5 % Various nicer mathematical things
7 % (c) 2003 Mark Wooding
11 % \begin{meta-comment} <general public licence>
13 %% mdwmath package -- various nicer mathematical things
14 %% Copyright (c) 2003 Mark Wooding
16 %% This program is free software; you can redistribute it and/or modify
17 %% it under the terms of the GNU General Public License as published by
18 %% the Free Software Foundation; either version 2 of the License, or
19 %% (at your option) any later version.
21 %% This program is distributed in the hope that it will be useful,
22 %% but WITHOUT ANY WARRANTY; without even the implied warranty of
23 %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
24 %% GNU General Public License for more details.
26 %% You should have received a copy of the GNU General Public License
27 %% along with this program; if not, write to the Free Software
28 %% Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
32 % \begin{meta-comment} <Package preamble>
33 %<+package>\NeedsTeXFormat{LaTeX2e}
34 %<+package>\ProvidesPackage{mdwmath}
35 %<+package> [2003/08/25 1.3 Nice mathematical things]
36 %<+oldeqnarray>\NeedsTeXFormat{LaTeX2e}
37 %<+oldeqnarray>\ProvidesPackage{eqnarray}
38 %<+oldeqnarray> [1996/04/11 1.1 Old enhanced eqnarray]
43 %% {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
44 %% 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
45 %% Digits \0\1\2\3\4\5\6\7\8\9
46 %% Exclamation \! Double quote \" Hash (number) \#
47 %% Dollar \$ Percent \% Ampersand \&
48 %% Acute accent \' Left paren \( Right paren \)
49 %% Asterisk \* Plus \+ Comma \,
50 %% Minus \- Point \. Solidus \/
51 %% Colon \: Semicolon \; Less than \<
52 %% Equals \= Greater than \> Question mark \?
53 %% Commercial at \@ Left bracket \[ Backslash \\
54 %% Right bracket \] Circumflex \^ Underscore \_
55 %% Grave accent \` Left brace \{ Vertical bar \|
56 %% Right brace \} Tilde \~}
59 % \begin{meta-comment}
65 \describespackage{mdwmath}
66 %\describespackage{eqnarray}
67 \ignoreenv{old-eqnarray}
68 %\unignoreenv{old-eqnarray}
74 % \section{User guide}
76 % \subsection{Square root typesetting}
78 % \DescribeMacro{\sqrt}
79 % The package supplies a star variant of the |\sqrt| command which omits the
80 % vinculum over the operand (the line over the top). While this is most
81 % useful in simple cases like $\sqrt*{2}$ it works for any size of operand.
82 % The package also re-implements the standard square root command so that it
83 % positions the root number rather better.
86 % \begin{demo}[w]{Examples of the new square root command}
87 %\[ \sqrt*{2} \quad \mbox{rather than} \quad \sqrt{2} \]
88 %\[ \sqrt*[3]{2} \quad \mbox{ rather than } \quad \sqrt[3]{2} \]
89 %\[ \sqrt{x^3 + \sqrt*[y]{\alpha}} - \sqrt*[n+1]{a} \]
90 %\[ x = \sqrt*[3]{\frac{3y}{7}} \]
91 %\[ q = \frac{2\sqrt*{2}}{5}+\sqrt[\frac{n+1}{2}]{2x^2+3xy-y^2} \]
95 % [Note that omission of the vinculum was originally a cost-cutting exercise
96 % because the radical symbol can just fit in next to its operand and
97 % everything ends up being laid out along a line. However, I find that the
98 % square root without vinculum is less cluttered, so I tend to use it when
99 % it doesn't cause ambiguity.]
101 % \subsection{Modular arithmetic}
103 % In standard maths mode, there's too much space before the parentheses in
104 % the output of the |\pmod| command. Suppose that $x \equiv y^2 \opmod n$:
105 % then the spacing looks awful. Go on, admit it.
107 % It looks OK in a display. For example, if
108 % \[ c \equiv m^e \opmod n \]
109 % then it's fine. The package redefines the |\pmod| command to do something
110 % more sensible. So now $c^d \equiv m^{ed} \equiv m \pmod n$ and all looks
113 % \subsection{Some maths symbols you already have}
115 % \DescribeMacro\bitor
116 % \DescribeMacro\bitand
117 % \DescribeMacro\dblor
118 % \DescribeMacro\dbland
119 % Having just tried to do some simple things, I've found that there are maths
120 % symbols missing. Here they are, in all their glory:
121 % \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
122 % $\&$ & "\&" & $\bitor$ & "\bitor" & $\dbland$ & "\dbland" \\
123 % $\bitand$ & "\bitand" & $\dblor$ & "\dblor" &
124 % \end{tabular} \end{center}
128 % I also set up the |\xor| command to typeset `$\xor$', which is commonly
129 % used to represent the bitsize exclusive-or operation among cryptographers.
130 % The command |\cat| typesets `$\cat$', which is a common operator indicating
131 % concatenation of strings.
137 % The commands |\lsl| and |\lsr| typeset binary operators `$\lsl$' and
138 % `$\lsr$' respectively, and |\rol| and |\ror| typeset `$\rol$' and `$\ror$'.
139 % Note that these are spaced as binary operators, rather than relations.
141 % \DescribeMacro\compose
142 % \DescribeMacro\implies
143 % \DescribeMacro\vect
144 % The |\compose| command typesets `$\compose$', which is usually used to
145 % denote function composition. The |\implies| command is made to typeset
146 % `$\implies$'. And \syntax{"\\vect{"<x>"}"} typesets `$\vect{x}$'.
148 % \DescribeMacro\statclose
149 % \DescribeMacro\compind
150 % The |\statclose| command typesets `$\statclose$', which indicates
151 % `statistical closeness' of probability distributions; |\compind| typesets
152 % `$\compind$', which indicates computational indistinguishability.
154 % \subsection{Fractions}
156 % \DescribeMacro\fracdef
157 % We provide a general fraction system, a little tiny bit like
158 % \package{amsmath}'s |\genfrac|. Say
159 % \syntax{"\\fracdef{"<name>"}{"<frac-params>"}"} to define a new
160 % |\frac|-like operator. The \<frac-params> are a comma-separated list of
162 % \begin{description}
163 % \item[\lit*{line}] Include a horizontal line between the top and bottom
165 % \item[\lit*{line=}\<length>] Include a horizontal line with width
167 % \item[\lit*{noline}] Don't include a line (like |\binom|).
168 % \item[\lit*{leftdelim=}\<delim>] Use \<delim> as the left-hand delimiter.
169 % \item[\lit*{rightdelim=}\<delim>] Use \<delim> as the right-hand delimiter.
170 % \item[\lit*{nodelims}] Don't include delimiters.
171 % \item[\lit*{style=}\<style>] Typeset the fraction in \<style>, which is one
172 % of |display|, |text|, |script| or |scriptscript|.
173 % \item[\lit*{style}] Use the prevailing style for the fraction.
174 % \item[\lit*{innerstyle=}\<style>] Typeset the \emph{components} of the
175 % fraction in \<style>.
176 % \item[\lit*{innerstyle}] Typeset the fraction components according to the
179 % The commands created by |\fracdef| have the following syntax:
180 % \syntax{<name>"["<frac-params>"]{"<top>"}{"<bottom>"}"}. Thus, you can use
181 % the optional argument to `tweak' the fraction if necessary. This isn't
182 % such a good idea to do often.
184 % \DescribeMacro\frac
185 % \DescribeMacro\binom
186 % \DescribeMacro\jacobi
187 % The macros |\frac|, |\binom| and |\jacobi| are defined using |\fracdef|.
188 % They typset $\frac{x}{y}$, $\binom{n}{k}$ and $\jacobi{x}{n}$ respectively.
189 % (The last may be of use to number theorists talking about Jacobi or
192 % By way of example, these commands were defined using
194 %\fracdef\frac{nodelims, line}
195 %\fracdef\binom{leftdelim = (, rightdelim = ), noline}
196 %\fracdef\jacobi{leftdelim = (, rightdelim = ), line}
199 % \subsection{Rant about derivatives}
202 % There is a difference between UK and US typesetting of derivatives.
204 % \[ \frac{dy}{dx} \]
205 % while the British want
206 % \[ \frac{\d y}{\d x}. \]
207 % The command |\d| command is fixed to typeset a `$\d$'. (In text mode,
208 % |\d{x}| still typesets `\d{x}'.)
210 % \subsection{New operator names}
212 % \DescribeMacro\keys
215 % \DescribeMacro\supp
218 % \DescribeMacro\poly
219 % \DescribeMacro\negl
220 % A few esoteric new operator names are supplied.
221 % \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
222 % $\keys$ & "\keys" & $\dom$ & "\dom" & $\ran$ & "\ran" \\
223 % $\supp$ & "\supp" & $\lcm$ & "\lcm" & $\ord$ & "\ord" \\
224 % $\poly$ & "\poly" & $\negl$ & "\negl"
225 % \end{tabular} \end{center}
226 % I think |\lcm| ought to be self-explanatory. The |\dom| and |\ran|
227 % operators pick out the domain and range of a function, respectively; thus,
228 % if $F\colon X \to Y$ is a function, then $\dom F = X$ and $\ran F = Y$.
229 % The \emph{support} of a probability distribution $\mathcal{D}$ is the set
230 % of objects with nonzero probability; i.e., $\supp{D} = \{\, x \in
231 % \dom\mathcal{D} \mid \mathcal{D}(x) > 0 \,\}$. If $g \in G$ is a group
232 % element then $\ord g$ is the \emph{order} of $g$; i.e., the smallest
233 % positive integer $i$ where $g^i$ is the identity element, or $0$ if there
234 % is no such $i$. $\poly(n)$ is some polynomial function of $n$. A function
235 % $\nu(\cdot)$ is \emph{negligible} if, for every polynomial function
236 % $p(\cdot)$, there is an integer $N$ such that $\nu(n) < 1/p(n)$ for all $n
237 % > N$; $\negl(n)$ is some negligible function of $n$.
239 % \subsection{Standard set names}
247 % \DescribeMacro\powerset
249 % If you have a |\mathbb| command defined, the following magic is revealed:
250 % \begin{center} \unverb\| \begin{tabular}{cl|cl|cl}
251 % $\Z$ & "\Z" & $\Q$ & "\Q" & $\R$ & "\R" \\
252 % $\N$ & "\N" & $\F$ & "\F" & $\C$ & "\C"
253 % \end{tabular} \end{center}
254 % which are handy for various standard sets of things. Also the |\powerset|
255 % command typesets `$\powerset$', and \syntax{"\\gf{"<q>"}"}, which by default
256 % typesets $\gf{\syntax{<q>}}$ but you might choose to have it set
257 % $\mathrm{GF}(\syntax{<q>})$ intead.
259 % \subsection{Biggles}
261 % \DescribeMacro\bbigg
262 % \DescribeMacro\bbiggl
263 % \DescribeMacro\bbiggr
264 % \DescribeMacro\bbiggm
265 % The |\bbigg| commands generalizes the Plain \TeX\ |\bigg| family of
266 % macros. |\bbigg| produces an `ordinary' symbol; |\bbiggl| and |\bbiggr|
267 % produce left and right delimiters; and |\bbiggm| produces a relation. They
268 % produce symbols whose size is related to the prevailing text size -- so
269 % they adjust correctly in chapter headings, for example.
271 % The syntax is straightforward:
272 % \syntax{"\\"<bigop>"["$a$"]{"$n$"}{"<delim>"}"}. Describing it is a bit
273 % trickier. The size is based on the current |\strut| height. If |\strut|
274 % has a height of $h$ and a depth of $d$, then the delimiter produced has a
275 % height of $n \times (h + d + a)$.
277 % The old |\big| commands have been redefined in terms of |\bbigg|.
279 % \subsection{The `QED' symbol}
282 % \DescribeMacro\qedrule
283 % For use in proofs of theorems, we provide a `QED' symbol which behaves well
284 % under bizarre line-splitting conditions. To use it, just say |\qed|. The
285 % little `\qedrule' symbol is available on its own, by saying |\qedrule|.
286 % This also sets |\qedsymbol| if it's not set already.
289 % \subsection{Punctuation in displays}
291 % It's conventional to follow displayed equations with the necessary
292 % punctuation for them to fit into the surrounding prose. This isn't
293 % universal: Ian Stewart says in the preface to the third edition of his
294 % \emph{Galois Theory}:\footnote{^^A
295 % Chapman \& Hall/CRC Mathematics, 2004; ISBN 1-58488-393-6.} ^^A
297 % Along the way I made once change that may raise a few eyebrows. I have
298 % spent much of my career telling students that written mathematics should
299 % have punctuation as well as symbols. If a symbol or a formula would be
300 % followed by a comma if it were replaced by a word or phrase, then it
301 % should be followed by a comma; however strange the formula then looks.
303 % I still think that punctuation is essential for formulas in the main body
304 % of the text. If the formula is $t^2 + 1$, say, then it should have its
305 % terminating comma. But I have come to the conclusion that eliminating
306 % visual junk from the printed page is more important than punctuatory
307 % pedantry, so that when the same formula is \emph{displayed}, for example
309 % then it looks silly if the comma is included, like this,
310 % \[ t^2 + 1 \mpunct{,} \]
311 % and everything is much cleaner and less ambiguous without punctuation.
313 % Purists will hate this, though many of them would not have noticed had I
314 % not pointed it out here. Until recently, I would have agreed. But I
315 % think it is time we accepted that the act of displaying a formula equips
316 % it with \emph{implicit} (invisible) punctuation. This is the 21st
317 % century, and typography has moved on.
320 % \DescribeMacro\mpunct
321 % I tended to agree with Prof.\ Stewart, even before I read his preface; but
322 % now I'm not so sure, and it's clear that we're in the minority. Therefore,
323 % the command |\mpunct| sets its argument as text, a little distance from
324 % the preceding mathematics.
327 % There used to be an eqnarray here, but that's migrated its way into the
328 % \package{mdwtab} package. Maybe the original version, without dependency
329 % on \package{mdwtab} ought to be releasable separately. I'll keep it around
332 % The following is the documentation for the original version. There's an
333 % updated edition in \package{mdwtab}.
336 % \begin{old-eqnarray}
338 % \subsection{A new \env{eqnarray} environment}
340 % \LaTeX's built-in \env{eqnarray} is horrible -- it puts far too much space
341 % between the items in the array. This environment is rather nearer to the
342 % \env{amsmath} \env{align} environments, although rather less capable.
345 % \DescribeEnv{eqnarray}
347 % \setbox0\hbox{"\\begin{eqnarray}["<preamble>"]" \dots "\\end{eqnarray}"}
348 % \leavevmode \hskip-\parindent \fbox{\box0}
352 % The new version of \env{eqnarray} tries to do everything which you really
353 % want it to. The \synt{preamble} string allows you to define the column
354 % types in a vaguely similar way to the wonderful \env{tabular} environment.
355 % The types provided (and it's easy-ish to add more) are:
358 % \begin{description} \setdescriptionlabel{\normalfont\ttfamily#1}
359 % \item [r] Right aligned equation
360 % \item [c] Centre-aligned equation
361 % \item [l] Left aligned equation
362 % \item [\textrm{\texttt{Tr}, \texttt{Tc} and \texttt{Tl}}] Right, centre and
363 % left aligned text (not maths)
364 % \item [L] Left aligned zero-width equation
365 % \item [x] Centred entire equation
366 % \item [:] Big gap separating sets of equations
367 % \item [q] Quad space
368 % \item [>\ch\{\synt{text}\ch\}] Insert text before column
369 % \item [<\ch\{\synt{text}\ch\}] Insert text after column
372 % Some others are also defined: don't use them because they do complicated
373 % things which are hard to explain and they aren't much use anyway.
375 % The default preamble, if you don't supply one of your own, is \lit{rcl}.
376 % Most of the time, \lit{rl} is sufficient, although compatibility is more
379 % By default, there is no space between columns, which makes formul\ae\ in an
380 % \env{eqnarray} environment look just like formul\ae\ typeset on their own,
381 % except that things get aligned in columns. This is where the default
382 % \env{eqnarray} falls down: it leaves |\arraycolsep| space between each
383 % column making the thing look horrible.
385 % An example would be good here, I think. This one's from exercise 22.9 of
386 % the \textit{\TeX book}.
388 % \begin{demo}[w]{Simultaneous equations}
389 %\begin{eqnarray}[rcrcrcrl]
390 % 10w & + & 3x & + & 3y & + & 18z & = 1 \\
391 % 6w & - & 17x & & & - & 5z & = 2
395 % Choosing a more up-to-date example, here's one demonstrating the \lit{:}
396 % column specifier from the \textit{\LaTeX\ Companion}.
398 % \begin{demo}[w]{Lots of equations}
399 %\begin{eqnarray}[rl:rl:l]
400 % V_i &= v_i - q_i v_j, & X_i &= x_i - q_i x_j, &
401 % U_i = u_i, \qquad \mbox{for $i \ne j$} \label{eq:A} \\
402 % V_j &= v_j, & X_j &= x_j &
403 % U_j u_j + \sum_{i \ne j} q_i u_i.
407 % We can make things more interesting by adding a plain text column. Here we
410 % \begin{demo}[w]{Plain text column}
411 %\begin{eqnarray}[rlqqTl]
412 % x &= y & by (\ref{eq:A}) \\
413 % x' &= y' & by definition \\
414 % x + x' &= y + y' & by Axiom~1
418 % The new features also mean that you don't need to mess about with
419 % |\lefteqn| any more. This is handled by the \lit{L} column type:
421 % \begin{demo}{Splitting example}
422 %\begin{eqnarray*}[Ll]
429 % Finally, just to prove that the spacing's right at last, here's another one
430 % from the \textit{Companion}.
432 % \begin{demo}{Spacing demonstration}
436 %\begin{eqnarray}[rl]
437 % x^2 + y^2 &= z^2 \\
442 % Well, that was easy enough. Now on to numbering. As you've noticed, the
443 % equations above are numbered. You can use the \env{eqnarray$*$}
444 % environment to turn off the numbering in the whole environment, or say
445 % |\nonumber| on a line to suppress numbering of that one in particular.
446 % More excitingly, you can say \syntax{"\\nonumber["<text>"]"} to choose
447 % what text to display.
449 % A note for cheats: you can use the sparkly new \env{eqnarray} for simple
450 % equations simply by specifying \lit{x} as the column description. Who
451 % needs \AmSTeX? |;-)|
457 % \section{Implementation}
459 % This isn't really complicated (honest) although it is a lot hairier than I
460 % think it ought to be.
464 \RequirePackage{amssymb}
465 \RequirePackage{mdwkey}
468 % \subsection{Square roots}
470 % \subsubsection{Where is the square root sign?}
472 % \LaTeX\ hides the square root sign away somewhere without telling anyone
473 % where it is. I extract it forcibly by peeking inside the |\sqrtsign| macro
474 % and scrutinising the contents. Here we go: prepare for yukkiness.
477 \newcount\sq@sqrt \begingroup \catcode`\|0 \catcode`\\12
478 |def|sq@readrad#1"#2\#3|relax{|global|sq@sqrt"#2|relax}
479 |expandafter|sq@readrad|meaning|sqrtsign|relax |endgroup
480 \def\sq@delim{\delimiter\sq@sqrt\relax}
483 % \subsubsection{Drawing fake square root signs}
485 % \TeX\ absolutely insists on drawing square root signs with a vinculum over
486 % the top. In order to get the same effect, we have to attempt to emulate
489 % \begin{macro}{\sqrtdel}
491 % This does the main job of typesetting a vinculum-free radical.\footnote{^^A
492 % Note for chemists: this is nothing to do with short-lived things which
493 % don't have their normal numbers of electrons. And it won't reduce the
494 % appearance of wrinkles either.}
495 % It's more or less a duplicate of what \TeX\ does internally, so it might be
496 % a good plan to have a copy of Appendix~G open while you examine this.
498 % We start off by using |\mathpalette| to help decide how big things should
502 \def\sqrtdel{\mathpalette\sqrtdel@i}
505 % Read the contents of the radical into a box, so we can measure it.
509 \setbox\z@\hbox{$\m@th#1#2$}% %%% Bzzzt -- uncramps the mathstyle
512 % Now try and sort out the values needed in this calculation. We'll assume
513 % that $\xi_8$ is 0.6\,pt, the way it usually is. Next try to work out the
514 % value of $\varphi$.
524 % That was easy. Now for $\psi$.
528 \advance\@tempdimb.25\@tempdima%
531 % Build the `delimiter' in a box of height $h(x)+d(x)+\psi+\xi_8$, as
532 % requested. Box~2 will do well for this purpose.
536 \advance\dimen@\@tempdimb%
537 \advance\dimen@\ht\z@%
538 \advance\dimen@\dp\z@%
540 $\left\sq@delim\vcenter to\dimen@{}\right.\n@space$%
544 % Now we need to do some more calculating (don't you hate it?). As far as
545 % Appendix~G is concerned, $\theta=h(y)=0$, because we want no rule over the
550 \advance\@tempdima\dp\tw@%
551 \advance\@tempdima-\ht\z@%
552 \advance\@tempdima-\dp\z@%
553 \ifdim\@tempdima>\@tempdimb%
554 \advance\@tempdima\@tempdimb%
555 \@tempdimb.5\@tempdima%
559 % Work out how high to raise the radical symbol. Remember that Appendix~G
560 % thinks that the box has a very small height, although this is untrue here.
564 \advance\@tempdima\@tempdimb%
565 \advance\@tempdima-\ht\tw@%
568 % Build the output (finally). The brace group is there to turn the output
569 % into a mathord, one of the few times that this is actually desirable.
572 {\raise\@tempdima\box\tw@\vbox{\kern\@tempdimb\box\z@}}%
578 % \subsubsection{The new square root command}
580 % This is where we reimplement all the square root stuff. Most of this stuff
581 % comes from the \PlainTeX\ macros, although some is influenced by \AmSTeX\
582 % and \LaTeXe, and some is original. I've tried to make the spacing vaguely
583 % automatic, so although it's not configurable like \AmSTeX's version, the
584 % output should look nice more of the time. Maybe.
586 % \begin{macro}{\sqrt}
588 % \LaTeX\ says this must be robust, so we make it robust. The first thing to
589 % do is to see if there's a star and pass the appropriate squareroot-drawing
590 % command on to the rest of the code.
593 \DeclareRobustCommand\sqrt{\@ifstar{\sqrt@i\sqrtdel}{\sqrt@i\sqrtsign}}
596 % Now we can sort out an optional argument to be displayed on the root.
599 \def\sqrt@i#1{\@ifnextchar[{\sqrt@ii{#1}}{\sqrt@iv{#1}}}
602 % Stages~2 and~3 below are essentially equivalents of \PlainTeX's
603 % |\root|\dots|\of| and |\r@@t|. Here we also find the first wrinkle: the
604 % |\rootbox| used to store the number is spaced out on the left if necessary.
605 % There's a backspace after the end so that the root can slip underneath, and
606 % everything works out nicely. Unfortunately size is fixed here, although
607 % doesn't actually seem to matter.
611 \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#2}$}%
612 \ifdim\wd\rootbox<6\p@%
613 \setbox\rootbox\hb@xt@6\p@{\hfil\unhbox\rootbox}%
615 \mathpalette{\sqrt@iii{#1}}%
619 % Now we can actually build everything. Note that the root is raised by its
620 % depth -- this prevents a common problem with letters with descenders.
623 \def\sqrt@iii#1#2#3{%
624 \setbox\z@\hbox{$\m@th#2#1{#3}$}%
626 \advance\dimen@-\dp\z@%
628 \advance\dimen@\dp\rootbox%
630 \raise\dimen@\copy\rootbox%
636 % Finally handle a non-numbered root. We read the rooted text in as an
637 % argument, to stop problems when people omit the braces. (\AmSTeX\ does
641 \def\sqrt@iv#1#2{#1{#2}}
646 % \begin{macro}{\root}
648 % We also re-implement \PlainTeX's |\root| command, just in case someone uses
649 % it, and supply a star-variant. This is all very trivial.
652 \def\root{\@ifstar{\root@i\sqrtdel}{\root@i\sqrtsign}}
653 \def\root@i#1#2\of{\sqrt@ii{#1}[#2]}
658 % \subsection{Modular programming}
660 % \begin{macro}{\pmod}
662 % Do some hacking if not |\ifouter|.
666 \ifinner\;\else\allowbreak\mkern18mu\fi%
667 ({\operator@font mod}\,\,#1)%
673 % \subsection{Some magic new maths characters}
675 % \begin{macro}{\bitor}
676 % \begin{macro}{\bitand}
677 % \begin{macro}{\dblor}
678 % \begin{macro}{\dbland}
679 % \begin{macro}{\xor}
680 % \begin{macro}{\lor}
681 % \begin{macro}{\ror}
682 % \begin{macro}{\lsl}
683 % \begin{macro}{\lsr}
685 % The new boolean operators.
688 \DeclareMathSymbol{&}{\mathbin}{operators}{`\&}
689 \DeclareMathSymbol{\bitand}{\mathbin}{operators}{`\&}
690 \def\bitor{\mathbin\mid}
691 \def\dblor{\mathbin{\mid\mid}}
692 \def\dbland{\mathbin{\mathrel\bitand\mathrel\bitand}}
694 \def\lsl{\mathbin{<\!\!<}}
695 \def\lsr{\mathbin{>\!\!>}}
696 \def\rol{\mathbin{<\!\!<\!\!<}}
697 \def\ror{\mathbin{>\!\!>\!\!>}}
698 \AtBeginDocument{\ifx\lll\@@undefined\else
699 \def\lsl{\mathbin{\ll}}
700 \def\lsr{\mathbin{\gg}}
701 \def\rol{\mathbin{\lll}}
702 \def\ror{\mathbin{\ggg}}
716 % \begin{macro}{\cat}
717 % \begin{macro}{\compose}
718 % \begin{macro}{\implies}
719 % \begin{macro}{\vect}
721 % \begin{macro}{\jacobi}
723 % A mixed bag of stuff.
726 \def\cat{\mathbin{\|}}
728 \def\implies{\Rightarrow}
729 \def\vect#1{\mathord{\mathbf{#1}}}
731 \ifmmode\mathord{\operator@font d}%
732 \else\expandafter\a\expandafter d\fi%
734 \def\jacobi#1#2{{{#1}\overwithdelims()#2}}
744 % \begin{macro}{\statclose}
745 % \begin{macro}{\compind}
747 % Fancy new relations for probability distributions.
750 \def\statclose{\mathrel{\mathop{=}\limits^{\scriptscriptstyle s}}}
751 \def\compind{\mathrel{\mathop{\approx}\limits^{\scriptscriptstyle c}}}
757 % \begin{macro}{\keys}
758 % \begin{macro}{\dom}
759 % \begin{macro}{\ran}
760 % \begin{macro}{\supp}
761 % \begin{macro}{\lcm}
762 % \begin{macro}{\poly}
763 % \begin{macro}{\negl}
764 % \begin{macro}{\ord}
766 % And the new operator names.
769 \def\keys{\mathop{\operator@font keys}\nolimits}
770 \def\dom{\mathop{\operator@font dom}\nolimits}
771 \def\ran{\mathop{\operator@font ran}\nolimits}
772 \def\supp{\mathop{\operator@font supp}\nolimits}
773 \def\lcm{\mathop{\operator@font lcm}\nolimits}
774 \def\poly{\mathop{\operator@font poly}\nolimits}
775 \def\negl{\mathop{\operator@font negl}\nolimits}
776 \def\ord{\mathop{\operator@font ord}\nolimits}
788 % \subsection{Fractions}
790 % \begin{macro}{\@frac@parse}
792 % \syntax{"\\@frac@parse{"<stuff>"}{"<frac-params>"}"} -- run \<stuff>
793 % passing it three arguments: an infix fraction-making command, the `outer'
794 % style, and the `inner' style.
796 % This is rather tricky. We clear a load of parameters, parse the parameter
797 % list, and then build a token list containing the right stuff. Without the
798 % token list fiddling, we end up expanding things at the wrong times -- for
799 % example, |\{| expands to something terribly unpleasant in a document
802 % All of the nastiness is contained in a group.
805 \def\@frac@parse#1#2{%
807 \let\@wd\@empty\def\@ldel{.}\def\@rdel{.}%
808 \def\@op{over}\let\@dim\@empty\@tempswafalse%
809 \let\@is\@empty\let\@os\@empty%
810 \mkparse{mdwmath:frac}{#2}%
811 \toks\tw@{\endgroup#1}%
812 \toks@\expandafter{\csname @@\@op\@wd\endcsname}%
814 \toks@\expandafter{\the\expandafter\toks@\@ldel}%
815 \toks@\expandafter{\the\expandafter\toks@\@rdel}%
817 \expandafter\toks@\expandafter{\the\expandafter\toks@\@dim}%
818 \toks@\expandafter{\the\toks\expandafter\tw@\expandafter{\the\toks@}}
819 \toks@\expandafter{\the\expandafter\toks@\expandafter{\@os}}
820 \toks@\expandafter{\the\expandafter\toks@\expandafter{\@is}}
825 % The keyword definitions are relatively straightforward now. The error
826 % handling for \textsf{style} and \textsf{innerstyle} could do with
830 \def\@frac@del#1#2{\def\@wd{withdelims}\@tempswatrue\def#1{#2}}
831 \mkdef{mdwmath:frac}{leftdelim}{\@frac@del\@ldel{#1}}
832 \mkdef{mdwmath:frac}{rightdelim}{\@frac@del\@rdel{#1}}
833 \mkdef{mdwmath:frac}{nodelims}*{\let\@wd\@empty\@tempswafalse}
834 \mkdef{mdwmath:frac}{line}{%
835 \def\@op{above}\setlength\dimen@{#1}\edef\@dim{\the\dimen@\space}%
837 \mkdef{mdwmath:frac}{line}*{\def\@op{over}\let\@dim\@empty}
838 \mkdef{mdwmath:frac}{noline}*{\def\@op{atop}\let\@dim\@empty}
839 \def\@frac@style#1#2{%
840 \ifx\q@delim#2\q@delim\let#1\@empty%
842 \expandafter\ifx\csname #2style\endcsname\relax%
843 \PackageError{mdwmath}{Bad maths style `#2'}\@ehc%
845 \edef#1{\csname#2style\endcsname}%
849 \mkdef{mdwmath:frac}{style}[]{\@frac@style\@os{#1}}
850 \mkdef{mdwmath:frac}{innerstyle}[]{\@frac@style\@is{#1}}
855 % \begin{macro}{\fracdef}
857 % Here's where the rest of the pain is. We do a preliminary parse of the
858 % parameters and `compile' the result into the output macro. If there's no
859 % optional argument, then we don't need to do any really tedious formatting
860 % at the point of use.
863 \def\fracdef#1#2{\@frac@parse{\fracdef@i{#1}{#2}}{#2}}
864 \def\fracdef@i#1#2#3#4#5{\def#1{\@frac@do{#2}{#3}{#4}{#5}}}
865 \def\@frac@do#1#2#3#4{%
866 \@ifnextchar[{\@frac@complex{#1}}{\@frac@simple{#2}{#3}{#4}}%
868 \def\@frac@complex#1[#2]{\@frac@parse\@frac@simple{#1,#2}}
869 \def\@frac@simple#1#2#3#4#5{{#2{{#3#4}#1{#3#5}}}}
874 % \begin{macro}{\frac@fix}
875 % \begin{macro}{\@@over}
876 % \begin{macro}{\@@atop}
877 % \begin{macro}{\@@above}
878 % \begin{macro}{\@@overwithdelims}
879 % \begin{macro}{\@@atopwithdelims}
880 % \begin{macro}{\@@abovewithdelims}
882 % Finally, we need to fix up |\@@over| and friends. Maybe \package{amsmath}
883 % has hidden the commands away somewhere unhelpful. If not, we make the
887 \def\q@delim{\q@delim}
888 \def\frac@fix#1{\expandafter\frac@fix@i\string#1\q@delim}
889 \def\frac@fix@i#1#2\q@delim{\frac@fix@ii{#2}\frac@fix@ii{#2withdelims}}
891 \expandafter\ifx\csname @@#1\endcsname\relax%
892 \expandafter\let\csname @@#1\expandafter\endcsname\csname#1\endcsname%
895 \frac@fix\over \frac@fix\atop \frac@fix\above
906 % \begin{macro}{\frac}
907 % \begin{macro}{\binom}
908 % \begin{macro}{\jacobi}
910 % And finally, we define the fraction-making commands.
913 \fracdef\frac{nodelims, line}
914 \fracdef\binom{leftdelim = (, rightdelim = ), noline}
915 \fracdef\jacobi{leftdelim = (, rightdelim = ), line}
922 % \subsection{Blackboard bold stuff}
930 % \begin{macro}{\powerset}
933 % First of all, the signs.
942 \def\powerset{\mathbb{P}}
944 %\def\gf#1{\mathrm{GF}({#1})}
956 % And now, define |\mathbb| if it's not there already.
959 \AtBeginDocument{\ifx\mathbb\@@undefined\let\mathbb\mathbf\fi}
962 % \subsection{Biggles}
964 % Now for some user-controlled delimiter sizing. The standard bigness of
965 % plain \TeX's delimiters are all right, but it's a little limiting.
967 % The biggness of delimiters is based on the size of the current |\strut|,
968 % which \LaTeX\ keeps up to date all the time. This will make the various
969 % delimiters grow in proportion when the text gets bigger. Actually, I'm
970 % not sure that this is exactly right -- maybe it should be nonlinear,
972 % \begin{macro}{\bbigg}
973 % \begin{macro}{\bbiggl}
974 % \begin{macro}{\bbiggr}
975 % \begin{macro}{\bbiggm}
977 % This is where the bigness is done. This is more similar to the plain \TeX\
978 % big delimiter stuff than to the \package{amsmath} stuff, although there's
979 % not really a lot of difference.
981 % The two arguments are a multiplier for the delimiter size, and a small
982 % increment applied \emph{before} the multiplication (which is optional).
984 % This is actually a front for a low-level interface which can be called
985 % directly for efficiency.
988 \def\bbigg{\@bbigg\mathord} \def\bbiggl{\@bbigg\mathopen}
989 \def\bbiggr{\@bbigg\mathclose} \def\bbiggm{\@bbigg\mathrel}
997 % \begin{macro}{\@bbigg}
999 % This is an optional argument parser providing a front end for the main
1003 \def\@bbigg#1{\@ifnextchar[{\@bigg@i{#1}}{\@bigg@i{#1}[\z@]}}
1004 \def\@bigg@i#1[#2]#3#4{#1{\bbigg@{#2}{#3}{#4}}}
1009 % \begin{macro}{\bbigg@}
1011 % This is it, at last. The arguments are as described above: an addition
1012 % to be made to the strut height, and a multiplier. Oh, and the delimiter,
1015 % This is a bit messy. The smallest `big' delimiter, |\big|, is the same
1016 % height as the current strut box. Other delimiters are~$1\frac12$, $2$
1017 % and~$2\frac12$ times this height. I'll set the height of the delimiter by
1018 % putting in a |\vcenter| of the appropriate size.
1020 % Given an extra height~$x$, a multiplication factor~$f$ and a strut
1021 % height~$h$ and depth~$d$, I'll create a vcenter with total height
1022 % $f(h+d+x)$. Easy, isn't it?
1027 \dimen@\ht\strutbox\advance\dimen@\dp\strutbox%
1030 \left#3\vcenter to\dimen@{}\right.\n@space%
1037 % \begin{macro}{\big}
1038 % \begin{macro}{\Big}
1039 % \begin{macro}{\bigg}
1040 % \begin{macro}{\Bigg}
1042 % Now for the easy macros.
1045 \def\big{\bbigg@\z@\@ne}
1046 \def\Big{\bbigg@\z@{1.5}}
1047 \def\bigg{\bbigg@\z@\tw@}
1048 \def\Bigg{\bbigg@\z@{2.5}}
1056 % \subsection{The `QED' symbol}
1058 % \begin{macro}{\qed}
1059 % \begin{macro}{\qedrule}
1060 % \begin{macro}{\qedsymbol}
1062 % This is fairly simple. Just be careful will the glue and penalties. The
1063 % size of the little box is based on the current font size.
1065 % The horizontal list constructed by the macro is like this:
1068 % \item A |\quad| of space. This might get eaten if there's a break here or
1069 % before. That's OK, though.
1070 % \item An empty box, to break a run of discardable items.
1071 % \item A |\penalty 10000| to ensure that the spacing glue isn't discarded.
1072 % \item |\hfill| glue to push the little rule to the end of the line.
1073 % \item A little square rule `\qedrule', with some small kerns around it.
1074 % \item A glue item to counter the effect of glue added at the paragraph
1078 % The vertical mode case is simpler, but less universal. It copes with
1079 % relatively simple cases only.
1081 % A |\qed| commend ends the paragraph.
1087 \setbox\z@\hb@xt@\linewidth{\hfil\strut\qedsymbol}%
1089 \ifdim\prevdepth>\dp\strutbox%
1090 \dimen@\prevdepth\advance\dimen@-\dp\strutbox%
1093 \penalty\@M\vskip-\baselineskip\box\z@%
1097 \hbox{}\penalty200\quad%
1098 \hbox{}\penalty\@M\hfill\qedsymbol\hskip-\parfillskip\par%
1102 \dimen@\ht\strutbox%
1103 \advance\dimen@\dp\strutbox%
1105 \advance\dimen@-\dimen@ii%
1107 \advance\dimen@-\dp\strutbox%
1108 \advance\dimen@\dimen@ii%
1109 \advance\dimen@ii-\dimen@%
1111 \vrule\@width1ex\@height\dimen@\@depth\dimen@ii%
1114 \providecommand\qedsymbol{\qedrule}
1121 % \subsection{Punctuation in displays}
1123 % \begin{macro}{\mpunct}
1125 % This is actually a little more subtle than you'd expect. If the
1126 % \package{amstext} package is loaded, or something else has defined the
1127 % |\text| command, then we should use that; otherwise, just drop a box in and
1128 % hope for the best.
1133 \ifx\text\@@undefined\hbox%
1134 \else\expandafter\text\fi%
1142 % The following is the original definition of the enhanced eqnarray
1143 % environment. It's not supported, although if you can figure out how to
1144 % extract it, it's all yours.
1147 % \begin{old-eqnarray}
1149 % \subsection{The sparkly new \env{eqnarray}}
1151 % Start off by writing a different package.
1158 % \subsubsection{Options handling}
1160 % We need to be able to cope with \textsf{fleqn} and \textsf{leqno} options.
1161 % This will adjust our magic modified \env{eqnarray} environment
1167 \DeclareOption{fleqn}{\@fleqntrue}
1168 \DeclareOption{leqno}{\@leqnotrue}
1172 % This is all really different to the \LaTeX\ version. I've looked at the
1173 % various \env{tabular} implementations, the original \env{eqnarray} and the
1174 % \textit{\TeX book} to see how best to do this, and then went my own way.
1175 % If it doesn't work it's all my fault.
1177 % \subsubsection{Some useful registers}
1179 % The old \LaTeX\ version puts the equation numbers in by keeping a count of
1180 % where it is in the alignment. Since I don't know how may columns there are
1181 % going to be, I'll just use a switch in the preamble to tell me to stop
1188 % Now define some useful length parameters. First allocate them:
1191 \newskip\eqaopenskip
1192 \newskip\eqacloseskip
1197 % Now assign some default values. Users can play with these if they really
1198 % want although I can't see the point myself.
1202 \AtBeginDocument{\eqaopenskip\leftmargini}
1204 \eqaopenskip\@centering
1206 \eqacloseskip\@centering
1207 \eqacolskip\@centering
1211 % We allow the user to play with the style if this is really wanted. I dunno
1212 % why, really. Maybe someone wants very small alignments.
1215 \let\eqa@style\displaystyle
1218 % \subsubsection{The main environments}
1220 % We define the toplevel commands here. They just add in default arguments
1221 % and then call |\@eqnarray| with a preamble string. The only difference is
1222 % the last column they add in -- \env{eqnarray$*$} throws away the last
1223 % column by sticking it in box~0. (I used to |\@gobble| it but that caused
1224 % the |\cr| to be lost.)
1227 \def\eqnarray{\@ifnextchar[\eqnarray@i{\eqnarray@i[rcl]}}
1228 \def\eqnarray@i[#1]{%
1229 \@eqnarray{#1!{\hb@xt@\z@{\hss##}\tabskip\z@}}
1231 \@namedef{eqnarray*}{\@ifnextchar[\eqnarray@s@i{\eqnarray@s@i[rcl]}}
1232 \def\eqnarray@s@i[#1]{%
1233 \@eqnarray{#1!{\nonumber\setbox\z@\hbox{##}\tabskip\z@}}%
1237 % \subsubsection{Set up the initial display}
1239 % \begin{macro}{\@eqnarray}
1241 % The |\@eqnarray| command does most of the initial work. It sets up some
1242 % flags and things, builds the |\halign| preamble, and returns.
1248 % Start playing with the counter here. The original does some icky internal
1249 % playing, which isn't necessary. The |\if@eqnsw| switch is |true| if the
1250 % user hasn't supplied an equation number. The |\if@eqalast| switch is
1251 % |true| in the final equation-number column.
1254 \refstepcounter{equation}%
1260 % Set things up for the |\halign| which is coming up.
1264 \tabskip\eqaopenskip%
1270 % We'll build the real |\halign| and preamble in a token register. All we
1271 % need to do is stuff the header in the token register, clear a switch
1272 % (that'll be explained later), parse the preamble and then expand the
1273 % tokens we collected. Easy, no?
1276 \toks@{\halign to\displaywidth\bgroup}%
1278 \eqa@preamble#1\end%
1285 % \subsubsection{Parsing the preamble}
1287 % All this actually involves is reading the next character and building a
1288 % command from it. That can pull off an argument if it needs it. Just make
1289 % sure we don't fall off the end and we'll be OK.
1292 \def\eqa@preamble#1{%
1293 \ifx\end#1\else\csname eqa@char@#1\expandafter\endcsname\fi%
1297 % Adding stuff to the preamble tokens is a simple matter of using
1298 % |\expandafter| in the correct way.\footnote{^^A
1299 % I have no idea why \LaTeX\ uses \cmd\edef\ for building its preamble. It
1300 % seems utterly insane to me -- the amount of bodgery that \env{tabular}
1301 % has to go through to make everything expand at the appropriate times is
1302 % scary. Maybe Messrs~Lamport and Mittelbach just forgot about token
1303 % registers when they were writing the code. Maybe I ought to rewrite the
1304 % thing properly some time. Sigh.
1306 % As a sort of postscript to the above, I \emph{have} rewritten the
1307 % \env{tabular} environment, and made a damned fine job of it, in my
1308 % oh-so-humble opinion. All this \env{eqnarray} stuff has been remoulded
1309 % in terms of the generic column-defining things in \package{mdwtab}.
1310 % You're reading the documentation of the old version, which isn't
1311 % supported any more, so any bugs here are your own problem.}
1314 \def\eqa@addraw#1{\expandafter\toks@\expandafter{\the\toks@#1}}
1317 % Now for some cleverness again. In order to put all the right bits of
1318 % |\tabskip| glue in the right places we must \emph{not} terminate each
1319 % column until we know what the next one is. We set |\if@tempswa| to be
1320 % |true| if there's a column waiting to be closed (so it's initially
1321 % |false|). The following macro adds a column correctly, assuming we're in
1322 % a formula. Other column types make their own arrangements.
1327 \eqa@addraw{\tabskip\eqainskip}%
1335 % Now to defining column types. Let's define a macro which allows us to
1336 % define column types:
1339 \def\eqa@def#1{\expandafter\def\csname eqa@char@#1\endcsname}
1342 % Now we can define the column types. Each column type must loop back to
1343 % |\eqa@preamble| once it's finished, to read the rest of the preamble
1344 % string. Note the positioning of ord atoms in the stuff below. This will
1345 % space out relations and binops correctly when they occur at the edges of
1346 % columns, and won't affect ord atoms at the edges, because ords pack
1349 % First the easy onces. Just stick |\hfil| in the right places and
1350 % everything will be all right.
1353 \eqa@def r{\eqa@add{\hfil$\eqa@style##{}$}\eqa@preamble}
1354 \eqa@def c{\eqa@add{\hfil$\eqa@style{}##{}$\hfil}\eqa@preamble}
1355 \eqa@def l{\eqa@add{$\eqa@style{}##$\hfil}\eqa@preamble}
1356 \eqa@def x{\eqa@add{\hfil$\eqa@style##$\hfil}\eqa@preamble}
1359 % Now for the textual ones. This is also fairly easy.
1364 \if#1l\else\eqa@addraw{\hfil}\fi%
1366 \if#1r\else\eqa@addraw{\hfil}\fi%
1371 % Sort of split types of equations. I mustn't use |\rlap| here, or
1372 % everything goes wrong -- |\\| doesn't get noticed by \TeX\ in the same way
1376 \eqa@def L{\eqa@add{\hb@xt@\z@{$\eqa@style##$\hss}\qquad}\eqa@preamble}
1379 % The \lit{:} column type is fairly simple. We set |\tabskip| up to make
1380 % lots of space and close the current column, because there must be one.^^A
1381 % \footnote{This is an assumption.}
1385 \eqa@addraw{\tabskip\eqacolskip&}\@tempswafalse\eqa@preamble%
1387 \eqa@def q{\eqa@add{\quad}\@tempswafalse\eqa@preamble}
1390 % The other column types just insert given text in an appropriate way.
1393 \eqa@def >#1{\eqa@add{#1}\@tempswafalse\eqa@preamble}
1394 \eqa@def <#1{\eqa@addraw{#1}\eqa@preamble}
1397 % Finally, the magical \lit{!} column type, which sets the equation number.
1398 % We set up the |\tabskip| glue properly, tab on, and set the flag which
1399 % marks the final column.
1403 \eqa@addraw{\tabskip\eqacloseskip&\@eqalasttrue#1}\eqa@preamble%
1407 % \subsubsection{Newline codes}
1409 % Newline sequences (|\\|) get turned into calls of |\@eqncr|. The job is
1410 % fairly simple, really. However, to avoid reading `|&|' characters
1411 % prematurely, we set up a magic brace (from the \package{array} package --
1412 % this avoids creating ord atoms and other nastyness).
1416 \iffalse{\fi\ifnum0=`}\fi%
1417 \@ifstar{\eqacr@i{\@M}}{\eqacr@i{\interdisplaylinepenalty}}%
1419 \def\eqacr@i#1{\@ifnextchar[{\eqacr@ii{#1}}{\eqacr@ii{#1}[\z@]}}
1420 \def\eqacr@ii#1[#2]{%
1423 \noalign{\penalty#1\vskip#2\relax}%
1427 % \subsubsection{Setting equation numbers}
1429 % Before we start, we need to generalise the flush-left number handling bits.
1430 % The macro |\eqa@eqpos| will put its argument in the right place.
1435 \hb@xt@.01\p@{}\rlap{\normalfont\normalcolor\hskip-\displaywidth#1}%
1438 \def\eqa@eqpos#1{\normalfont\normalcolor#1}
1442 % First we need to move into the right column. Then we just set the equation
1443 % number appropriately. There is some subtlety here, ish. The |\relax| is
1444 % important, to delay expansion of the |\if|\dots\ until the new column has
1445 % been started. The two helper macros are important too, to hide `|&|'s and
1446 % `|\cr|'s from \TeX's scanner until the right time.
1451 \if@eqalast\expandafter\eqa@eqnum@i\else\expandafter\eqa@eqnum@ii\fi%
1455 \eqa@eqpos{(\theequation)}\stepcounter{equation}%
1457 \eqa@eqpos\eqa@number%
1462 \def\eqa@eqnum@ii{&\eqa@eqnum}
1465 % \subsubsection{Numbering control}
1467 % This is trivial. We set the |\if@eqnsw| flag to be |false| and store the
1472 \newcommand\nonumber[1][]{\global\@eqnswfalse\global\def\eqa@number{#1}}
1475 % \subsubsection{Closing the environments off}
1477 % This is really easy. Set the final equation number, close the |\halign|,
1478 % tidy up the equation counter (it's been stepped once too many times) and
1479 % close the display.
1485 \global\advance\c@equation\m@ne%
1487 \global\@ignoretrue%
1489 \expandafter\let\csname endeqnarray*\endcsname\endeqnarray
1492 % Now start up the other package again.
1499 % \end{old-eqnarray}
1501 % That's all there is. Byebye.
1507 % \hfill Mark Wooding, \today