 % Read the contents of the radical into a box, so we can measure it.
501 \setbox\z@\hbox{$\m@th#1#2$}% %%% Bzzzt -- uncramps the mathstyle
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 $\varphi$.
516 % That was easy. Now for $\psi$.
520 \advance\@tempdimb.25\@tempdima%
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.
528 \advance\dimen@\@tempdimb%
529 \advance\dimen@\ht\z@%
530 \advance\dimen@\dp\z@%
532 $\left\sq@delim\vcenter to\dimen@{}\right.\n@space$%
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
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%
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.
556 \advance\@tempdima\@tempdimb%
557 \advance\@tempdima-\ht\tw@%
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.
564 {\raise\@tempdima\box\tw@\vbox{\kern\@tempdimb\box\z@}}%
570 % \subsubsection{The new square root command}
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.
578 % \begin{macro}{\sqrt}
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.
585 \DeclareRobustCommand\sqrt{\@ifstar{\sqrt@i\sqrtdel}{\sqrt@i\sqrtsign}}
588 % Now we can sort out an optional argument to be displayed on the root.
591 \def\sqrt@i#1{\@ifnextchar[{\sqrt@ii{#1}}{\sqrt@iv{#1}}}
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.
603 \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#2}$}%
604 \ifdim\wd\rootbox<6\p@%
605 \setbox\rootbox\hb@xt@6\p@{\hfil\unhbox\rootbox}%
607 \mathpalette{\sqrt@iii{#1}}%
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.
615 \def\sqrt@iii#1#2#3{%
616 \setbox\z@\hbox{$\m@th#2#1{#3}$}%
618 \advance\dimen@-\dp\z@%
620 \advance\dimen@\dp\rootbox%
622 \raise\dimen@\copy\rootbox%
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
633 \def\sqrt@iv#1#2{#1{#2}}
638 % \begin{macro}{\root}
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.
644 \def\root{\@ifstar{\root@i\sqrtdel}{\root@i\sqrtsign}}
645 \def\root@i#1#2\of{\sqrt@ii{#1}[#2]}
650 % \subsection{Modular programming}
652 % \begin{macro}{\pmod}
654 % Do some hacking if not |\ifouter|.
658 \ifinner\;\else\allowbreak\mkern18mu\fi%
659 ({\operator@font mod}\,\,#1)%
665 % \subsection{Some magic new maths characters}
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}
677 % The new boolean operators.
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}}
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}}
708 % \begin{macro}{\cat}
709 % \begin{macro}{\compose}
710 % \begin{macro}{\implies}
711 % \begin{macro}{\vect}
713 % \begin{macro}{\jacobi}
715 % A mixed bag of stuff.
718 \def\cat{\mathbin{\|}}
720 \def\implies{\Rightarrow}
721 \def\vect#1{\mathord{\mathbf{#1}}}
723 \ifmmode\mathord{\operator@font d}%
724 \else\expandafter\a\expandafter d\fi%
726 \def\jacobi#1#2{{{#1}\overwithdelims()#2}}
736 % \begin{macro}{\statclose}
737 % \begin{macro}{\compind}
739 % Fancy new relations for probability distributions.
742 \def\statclose{\mathrel{\mathop{=}\limits^{\scriptscriptstyle s}}}
743 \def\compind{\mathrel{\mathop{\approx}\limits^{\scriptscriptstyle c}}}
749 % \begin{macro}{\keys}
750 % \begin{macro}{\dom}
751 % \begin{macro}{\ran}
752 % \begin{macro}{\supp}
753 % \begin{macro}{\lcm}
754 % \begin{macro}{\poly}
755 % \begin{macro}{\negl}
756 % \begin{macro}{\ord}
758 % And the new operator names.
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}
766 \def\poly{\mathop{\operator@font poly}\nolimits}
767 \def\negl{\mathop{\operator@font negl}\nolimits}
768 \def\ord{\mathop{\operator@font ord}\nolimits}
780 % \subsection{Fractions}
782 % \begin{macro}{\@frac@parse}
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.
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
794 % All of the nastiness is contained in a group.
797 \def\@frac@parse#1#2{%
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}%
806 \toks@\expandafter{\the\expandafter\toks@\@ldel}%
807 \toks@\expandafter{\the\expandafter\toks@\@rdel}%
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}}
817 % The keyword definitions are relatively straightforward now. The error
818 % handling for \textsf{style} and \textsf{innerstyle} could do with
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}%
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%
834 \expandafter\ifx\csname #2style\endcsname\relax%
835 \PackageError{mdwmath}{Bad maths style `#2'}\@ehc%
837 \edef#1{\csname#2style\endcsname}%
841 \mkdef{mdwmath:frac}{style}[]{\@frac@style\@os{#1}}
842 \mkdef{mdwmath:frac}{innerstyle}[]{\@frac@style\@is{#1}}
847 % \begin{macro}{\fracdef}
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.
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}}%
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}}}}
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}
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
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}}
883 \expandafter\ifx\csname @@#1\endcsname\relax%
884 \expandafter\let\csname @@#1\expandafter\endcsname\csname#1\endcsname%
887 \frac@fix\over \frac@fix\atop \frac@fix\above
898 % \begin{macro}{\frac}
899 % \begin{macro}{\binom}
900 % \begin{macro}{\jacobi}
902 % And finally, we define the fraction-making commands.
905 \fracdef\frac{nodelims, line}
906 \fracdef\binom{leftdelim = (, rightdelim = ), noline}
907 \fracdef\jacobi{leftdelim = (, rightdelim = ), line}
914 % \subsection{Blackboard bold stuff}
922 % \begin{macro}{\powerset}
925 % First of all, the signs.
934 \def\powerset{\mathbb{P}}
936 %\def\gf#1{\mathrm{GF}({#1})}
948 % And now, define |\mathbb| if it's not there already.
951 \AtBeginDocument{\ifx\mathbb\@@undefined\let\mathbb\mathbf\fi}
954 % \subsection{Biggles}
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.
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,
964 % \begin{macro}{\bbigg}
965 % \begin{macro}{\bbiggl}
966 % \begin{macro}{\bbiggr}
967 % \begin{macro}{\bbiggm}
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.
973 % The two arguments are a multiplier for the delimiter size, and a small
974 % increment applied \emph{before} the multiplication (which is optional).
976 % This is actually a front for a low-level interface which can be called
977 % directly for efficiency.
980 \def\bbigg{\@bbigg\mathord} \def\bbiggl{\@bbigg\mathopen}
981 \def\bbiggr{\@bbigg\mathclose} \def\bbiggm{\@bbigg\mathrel}
989 % \begin{macro}{\@bbigg}
991 % This is an optional argument parser providing a front end for the main
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}}}
1001 % \begin{macro}{\bbigg@}
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,
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.
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?
1019 \dimen@\ht\strutbox\advance\dimen@\dp\strutbox%
1022 \left#3\vcenter to\dimen@{}\right.\n@space%
1029 % \begin{macro}{\big}
1030 % \begin{macro}{\Big}
1031 % \begin{macro}{\bigg}
1032 % \begin{macro}{\Bigg}
1034 % Now for the easy macros.
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}}
1048 % \subsection{The `QED' symbol}
1050 % \begin{macro}{\qed}
1051 % \begin{macro}{\qedrule}
1052 % \begin{macro}{\qedsymbol}
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.
1057 % The horizontal list constructed by the macro is like this:
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
1070 % The vertical mode case is simpler, but less universal. It copes with
1071 % relatively simple cases only.
1073 % A |\qed| commend ends the paragraph.
1079 \setbox\z@\hb@xt@\linewidth{\hfil\strut\qedsymbol}%
1081 \ifdim\prevdepth>\dp\strutbox%
1082 \dimen@\prevdepth\advance\dimen@-\dp\strutbox%
1085 \penalty\@M\vskip-\baselineskip\box\z@%
1089 \hbox{}\penalty200\quad%
1090 \hbox{}\penalty\@M\hfill\qedsymbol\hskip-\parfillskip\par%
1094 \dimen@\ht\strutbox%
1095 \advance\dimen@\dp\strutbox%
1097 \advance\dimen@-\dimen@ii%
1099 \advance\dimen@-\dp\strutbox%
1100 \advance\dimen@\dimen@ii%
1101 \advance\dimen@ii-\dimen@%
1103 \vrule\@width1ex\@height\dimen@\@depth\dimen@ii%
1106 \providecommand\qedsymbol{\qedrule}
1113 % \subsection{Punctuation in displays}
1115 % \begin{macro}{\mpunct}
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.
1125 \ifx\text\@@undefined\hbox%
1126 \else\expandafter\text\fi%
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.
1139 % \begin{old-eqnarray}
1141 % \subsection{The sparkly new \env{eqnarray}}
1143 % Start off by writing a different package.
1150 % \subsubsection{Options handling}
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
1159 \DeclareOption{fleqn}{\@fleqntrue}
1160 \DeclareOption{leqno}{\@leqnotrue}
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.
1169 % \subsubsection{Some useful registers}
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
1180 % Now define some useful length parameters. First allocate them:
1183 \newskip\eqaopenskip
1184 \newskip\eqacloseskip
1189 % Now assign some default values. Users can play with these if they really
1190 % want although I can't see the point myself.
1194 \AtBeginDocument{\eqaopenskip\leftmargini}
1196 \eqaopenskip\@centering
1198 \eqacloseskip\@centering
1199 \eqacolskip\@centering
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.
1207 \let\eqa@style\displaystyle
1210 % \subsubsection{The main environments}
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.)
1219 \def\eqnarray{\@ifnextchar[\eqnarray@i{\eqnarray@i[rcl]}}
1220 \def\eqnarray@i[#1]{%
1221 \@eqnarray{#1!{\hb@xt@\z@{\hss##}\tabskip\z@}}
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@}}%
1229 % \subsubsection{Set up the initial display}
1231 % \begin{macro}{\@eqnarray}
1233 % The |\@eqnarray| command does most of the initial work. It sets up some
1234 % flags and things, builds the |\halign| preamble, and returns.
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.
1246 \refstepcounter{equation}%
1252 % Set things up for the |\halign| which is coming up.
1256 \tabskip\eqaopenskip%
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?
1268 \toks@{\halign to\displaywidth\bgroup}%
1270 \eqa@preamble#1\end%
1277 % \subsubsection{Parsing the preamble}
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.
1284 \def\eqa@preamble#1{%
1285 \ifx\end#1\else\csname eqa@char@#1\expandafter\endcsname\fi%
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.
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.}
1306 \def\eqa@addraw#1{\expandafter\toks@\expandafter{\the\toks@#1}}
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.
1319 \eqa@addraw{\tabskip\eqainskip}%
1327 % Now to defining column types. Let's define a macro which allows us to
1328 % define column types:
1331 \def\eqa@def#1{\expandafter\def\csname eqa@char@#1\endcsname}
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
1341 % First the easy onces. Just stick |\hfil| in the right places and
1342 % everything will be all right.
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}
1351 % Now for the textual ones. This is also fairly easy.
1356 \if#1l\else\eqa@addraw{\hfil}\fi%
1358 \if#1r\else\eqa@addraw{\hfil}\fi%
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
1368 \eqa@def L{\eqa@add{\hb@xt@\z@{$\eqa@style##$\hss}\qquad}\eqa@preamble}
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.}
1377 \eqa@addraw{\tabskip\eqacolskip&}\@tempswafalse\eqa@preamble%
1379 \eqa@def q{\eqa@add{\quad}\@tempswafalse\eqa@preamble}
1382 % The other column types just insert given text in an appropriate way.
1385 \eqa@def >#1{\eqa@add{#1}\@tempswafalse\eqa@preamble}
1386 \eqa@def <#1{\eqa@addraw{#1}\eqa@preamble}
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.
1395 \eqa@addraw{\tabskip\eqacloseskip&\@eqalasttrue#1}\eqa@preamble%
1399 % \subsubsection{Newline codes}
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).
1408 \iffalse{\fi\ifnum0=`}\fi%
1409 \@ifstar{\eqacr@i{\@M}}{\eqacr@i{\interdisplaylinepenalty}}%
1411 \def\eqacr@i#1{\@ifnextchar[{\eqacr@ii{#1}}{\eqacr@ii{#1}[\z@]}}
1412 \def\eqacr@ii#1[#2]{%
1415 \noalign{\penalty#1\vskip#2\relax}%
1419 % \subsubsection{Setting equation numbers}
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.
1427 \hb@xt@.01\p@{}\rlap{\normalfont\normalcolor\hskip-\displaywidth#1}%
1430 \def\eqa@eqpos#1{\normalfont\normalcolor#1}
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.
1443 \if@eqalast\expandafter\eqa@eqnum@i\else\expandafter\eqa@eqnum@ii\fi%
1447 \eqa@eqpos{(\theequation)}\stepcounter{equation}%
1449 \eqa@eqpos\eqa@number%
1454 \def\eqa@eqnum@ii{&\eqa@eqnum}
1457 % \subsubsection{Numbering control}
1459 % This is trivial. We set the |\if@eqnsw| flag to be |false| and store the
1464 \newcommand\nonumber[1][]{\global\@eqnswfalse\global\def\eqa@number{#1}}
1467 % \subsubsection{Closing the environments off}
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.
1477 \global\advance\c@equation\m@ne%
1479 \global\@ignoretrue%
1481 \expandafter\let\csname endeqnarray*\endcsname\endeqnarray
1484 % Now start up the other package again.
1491 % \end{old-eqnarray}
1493 % That's all there is. Byebye.
1499 % \hfill Mark Wooding, \today