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1 | % \begin{meta-comment} |
2 | % |
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3 | % $Id: mdwmath.dtx,v 1.2 2003/09/05 16:14:36 mdw Exp $ |
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4 | % |
5 | % Various nicer mathematical things |
6 | % |
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7 | % (c) 2003 Mark Wooding |
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8 | % |
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9 | % \end{meta-comment} |
10 | % |
11 | % \begin{meta-comment} <general public licence> |
12 | %% |
13 | %% mdwmath package -- various nicer mathematical things |
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14 | %% Copyright (c) 2003 Mark Wooding |
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15 | %% |
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. |
20 | %% |
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. |
25 | %% |
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. |
29 | %% |
30 | % \end{meta-comment} |
31 | % |
32 | % \begin{meta-comment} <Package preamble> |
33 | %<+package>\NeedsTeXFormat{LaTeX2e} |
34 | %<+package>\ProvidesPackage{mdwmath} |
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35 | %<+package> [2003/08/25 1.3 Nice mathematical things] |
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36 | %<+oldeqnarray>\NeedsTeXFormat{LaTeX2e} |
37 | %<+oldeqnarray>\ProvidesPackage{eqnarray} |
38 | %<+oldeqnarray> [1996/04/11 1.1 Old enhanced eqnarray] |
39 | % \end{meta-comment} |
40 | % |
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41 | % \CheckSum{729} |
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42 | %% \CharacterTable |
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 \~} |
57 | %% |
58 | % |
59 | % \begin{meta-comment} |
60 | % |
61 | %<*driver> |
62 | \input{mdwtools} |
63 | \let\opmod\pmod |
64 | \usepackage{amssymb} |
65 | \describespackage{mdwmath} |
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66 | %\describespackage{eqnarray} |
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67 | \ignoreenv{old-eqnarray} |
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68 | %\unignoreenv{old-eqnarray} |
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69 | \mdwdoc |
70 | %</driver> |
71 | % |
72 | % \end{meta-comment} |
73 | % |
74 | % \section{User guide} |
75 | % |
76 | % \subsection{Square root typesetting} |
77 | % |
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. |
84 | % |
85 | % \begin{figure} |
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 | %\[ q = \frac{2\sqrt*{2}}{5}+\sqrt[\frac{n+1}{2}]{2x^2+3xy-y^2} \] |
92 | % \end{demo} |
93 | % \end{figure} |
94 | % |
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.] |
100 | % |
101 | % \subsection{Modular arithmetic} |
102 | % |
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. |
106 | % |
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 |
111 | % fine. |
112 | % |
113 | % \subsection{Some maths symbols you already have} |
114 | % |
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" \\ |
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123 | % $\bitand$ & "\bitand" & $\dblor$ & "\dblor" & |
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124 | % \end{tabular} \end{center} |
125 | % |
126 | % \DescribeMacro\xor |
127 | % \DescribeMacro\cat |
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. |
132 | % |
133 | % \DescribeMacro\lsl |
134 | % \DescribeMacro\lsr |
135 | % \DescribeMacro\rol |
136 | % \DescribeMacro\ror |
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. |
140 | % |
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 `$\vect{x}$'. |
147 | % |
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. |
153 | % |
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154 | % \subsection{Fractions} |
155 | % |
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 |
161 | % parameters: |
162 | % \begin{description} |
163 | % \item[\lit*{line}] Include a horizontal line between the top and bottom |
164 | % (like |\frac|). |
165 | % \item[\lit*{line=}\<length>] Include a horizontal line with width |
166 | % \<length>. |
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 |
177 | % prevailing style. |
178 | % \end{description} |
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. |
183 | % |
184 | % \DescribeMacro\frac |
185 | % \DescribeMacro\binom |
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186 | % \DescribeMacro\jacobi |
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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 |
190 | % Lagrange symbols.) |
191 | % |
192 | % By way of example, these commands were defined using |
193 | %\begin{verbatim} |
194 | %\fracdef\frac{nodelims, line} |
195 | %\fracdef\binom{leftdelim = (, rightdelim = ), noline} |
196 | %\fracdef\jacobi{leftdelim = (, rightdelim = ), line} |
197 | %\end{verbatim} |
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198 | % |
199 | % \subsection{Rant about derivatives} |
200 | % |
201 | % \DescribeMacro\d |
202 | % There is a difference between UK and US typesetting of derivatives. |
203 | % Americans typeset |
204 | % \[ \frac{dy}{dx} \] |
205 | % while the British want |
206 | % \[ \frac{\d y}{\d x}. \] |
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207 | % The command |\d| command is fixed to typeset a `$\d$'. (In text mode, |
208 | % |\d{x}| still typesets `\d{x}'.) |
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209 | % |
210 | % \subsection{New operator names} |
211 | % |
212 | % \DescribeMacro\keys |
213 | % \DescribeMacro\dom |
214 | % \DescribeMacro\ran |
215 | % \DescribeMacro\supp |
216 | % \DescribeMacro\lcm |
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217 | % \DescribeMacro\ord |
218 | % \DescribeMacro\poly |
219 | % \DescribeMacro\negl |
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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" \\ |
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223 | % $\supp$ & "\supp" & $\lcm$ & "\lcm" & $\ord$ & "\ord" \\ |
224 | % $\poly$ & "\poly" & $\negl$ & "\negl" |
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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., $\supp{D} = \{\, x \in |
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231 | % \dom\mathcal{D} \mid \mathcal{D}(x) > 0 \,\}$. 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 $n$. |
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238 | % |
239 | % \subsection{Standard set names} |
240 | % |
241 | % \DescribeMacro\Z |
242 | % \DescribeMacro\Q |
243 | % \DescribeMacro\R |
244 | % \DescribeMacro\C |
245 | % \DescribeMacro\N |
246 | % \DescribeMacro\F |
247 | % \DescribeMacro\powerset |
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248 | % \DescribeMacro\gf |
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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| |
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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. |
258 | % |
259 | % \subsection{Biggles} |
260 | % |
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. |
270 | % |
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 $n \times (h + d + a)$. |
276 | % |
277 | % The old |\big| commands have been redefined in terms of |\bbigg|. |
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278 | % |
279 | % \subsection{The `QED' symbol} |
280 | % |
281 | % \DescribeMacro\qed |
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. |
287 | % \qed |
288 | % |
289 | % \begin{ignore} |
290 | % There used to be an eqnarray here, but that's migrated its way into the |
291 | % \package{mdwtab} package. Maybe the original version, without dependency |
292 | % on \package{mdwtab} ought to be releasable separately. I'll keep it around |
293 | % just in case. |
294 | % |
295 | % The following is the documentation for the original version. There's an |
296 | % updated edition in \package{mdwtab}. |
297 | % \end{ignore} |
298 | % |
299 | % \begin{old-eqnarray} |
300 | % |
301 | % \subsection{A new \env{eqnarray} environment} |
302 | % |
303 | % \LaTeX's built-in \env{eqnarray} is horrible -- it puts far too much space |
304 | % between the items in the array. This environment is rather nearer to the |
305 | % \env{amsmath} \env{align} environments, although rather less capable. |
306 | % |
307 | % \bigskip |
308 | % \DescribeEnv{eqnarray} |
309 | % {\synshorts |
310 | % \setbox0\hbox{"\\begin{eqnarray}["<preamble>"]" \dots "\\end{eqnarray}"} |
311 | % \leavevmode \hskip-\parindent \fbox{\box0} |
312 | % } |
313 | % \smallskip |
314 | % |
315 | % The new version of \env{eqnarray} tries to do everything which you really |
316 | % want it to. The \synt{preamble} string allows you to define the column |
317 | % types in a vaguely similar way to the wonderful \env{tabular} environment. |
318 | % The types provided (and it's easy-ish to add more) are: |
319 | % |
320 | % \def\ch{\char`} |
321 | % \begin{description} \def\makelabel{\hskip\labelsep\normalfont\ttfamily} |
322 | % \item [r] Right aligned equation |
323 | % \item [c] Centre-aligned equation |
324 | % \item [l] Left aligned equation |
325 | % \item [\textrm{\texttt{Tr}, \texttt{Tc} and \texttt{Tl}}] Right, centre and |
326 | % left aligned text (not maths) |
327 | % \item [L] Left aligned zero-width equation |
328 | % \item [x] Centred entire equation |
329 | % \item [:] Big gap separating sets of equations |
330 | % \item [q] Quad space |
331 | % \item [>\ch\{\synt{text}\ch\}] Insert text before column |
332 | % \item [<\ch\{\synt{text}\ch\}] Insert text after column |
333 | % \end{description} |
334 | % |
335 | % Some others are also defined: don't use them because they do complicated |
336 | % things which are hard to explain and they aren't much use anyway. |
337 | % |
338 | % The default preamble, if you don't supply one of your own, is \lit{rcl}. |
339 | % Most of the time, \lit{rl} is sufficient, although compatibility is more |
340 | % important to me. |
341 | % |
342 | % By default, there is no space between columns, which makes formul\ae\ in an |
343 | % \env{eqnarray} environment look just like formul\ae\ typeset on their own, |
344 | % except that things get aligned in columns. This is where the default |
345 | % \env{eqnarray} falls down: it leaves |\arraycolsep| space between each |
346 | % column making the thing look horrible. |
347 | % |
348 | % An example would be good here, I think. This one's from exercise 22.9 of |
349 | % the \textit{\TeX book}. |
350 | % |
351 | % \begin{demo}[w]{Simultaneous equations} |
352 | %\begin{eqnarray}[rcrcrcrl] |
353 | % 10w & + & 3x & + & 3y & + & 18z & = 1 \\ |
354 | % 6w & - & 17x & & & - & 5z & = 2 |
355 | %\end{eqnarray} |
356 | % \end{demo} |
357 | % |
358 | % Choosing a more up-to-date example, here's one demonstrating the \lit{:} |
359 | % column specifier from the \textit{\LaTeX\ Companion}. |
360 | % |
361 | % \begin{demo}[w]{Lots of equations} |
362 | %\begin{eqnarray}[rl:rl:l] |
363 | % V_i &= v_i - q_i v_j, & X_i &= x_i - q_i x_j, & |
364 | % U_i = u_i, \qquad \mbox{for $i \ne j$} \label{eq:A} \\ |
365 | % V_j &= v_j, & X_j &= x_j & |
366 | % U_j u_j + \sum_{i \ne j} q_i u_i. |
367 | %\end{eqnarray} |
368 | % \end{demo} |
369 | % |
370 | % We can make things more interesting by adding a plain text column. Here we |
371 | % go: |
372 | % |
373 | % \begin{demo}[w]{Plain text column} |
374 | %\begin{eqnarray}[rlqqTl] |
375 | % x &= y & by (\ref{eq:A}) \\ |
376 | % x' &= y' & by definition \\ |
377 | % x + x' &= y + y' & by Axiom~1 |
378 | %\end{eqnarray} |
379 | % \end{demo} |
380 | % |
381 | % The new features also mean that you don't need to mess about with |
382 | % |\lefteqn| any more. This is handled by the \lit{L} column type: |
383 | % |
384 | % \begin{demo}{Splitting example} |
385 | %\begin{eqnarray*}[Ll] |
386 | % w+x+y+z = \\ |
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387 | % & a+b+c+d+e+{} \\ |
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388 | % & f+g+h+i+j |
389 | %\end{eqnarray*} |
390 | % \end{demo} |
391 | % |
392 | % Finally, just to prove that the spacing's right at last, here's another one |
393 | % from the \textit{Companion}. |
394 | % |
395 | % \begin{demo}{Spacing demonstration} |
396 | %\begin{equation} |
397 | % x^2 + y^2 = z^2 |
398 | %\end{equation} |
399 | %\begin{eqnarray}[rl] |
400 | % x^2 + y^2 &= z^2 \\ |
401 | % y^2 &< z^2 |
402 | %\end{eqnarray} |
403 | % \end{demo} |
404 | % |
405 | % Well, that was easy enough. Now on to numbering. As you've noticed, the |
406 | % equations above are numbered. You can use the \env{eqnarray$*$} |
407 | % environment to turn off the numbering in the whole environment, or say |
408 | % |\nonumber| on a line to suppress numbering of that one in particular. |
409 | % More excitingly, you can say \syntax{"\\nonumber["<text>"]"} to choose |
410 | % what text to display. |
411 | % |
412 | % A note for cheats: you can use the sparkly new \env{eqnarray} for simple |
413 | % equations simply by specifying \lit{x} as the column description. Who |
414 | % needs \AmSTeX? |;-)| |
415 | % |
416 | % \end{old-eqnarray} |
417 | % |
418 | % \implementation |
419 | % |
420 | % \section{Implementation} |
421 | % |
422 | % This isn't really complicated (honest) although it is a lot hairier than I |
423 | % think it ought to be. |
424 | % |
425 | % \begin{macrocode} |
426 | %<*package> |
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427 | \RequirePackage{amssymb} |
428 | \RequirePackage{mdwkey} |
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429 | % \end{macrocode} |
430 | % |
431 | % \subsection{Square roots} |
432 | % |
433 | % \subsubsection{Where is the square root sign?} |
434 | % |
435 | % \LaTeX\ hides the square root sign away somewhere without telling anyone |
436 | % where it is. I extract it forcibly by peeking inside the |\sqrtsign| macro |
437 | % and scrutinising the contents. Here we go: prepare for yukkiness. |
438 | % |
439 | % \begin{macrocode} |
440 | \newcount\sq@sqrt \begingroup \catcode`\|0 \catcode`\\12 |
441 | |def|sq@readrad#1"#2\#3|relax{|global|sq@sqrt"#2|relax} |
442 | |expandafter|sq@readrad|meaning|sqrtsign|relax |endgroup |
443 | \def\sq@delim{\delimiter\sq@sqrt\relax} |
444 | % \end{macrocode} |
445 | % |
446 | % \subsubsection{Drawing fake square root signs} |
447 | % |
448 | % \TeX\ absolutely insists on drawing square root signs with a vinculum over |
449 | % the top. In order to get the same effect, we have to attempt to emulate |
450 | % \TeX's behaviour. |
451 | % |
452 | % \begin{macro}{\sqrtdel} |
453 | % |
454 | % This does the main job of typesetting a vinculum-free radical.\footnote{^^A |
455 | % Note for chemists: this is nothing to do with short-lived things which |
456 | % don't have their normal numbers of electrons. And it won't reduce the |
457 | % appearance of wrinkles either.} |
458 | % It's more or less a duplicate of what \TeX\ does internally, so it might be |
459 | % a good plan to have a copy of Appendix~G open while you examine this. |
460 | % |
461 | % We start off by using |\mathpalette| to help decide how big things should |
462 | % be. |
463 | % |
464 | % \begin{macrocode} |
465 | \def\sqrtdel{\mathpalette\sqrtdel@i} |
466 | % \end{macrocode} |
467 | % |
468 | % Read the contents of the radical into a box, so we can measure it. |
469 | % |
470 | % \begin{macrocode} |
471 | \def\sqrtdel@i#1#2{% |
472 | \setbox\z@\hbox{$\m@th#1#2$}% %%% Bzzzt -- uncramps the mathstyle |
473 | % \end{macrocode} |
474 | % |
475 | % Now try and sort out the values needed in this calculation. We'll assume |
476 | % that $\xi_8$ is 0.6\,pt, the way it usually is. Next try to work out the |
477 | % value of $\varphi$. |
478 | % |
479 | % \begin{macrocode} |
480 | \ifx#1\displaystyle% |
481 | \@tempdima1ex% |
482 | \else% |
483 | \@tempdima.6\p@% |
484 | \fi% |
485 | % \end{macrocode} |
486 | % |
487 | % That was easy. Now for $\psi$. |
488 | % |
489 | % \begin{macrocode} |
490 | \@tempdimb.6\p@% |
491 | \advance\@tempdimb.25\@tempdima% |
492 | % \end{macrocode} |
493 | % |
494 | % Build the `delimiter' in a box of height $h(x)+d(x)+\psi+\xi_8$, as |
495 | % requested. Box~2 will do well for this purpose. |
496 | % |
497 | % \begin{macrocode} |
498 | \dimen@.6\p@% |
499 | \advance\dimen@\@tempdimb% |
500 | \advance\dimen@\ht\z@% |
501 | \advance\dimen@\dp\z@% |
502 | \setbox\tw@\hbox{% |
503 | $\left\sq@delim\vcenter to\dimen@{}\right.\n@space$% |
504 | }% |
505 | % \end{macrocode} |
506 | % |
507 | % Now we need to do some more calculating (don't you hate it?). As far as |
508 | % Appendix~G is concerned, $\theta=h(y)=0$, because we want no rule over the |
e8e9e5d8 |
509 | % top. |
86f6a31e |
510 | % |
511 | % \begin{macrocode} |
512 | \@tempdima\ht\tw@% |
513 | \advance\@tempdima\dp\tw@% |
514 | \advance\@tempdima-\ht\z@% |
515 | \advance\@tempdima-\dp\z@% |
516 | \ifdim\@tempdima>\@tempdimb% |
517 | \advance\@tempdima\@tempdimb% |
518 | \@tempdimb.5\@tempdima% |
519 | \fi% |
520 | % \end{macrocode} |
521 | % |
522 | % Work out how high to raise the radical symbol. Remember that Appendix~G |
523 | % thinks that the box has a very small height, although this is untrue here. |
524 | % |
525 | % \begin{macrocode} |
526 | \@tempdima\ht\z@% |
527 | \advance\@tempdima\@tempdimb% |
528 | \advance\@tempdima-\ht\tw@% |
529 | % \end{macrocode} |
530 | % |
531 | % Build the output (finally). The brace group is there to turn the output |
532 | % into a mathord, one of the few times that this is actually desirable. |
533 | % |
534 | % \begin{macrocode} |
535 | {\raise\@tempdima\box\tw@\vbox{\kern\@tempdimb\box\z@}}% |
536 | } |
537 | % \end{macrocode} |
538 | % |
539 | % \end{macro} |
540 | % |
541 | % \subsubsection{The new square root command} |
542 | % |
543 | % This is where we reimplement all the square root stuff. Most of this stuff |
544 | % comes from the \PlainTeX\ macros, although some is influenced by \AmSTeX\ |
545 | % and \LaTeXe, and some is original. I've tried to make the spacing vaguely |
546 | % automatic, so although it's not configurable like \AmSTeX's version, the |
547 | % output should look nice more of the time. Maybe. |
548 | % |
549 | % \begin{macro}{\sqrt} |
550 | % |
551 | % \LaTeX\ says this must be robust, so we make it robust. The first thing to |
552 | % do is to see if there's a star and pass the appropriate squareroot-drawing |
553 | % command on to the rest of the code. |
554 | % |
555 | % \begin{macrocode} |
556 | \DeclareRobustCommand\sqrt{\@ifstar{\sqrt@i\sqrtdel}{\sqrt@i\sqrtsign}} |
557 | % \end{macrocode} |
558 | % |
559 | % Now we can sort out an optional argument to be displayed on the root. |
560 | % |
561 | % \begin{macrocode} |
562 | \def\sqrt@i#1{\@ifnextchar[{\sqrt@ii{#1}}{\sqrt@iv{#1}}} |
563 | % \end{macrocode} |
564 | % |
565 | % Stages~2 and~3 below are essentially equivalents of \PlainTeX's |
566 | % |\root|\dots|\of| and |\r@@t|. Here we also find the first wrinkle: the |
567 | % |\rootbox| used to store the number is spaced out on the left if necessary. |
568 | % There's a backspace after the end so that the root can slip underneath, and |
569 | % everything works out nicely. Unfortunately size is fixed here, although |
570 | % doesn't actually seem to matter. |
571 | % |
572 | % \begin{macrocode} |
573 | \def\sqrt@ii#1[#2]{% |
574 | \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#2}$}% |
575 | \ifdim\wd\rootbox<6\p@% |
576 | \setbox\rootbox\hb@xt@6\p@{\hfil\unhbox\rootbox}% |
577 | \fi% |
578 | \mathpalette{\sqrt@iii{#1}}% |
579 | } |
580 | % \end{macrocode} |
581 | % |
582 | % Now we can actually build everything. Note that the root is raised by its |
583 | % depth -- this prevents a common problem with letters with descenders. |
584 | % |
585 | % \begin{macrocode} |
586 | \def\sqrt@iii#1#2#3{% |
587 | \setbox\z@\hbox{$\m@th#2#1{#3}$}% |
588 | \dimen@\ht\z@% |
589 | \advance\dimen@-\dp\z@% |
590 | \dimen@.6\dimen@% |
591 | \advance\dimen@\dp\rootbox% |
592 | \mkern-3mu% |
593 | \raise\dimen@\copy\rootbox% |
594 | \mkern-10mu% |
595 | \box\z@% |
596 | } |
597 | % \end{macrocode} |
598 | % |
599 | % Finally handle a non-numbered root. We read the rooted text in as an |
600 | % argument, to stop problems when people omit the braces. (\AmSTeX\ does |
601 | % this too.) |
602 | % |
603 | % \begin{macrocode} |
604 | \def\sqrt@iv#1#2{#1{#2}} |
605 | % \end{macrocode} |
606 | % |
607 | % \end{macro} |
608 | % |
609 | % \begin{macro}{\root} |
610 | % |
611 | % We also re-implement \PlainTeX's |\root| command, just in case someone uses |
612 | % it, and supply a star-variant. This is all very trivial. |
613 | % |
614 | % \begin{macrocode} |
615 | \def\root{\@ifstar{\root@i\sqrtdel}{\root@i\sqrtsign}} |
616 | \def\root@i#1#2\of{\sqrt@ii{#1}[#2]} |
617 | % \end{macrocode} |
618 | % |
619 | % \end{macro} |
620 | % |
621 | % \subsection{Modular programming} |
622 | % |
623 | % \begin{macro}{\pmod} |
624 | % |
625 | % Do some hacking if not |\ifouter|. |
626 | % |
627 | % \begin{macrocode} |
628 | \def\pmod#1{% |
629 | \ifinner\;\else\allowbreak\mkern18mu\fi% |
630 | ({\operator@font mod}\,\,#1)% |
631 | } |
632 | % \end{macrocode} |
633 | % |
634 | % \end{macro} |
635 | % |
636 | % \subsection{Some magic new maths characters} |
637 | % |
638 | % \begin{macro}{\bitor} |
639 | % \begin{macro}{\bitand} |
640 | % \begin{macro}{\dblor} |
641 | % \begin{macro}{\dbland} |
642 | % \begin{macro}{\xor} |
643 | % \begin{macro}{\lor} |
644 | % \begin{macro}{\ror} |
645 | % \begin{macro}{\lsl} |
646 | % \begin{macro}{\lsr} |
647 | % |
648 | % The new boolean operators. |
649 | % |
650 | % \begin{macrocode} |
651 | \DeclareMathSymbol{&}{\mathbin}{operators}{`\&} |
652 | \DeclareMathSymbol{\bitand}{\mathbin}{operators}{`\&} |
653 | \def\bitor{\mathbin\mid} |
654 | \def\dblor{\mathbin{\mid\mid}} |
655 | \def\dbland{\mathbin{\mathrel\bitand\mathrel\bitand}} |
656 | \let\xor\oplus |
657 | \def\lsl{\mathbin{<\!\!<}} |
658 | \def\lsr{\mathbin{>\!\!>}} |
659 | \def\rol{\mathbin{<\!\!<\!\!<}} |
660 | \def\ror{\mathbin{>\!\!>\!\!>}} |
661 | \AtBeginDocument{\ifx\lll\@@undefined\else |
662 | \def\lsl{\mathbin{\ll}} |
663 | \def\lsr{\mathbin{\gg}} |
664 | \def\rol{\mathbin{\lll}} |
665 | \def\ror{\mathbin{\ggg}} |
666 | \fi} |
667 | % \end{macrocode} |
668 | % |
669 | % \end{macro} |
670 | % \end{macro} |
671 | % \end{macro} |
672 | % \end{macro} |
673 | % \end{macro} |
674 | % \end{macro} |
675 | % \end{macro} |
676 | % \end{macro} |
677 | % \end{macro} |
678 | % |
679 | % \begin{macro}{\cat} |
680 | % \begin{macro}{\compose} |
681 | % \begin{macro}{\implies} |
682 | % \begin{macro}{\vect} |
683 | % \begin{macro}{\d} |
684 | % \begin{macro}{\jacobi} |
685 | % |
686 | % A mixed bag of stuff. |
687 | % |
688 | % \begin{macrocode} |
689 | \def\cat{\mathbin{\|}} |
690 | \let\compose\circ |
691 | \def\implies{\Rightarrow} |
692 | \def\vect#1{\mathord{\mathbf{#1}}} |
4a655c6f |
693 | \def\d{% |
694 | \ifmmode\mathord{\operator@font d}% |
695 | \else\expandafter\a\expandafter d\fi% |
696 | } |
86f6a31e |
697 | \def\jacobi#1#2{{{#1}\overwithdelims()#2}} |
698 | % \end{macrocode} |
699 | % |
700 | % \end{macro} |
701 | % \end{macro} |
702 | % \end{macro} |
703 | % \end{macro} |
704 | % \end{macro} |
705 | % \end{macro} |
706 | % |
707 | % \begin{macro}{\statclose} |
708 | % \begin{macro}{\compind} |
709 | % |
710 | % Fancy new relations for probability distributions. |
711 | % |
712 | % \begin{macrocode} |
713 | \def\statclose{\mathrel{\mathop{=}\limits^{\scriptscriptstyle s}}} |
714 | \def\compind{\mathrel{\mathop{\approx}\limits^{\scriptscriptstyle c}}} |
715 | % \end{macrocode} |
716 | % |
717 | % \end{macro} |
718 | % \end{macro} |
719 | % |
720 | % \begin{macro}{\keys} |
721 | % \begin{macro}{\dom} |
722 | % \begin{macro}{\ran} |
723 | % \begin{macro}{\supp} |
724 | % \begin{macro}{\lcm} |
4a655c6f |
725 | % \begin{macro}{\poly} |
726 | % \begin{macro}{\negl} |
727 | % \begin{macro}{\ord} |
86f6a31e |
728 | % |
729 | % And the new operator names. |
730 | % |
731 | % \begin{macrocode} |
732 | \def\keys{\mathop{\operator@font keys}\nolimits} |
733 | \def\dom{\mathop{\operator@font dom}\nolimits} |
734 | \def\ran{\mathop{\operator@font ran}\nolimits} |
735 | \def\supp{\mathop{\operator@font supp}\nolimits} |
736 | \def\lcm{\mathop{\operator@font lcm}\nolimits} |
4a655c6f |
737 | \def\poly{\mathop{\operator@font poly}\nolimits} |
738 | \def\negl{\mathop{\operator@font negl}\nolimits} |
739 | \def\ord{\mathop{\operator@font ord}\nolimits} |
86f6a31e |
740 | % \end{macrocode} |
741 | % |
742 | % \end{macro} |
743 | % \end{macro} |
744 | % \end{macro} |
745 | % \end{macro} |
746 | % \end{macro} |
4a655c6f |
747 | % \end{macro} |
748 | % \end{macro} |
749 | % \end{macro} |
750 | % |
751 | % \subsection{Fractions} |
752 | % |
753 | % \begin{macro}{\@frac@parse} |
754 | % |
755 | % \syntax{"\\@frac@parse{"<stuff>"}{"<frac-params>"}"} -- run \<stuff> |
756 | % passing it three arguments: an infix fraction-making command, the `outer' |
757 | % style, and the `inner' style. |
758 | % |
759 | % This is rather tricky. We clear a load of parameters, parse the parameter |
760 | % list, and then build a token list containing the right stuff. Without the |
761 | % token list fiddling, we end up expanding things at the wrong times -- for |
762 | % example, |\{| expands to something terribly unpleasant in a document |
763 | % preamble. |
764 | % |
765 | % All of the nastiness is contained in a group. |
766 | % |
767 | % \begin{macrocode} |
768 | \def\@frac@parse#1#2{% |
769 | \begingroup% |
770 | \let\@wd\@empty\def\@ldel{.}\def\@rdel{.}% |
771 | \def\@op{over}\let\@dim\@empty\@tempswafalse% |
772 | \let\@is\@empty\let\@os\@empty% |
773 | \mkparse{mdwmath:frac}{#2}% |
774 | \toks\tw@{\endgroup#1}% |
775 | \toks@\expandafter{\csname @@\@op\@wd\endcsname}% |
776 | \if@tempswa% |
777 | \toks@\expandafter{\the\expandafter\toks@\@ldel}% |
778 | \toks@\expandafter{\the\expandafter\toks@\@rdel}% |
779 | \fi% |
780 | \expandafter\toks@\expandafter{\the\expandafter\toks@\@dim}% |
781 | \toks@\expandafter{\the\toks\expandafter\tw@\expandafter{\the\toks@}} |
782 | \toks@\expandafter{\the\expandafter\toks@\expandafter{\@os}} |
783 | \toks@\expandafter{\the\expandafter\toks@\expandafter{\@is}} |
784 | \the\toks@% |
785 | } |
786 | % \end{macrocode} |
787 | % |
788 | % The keyword definitions are relatively straightforward now. The error |
789 | % handling for \textsf{style} and \textsf{innerstyle} could do with |
790 | % improvement. |
791 | % |
792 | % \begin{macrocode} |
793 | \def\@frac@del#1#2{\def\@wd{withdelims}\@tempswatrue\def#1{#2}} |
794 | \mkdef{mdwmath:frac}{leftdelim}{\@frac@del\@ldel{#1}} |
795 | \mkdef{mdwmath:frac}{rightdelim}{\@frac@del\@rdel{#1}} |
796 | \mkdef{mdwmath:frac}{nodelims}*{\let\@wd\@empty\@tempswafalse} |
797 | \mkdef{mdwmath:frac}{line}{% |
798 | \def\@op{above}\setlength\dimen@{#1}\edef\@dim{\the\dimen@\space}% |
799 | } |
800 | \mkdef{mdwmath:frac}{line}*{\def\@op{over}\let\@dim\@empty} |
801 | \mkdef{mdwmath:frac}{noline}*{\def\@op{atop}\let\@dim\@empty} |
802 | \def\@frac@style#1#2{% |
803 | \ifx\q@delim#2\q@delim\let#1\@empty% |
804 | \else% |
805 | \expandafter\ifx\csname #2style\endcsname\relax% |
806 | \PackageError{mdwmath}{Bad maths style `#2'}\@ehc% |
807 | \else% |
808 | \edef#1{\csname#2style\endcsname}% |
809 | \fi% |
810 | \fi% |
811 | } |
812 | \mkdef{mdwmath:frac}{style}[]{\@frac@style\@os{#1}} |
813 | \mkdef{mdwmath:frac}{innerstyle}[]{\@frac@style\@is{#1}} |
814 | % \end{macrocode} |
815 | % |
816 | % \end{macro} |
817 | % |
818 | % \begin{macro}{\fracdef} |
819 | % |
820 | % Here's where the rest of the pain is. We do a preliminary parse of the |
821 | % parameters and `compile' the result into the output macro. If there's no |
822 | % optional argument, then we don't need to do any really tedious formatting |
823 | % at the point of use. |
824 | % |
825 | % \begin{macrocode} |
826 | \def\fracdef#1#2{\@frac@parse{\fracdef@i{#1}{#2}}{#2}} |
827 | \def\fracdef@i#1#2#3#4#5{\def#1{\@frac@do{#2}{#3}{#4}{#5}}} |
828 | \def\@frac@do#1#2#3#4{% |
829 | \@ifnextchar[{\@frac@complex{#1}}{\@frac@simple{#2}{#3}{#4}}% |
830 | } |
831 | \def\@frac@complex#1[#2]{\@frac@parse\@frac@simple{#1,#2}} |
832 | \def\@frac@simple#1#2#3#4#5{{#2{{#3#4}#1{#3#5}}}} |
833 | % \end{macrocode} |
834 | % |
835 | % \end{macro} |
836 | % |
837 | % \begin{macro}{\frac@fix} |
838 | % \begin{macro}{\@@over} |
839 | % \begin{macro}{\@@atop} |
840 | % \begin{macro}{\@@above} |
841 | % \begin{macro}{\@@overwithdelims} |
842 | % \begin{macro}{\@@atopwithdelims} |
843 | % \begin{macro}{\@@abovewithdelims} |
844 | % |
845 | % Finally, we need to fix up |\@@over| and friends. Maybe \package{amsmath} |
846 | % has hidden the commands away somewhere unhelpful. If not, we make the |
847 | % requisite copies. |
848 | % |
849 | % \begin{macrocode} |
850 | \def\q@delim{\q@delim} |
851 | \def\frac@fix#1{\expandafter\frac@fix@i\string#1\q@delim} |
852 | \def\frac@fix@i#1#2\q@delim{\frac@fix@ii{#2}\frac@fix@ii{#2withdelims}} |
853 | \def\frac@fix@ii#1{% |
854 | \expandafter\ifx\csname @@#1\endcsname\relax% |
855 | \expandafter\let\csname @@#1\expandafter\endcsname\csname#1\endcsname% |
856 | \fi% |
857 | } |
858 | \frac@fix\over \frac@fix\atop \frac@fix\above |
859 | % \end{macrocode} |
860 | % |
861 | % \end{macro} |
862 | % \end{macro} |
863 | % \end{macro} |
864 | % \end{macro} |
865 | % \end{macro} |
866 | % \end{macro} |
867 | % \end{macro} |
868 | % |
869 | % \begin{macro}{\frac} |
870 | % \begin{macro}{\binom} |
871 | % \begin{macro}{\jacobi} |
872 | % |
873 | % And finally, we define the fraction-making commands. |
874 | % |
875 | % \begin{macrocode} |
876 | \fracdef\frac{nodelims, line} |
877 | \fracdef\binom{leftdelim = (, rightdelim = ), noline} |
878 | \fracdef\jacobi{leftdelim = (, rightdelim = ), line} |
879 | % \end{macrocode} |
880 | % |
881 | % \end{macro} |
882 | % \end{macro} |
883 | % \end{macro} |
86f6a31e |
884 | % |
885 | % \subsection{Blackboard bold stuff} |
886 | % |
887 | % \begin{macro}{\Z} |
888 | % \begin{macro}{\Q} |
889 | % \begin{macro}{\R} |
890 | % \begin{macro}{\C} |
891 | % \begin{macro}{\N} |
892 | % \begin{macro}{\F} |
893 | % \begin{macro}{\powerset} |
4a655c6f |
894 | % \begin{macro}{\gf} |
86f6a31e |
895 | % |
896 | % First of all, the signs. |
897 | % |
898 | % \begin{macrocode} |
899 | \def\Z{\mathbb{Z}} |
900 | \def\Q{\mathbb{Q}} |
901 | \def\R{\mathbb{R}} |
902 | \def\C{\mathbb{C}} |
903 | \def\N{\mathbb{N}} |
904 | \def\F{\mathbb{F}} |
905 | \def\powerset{\mathbb{P}} |
4a655c6f |
906 | \def\gf#1{\F_{#1}} |
907 | %\def\gf#1{\mathrm{GF}({#1})} |
86f6a31e |
908 | % \end{macrocode} |
909 | % |
910 | % \end{macro} |
911 | % \end{macro} |
912 | % \end{macro} |
913 | % \end{macro} |
914 | % \end{macro} |
915 | % \end{macro} |
916 | % \end{macro} |
4a655c6f |
917 | % \end{macro} |
86f6a31e |
918 | % |
919 | % And now, define |\mathbb| if it's not there already. |
920 | % |
921 | % \begin{macrocode} |
922 | \AtBeginDocument{\ifx\mathbb\@@undefined\let\mathbb\mathbf\fi} |
923 | % \end{macrocode} |
924 | % |
925 | % \subsection{Biggles} |
926 | % |
927 | % Now for some user-controlled delimiter sizing. The standard bigness of |
928 | % plain \TeX's delimiters are all right, but it's a little limiting. |
929 | % |
930 | % The biggness of delimiters is based on the size of the current |\strut|, |
931 | % which \LaTeX\ keeps up to date all the time. This will make the various |
932 | % delimiters grow in proportion when the text gets bigger. Actually, I'm |
933 | % not sure that this is exactly right -- maybe it should be nonlinear, |
934 | % |
935 | % \begin{macro}{\bbigg} |
936 | % \begin{macro}{\bbiggl} |
937 | % \begin{macro}{\bbiggr} |
938 | % \begin{macro}{\bbiggm} |
939 | % |
940 | % This is where the bigness is done. This is more similar to the plain \TeX\ |
941 | % big delimiter stuff than to the \package{amsmath} stuff, although there's |
942 | % not really a lot of difference. |
943 | % |
944 | % The two arguments are a multiplier for the delimiter size, and a small |
945 | % increment applied \emph{before} the multiplication (which is optional). |
946 | % |
947 | % This is actually a front for a low-level interface which can be called |
948 | % directly for efficiency. |
949 | % |
950 | % \begin{macrocode} |
951 | \def\bbigg{\@bbigg\mathord} \def\bbiggl{\@bbigg\mathopen} |
952 | \def\bbiggr{\@bbigg\mathclose} \def\bbiggm{\@bbigg\mathrel} |
953 | % \end{macrocode} |
954 | % |
955 | % \end{macro} |
956 | % \end{macro} |
957 | % \end{macro} |
958 | % \end{macro} |
959 | % |
960 | % \begin{macro}{\@bbigg} |
961 | % |
962 | % This is an optional argument parser providing a front end for the main |
963 | % macro |\bbigg@|. |
964 | % |
965 | % \begin{macrocode} |
966 | \def\@bbigg#1{\@ifnextchar[{\@bigg@i{#1}}{\@bigg@i{#1}[\z@]}} |
967 | \def\@bigg@i#1[#2]#3#4{#1{\bbigg@{#2}{#3}{#4}}} |
968 | % \end{macrocode} |
969 | % |
970 | % \end{macro} |
971 | % |
972 | % \begin{macro}{\bbigg@} |
973 | % |
974 | % This is it, at last. The arguments are as described above: an addition |
975 | % to be made to the strut height, and a multiplier. Oh, and the delimiter, |
976 | % of course. |
977 | % |
978 | % This is a bit messy. The smallest `big' delimiter, |\big|, is the same |
979 | % height as the current strut box. Other delimiters are~$1\frac12$, $2$ |
980 | % and~$2\frac12$ times this height. I'll set the height of the delimiter by |
981 | % putting in a |\vcenter| of the appropriate size. |
982 | % |
983 | % Given an extra height~$x$, a multiplication factor~$f$ and a strut |
984 | % height~$h$ and depth~$d$, I'll create a vcenter with total height |
985 | % $f(h+d+x)$. Easy, isn't it? |
986 | % |
987 | % \begin{macrocode} |
988 | \def\bbigg@#1#2#3{% |
989 | {\hbox{$% |
990 | \dimen@\ht\strutbox\advance\dimen@\dp\strutbox% |
991 | \advance\dimen@#1% |
992 | \dimen@#2\dimen@% |
993 | \left#3\vcenter to\dimen@{}\right.\n@space% |
994 | $}}% |
995 | } |
996 | % \end{macrocode} |
997 | % |
998 | % \end{macro} |
999 | % |
1000 | % \begin{macro}{\big} |
1001 | % \begin{macro}{\Big} |
1002 | % \begin{macro}{\bigg} |
1003 | % \begin{macro}{\Bigg} |
1004 | % |
1005 | % Now for the easy macros. |
1006 | % |
1007 | % \begin{macrocode} |
1008 | \def\big{\bbigg@\z@\@ne} |
1009 | \def\Big{\bbigg@\z@{1.5}} |
1010 | \def\bigg{\bbigg@\z@\tw@} |
1011 | \def\Bigg{\bbigg@\z@{2.5}} |
1012 | % \end{macrocode} |
1013 | % |
1014 | % \end{macro} |
1015 | % \end{macro} |
1016 | % \end{macro} |
1017 | % \end{macro} |
1018 | % |
1019 | % \subsection{The `QED' symbol} |
1020 | % |
1021 | % \begin{macro}{\qed} |
1022 | % \begin{macro}{\qedrule} |
1023 | % \begin{macro}{\qedsymbol} |
1024 | % |
1025 | % This is fairly simple. Just be careful will the glue and penalties. The |
1026 | % size of the little box is based on the current font size. |
1027 | % |
1028 | % The horizontal list constructed by the macro is like this: |
1029 | % |
1030 | % \begin{itemize} |
1031 | % \item A |\quad| of space. This might get eaten if there's a break here or |
1032 | % before. That's OK, though. |
1033 | % \item An empty box, to break a run of discardable items. |
1034 | % \item A |\penalty 10000| to ensure that the spacing glue isn't discarded. |
1035 | % \item |\hfill| glue to push the little rule to the end of the line. |
1036 | % \item A little square rule `\qedrule', with some small kerns around it. |
1037 | % \item A glue item to counter the effect of glue added at the paragraph |
e8e9e5d8 |
1038 | % boundary. |
86f6a31e |
1039 | % \end{itemize} |
1040 | % |
4a655c6f |
1041 | % The vertical mode case is simpler, but less universal. It copes with |
1042 | % relatively simple cases only. |
1043 | % |
86f6a31e |
1044 | % A |\qed| commend ends the paragraph. |
1045 | % |
1046 | % \begin{macrocode} |
4a655c6f |
1047 | \def\qed{% |
1048 | \ifvmode% |
1049 | \unskip% |
1050 | \setbox\z@\hb@xt@\linewidth{\hfil\strut\qedsymbol}% |
1051 | \prevdepth-\@m\p@% |
1052 | \ifdim\prevdepth>\dp\strutbox% |
1053 | \dimen@\prevdepth\advance\dimen@-\dp\strutbox% |
1054 | \kern-\dimen@% |
1055 | \fi% |
1056 | \penalty\@M\vskip-\baselineskip\box\z@% |
1057 | \else% |
1058 | \unskip% |
1059 | \penalty\@M\hfill% |
1060 | \hbox{}\penalty200\quad% |
1061 | \hbox{}\penalty\@M\hfill\qedsymbol\hskip-\parfillskip\par% |
1062 | \fi% |
86f6a31e |
1063 | } |
1064 | \def\qedrule{{% |
1065 | \dimen@\ht\strutbox% |
4a655c6f |
1066 | \advance\dimen@\dp\strutbox% |
86f6a31e |
1067 | \dimen@ii1ex% |
1068 | \advance\dimen@-\dimen@ii% |
1069 | \divide\dimen@\tw@% |
1070 | \advance\dimen@-\dp\strutbox% |
1071 | \advance\dimen@\dimen@ii% |
1072 | \advance\dimen@ii-\dimen@% |
1073 | \kern\p@% |
1074 | \vrule\@width1ex\@height\dimen@\@depth\dimen@ii% |
1075 | \kern\p@% |
1076 | }} |
1077 | \providecommand\qedsymbol{\qedrule} |
1078 | % \end{macrocode} |
1079 | % |
1080 | % \end{macro} |
1081 | % \end{macro} |
1082 | % \end{macro} |
1083 | % |
1084 | % \begin{ignore} |
1085 | % The following is the original definition of the enhanced eqnarray |
1086 | % environment. It's not supported, although if you can figure out how to |
1087 | % extract it, it's all yours. |
1088 | % \end{ignore} |
1089 | % |
1090 | % \begin{old-eqnarray} |
1091 | % |
1092 | % \subsection{The sparkly new \env{eqnarray}} |
1093 | % |
1094 | % Start off by writing a different package. |
1095 | % |
1096 | % \begin{macrocode} |
1097 | %</package> |
1098 | %<*oldeqnarray> |
1099 | % \end{macrocode} |
1100 | % |
1101 | % \subsubsection{Options handling} |
1102 | % |
1103 | % We need to be able to cope with \textsf{fleqn} and \textsf{leqno} options. |
1104 | % This will adjust our magic modified \env{eqnarray} environment |
1105 | % appropriately. |
1106 | % |
1107 | % \begin{macrocode} |
1108 | \newif\if@fleqn |
1109 | \newif\if@leqno |
1110 | \DeclareOption{fleqn}{\@fleqntrue} |
1111 | \DeclareOption{leqno}{\@leqnotrue} |
1112 | \ProcessOptions |
1113 | % \end{macrocode} |
1114 | % |
1115 | % This is all really different to the \LaTeX\ version. I've looked at the |
1116 | % various \env{tabular} implementations, the original \env{eqnarray} and the |
1117 | % \textit{\TeX book} to see how best to do this, and then went my own way. |
1118 | % If it doesn't work it's all my fault. |
1119 | % |
1120 | % \subsubsection{Some useful registers} |
1121 | % |
1122 | % The old \LaTeX\ version puts the equation numbers in by keeping a count of |
1123 | % where it is in the alignment. Since I don't know how may columns there are |
1124 | % going to be, I'll just use a switch in the preamble to tell me to stop |
1125 | % tabbing. |
1126 | % |
1127 | % \begin{macrocode} |
1128 | \newif\if@eqalast |
1129 | % \end{macrocode} |
1130 | % |
1131 | % Now define some useful length parameters. First allocate them: |
1132 | % |
1133 | % \begin{macrocode} |
1134 | \newskip\eqaopenskip |
1135 | \newskip\eqacloseskip |
1136 | \newskip\eqacolskip |
1137 | \newskip\eqainskip |
1138 | % \end{macrocode} |
1139 | % |
1140 | % Now assign some default values. Users can play with these if they really |
1141 | % want although I can't see the point myself. |
1142 | % |
1143 | % \begin{macrocode} |
1144 | \if@fleqn |
1145 | \AtBeginDocument{\eqaopenskip\leftmargini} |
1146 | \else |
1147 | \eqaopenskip\@centering |
1148 | \fi |
1149 | \eqacloseskip\@centering |
1150 | \eqacolskip\@centering |
1151 | \eqainskip\z@ |
1152 | % \end{macrocode} |
1153 | % |
1154 | % We allow the user to play with the style if this is really wanted. I dunno |
1155 | % why, really. Maybe someone wants very small alignments. |
1156 | % |
1157 | % \begin{macrocode} |
1158 | \let\eqa@style\displaystyle |
1159 | % \end{macrocode} |
1160 | % |
1161 | % \subsubsection{The main environments} |
1162 | % |
1163 | % We define the toplevel commands here. They just add in default arguments |
1164 | % and then call |\@eqnarray| with a preamble string. The only difference is |
1165 | % the last column they add in -- \env{eqnarray$*$} throws away the last |
1166 | % column by sticking it in box~0. (I used to |\@gobble| it but that caused |
1167 | % the |\cr| to be lost.) |
1168 | % |
1169 | % \begin{macrocode} |
1170 | \def\eqnarray{\@ifnextchar[\eqnarray@i{\eqnarray@i[rcl]}} |
1171 | \def\eqnarray@i[#1]{% |
1172 | \@eqnarray{#1!{\hb@xt@\z@{\hss##}\tabskip\z@}} |
1173 | } |
1174 | \@namedef{eqnarray*}{\@ifnextchar[\eqnarray@s@i{\eqnarray@s@i[rcl]}} |
1175 | \def\eqnarray@s@i[#1]{% |
1176 | \@eqnarray{#1!{\nonumber\setbox\z@\hbox{##}\tabskip\z@}}% |
1177 | } |
1178 | % \end{macrocode} |
1179 | % |
1180 | % \subsubsection{Set up the initial display} |
1181 | % |
1182 | % \begin{macro}{\@eqnarray} |
1183 | % |
1184 | % The |\@eqnarray| command does most of the initial work. It sets up some |
1185 | % flags and things, builds the |\halign| preamble, and returns. |
1186 | % |
1187 | % \begin{macrocode} |
1188 | \def\@eqnarray#1{% |
1189 | % \end{macrocode} |
1190 | % |
1191 | % Start playing with the counter here. The original does some icky internal |
1192 | % playing, which isn't necessary. The |\if@eqnsw| switch is |true| if the |
1193 | % user hasn't supplied an equation number. The |\if@eqalast| switch is |
1194 | % |true| in the final equation-number column. |
1195 | % |
1196 | % \begin{macrocode} |
1197 | \refstepcounter{equation}% |
1198 | \@eqalastfalse% |
1199 | \global\@eqnswtrue% |
1200 | \m@th% |
1201 | % \end{macrocode} |
1202 | % |
1203 | % Set things up for the |\halign| which is coming up. |
1204 | % |
1205 | % \begin{macrocode} |
1206 | \openup\jot% |
1207 | \tabskip\eqaopenskip% |
1208 | \let\\\@eqncr% |
1209 | \everycr{}% |
1210 | $$% |
1211 | % \end{macrocode} |
1212 | % |
1213 | % We'll build the real |\halign| and preamble in a token register. All we |
1214 | % need to do is stuff the header in the token register, clear a switch |
1215 | % (that'll be explained later), parse the preamble and then expand the |
1216 | % tokens we collected. Easy, no? |
1217 | % |
1218 | % \begin{macrocode} |
1219 | \toks@{\halign to\displaywidth\bgroup}% |
1220 | \@tempswafalse% |
1221 | \eqa@preamble#1\end% |
1222 | \the\toks@\cr% |
1223 | } |
1224 | % \end{macrocode} |
1225 | % |
1226 | % \end{macro} |
1227 | % |
1228 | % \subsubsection{Parsing the preamble} |
1229 | % |
1230 | % All this actually involves is reading the next character and building a |
1231 | % command from it. That can pull off an argument if it needs it. Just make |
1232 | % sure we don't fall off the end and we'll be OK. |
1233 | % |
1234 | % \begin{macrocode} |
1235 | \def\eqa@preamble#1{% |
1236 | \ifx\end#1\else\csname eqa@char@#1\expandafter\endcsname\fi% |
1237 | } |
1238 | % \end{macrocode} |
1239 | % |
1240 | % Adding stuff to the preamble tokens is a simple matter of using |
1241 | % |\expandafter| in the correct way.\footnote{^^A |
1242 | % I have no idea why \LaTeX\ uses \cmd\edef\ for building its preamble. It |
1243 | % seems utterly insane to me -- the amount of bodgery that \env{tabular} |
1244 | % has to go through to make everything expand at the appropriate times is |
1245 | % scary. Maybe Messrs~Lamport and Mittelbach just forgot about token |
1246 | % registers when they were writing the code. Maybe I ought to rewrite the |
1247 | % thing properly some time. Sigh. |
1248 | % |
1249 | % As a sort of postscript to the above, I \emph{have} rewritten the |
1250 | % \env{tabular} environment, and made a damned fine job of it, in my |
1251 | % oh-so-humble opinion. All this \env{eqnarray} stuff has been remoulded |
1252 | % in terms of the generic column-defining things in \package{mdwtab}. |
1253 | % You're reading the documentation of the old version, which isn't |
1254 | % supported any more, so any bugs here are your own problem.} |
1255 | % |
1256 | % \begin{macrocode} |
1257 | \def\eqa@addraw#1{\expandafter\toks@\expandafter{\the\toks@#1}} |
1258 | % \end{macrocode} |
1259 | % |
1260 | % Now for some cleverness again. In order to put all the right bits of |
1261 | % |\tabskip| glue in the right places we must \emph{not} terminate each |
1262 | % column until we know what the next one is. We set |\if@tempswa| to be |
1263 | % |true| if there's a column waiting to be closed (so it's initially |
1264 | % |false|). The following macro adds a column correctly, assuming we're in |
1265 | % a formula. Other column types make their own arrangements. |
1266 | % |
1267 | % \begin{macrocode} |
1268 | \def\eqa@add#1{% |
1269 | \if@tempswa% |
1270 | \eqa@addraw{\tabskip\eqainskip}% |
1271 | \else% |
1272 | \eqa@addraw{#1}% |
1273 | \fi% |
1274 | \@tempswatrue% |
1275 | } |
1276 | % \end{macrocode} |
1277 | % |
1278 | % Now to defining column types. Let's define a macro which allows us to |
1279 | % define column types: |
1280 | % |
1281 | % \begin{macrocode} |
1282 | \def\eqa@def#1{\expandafter\def\csname eqa@char@#1\endcsname} |
1283 | % \end{macrocode} |
1284 | % |
1285 | % Now we can define the column types. Each column type must loop back to |
1286 | % |\eqa@preamble| once it's finished, to read the rest of the preamble |
1287 | % string. Note the positioning of ord atoms in the stuff below. This will |
1288 | % space out relations and binops correctly when they occur at the edges of |
1289 | % columns, and won't affect ord atoms at the edges, because ords pack |
1290 | % closely. |
1291 | % |
1292 | % First the easy onces. Just stick |\hfil| in the right places and |
1293 | % everything will be all right. |
1294 | % |
1295 | % \begin{macrocode} |
1296 | \eqa@def r{\eqa@add{\hfil$\eqa@style##{}$}\eqa@preamble} |
1297 | \eqa@def c{\eqa@add{\hfil$\eqa@style{}##{}$\hfil}\eqa@preamble} |
1298 | \eqa@def l{\eqa@add{$\eqa@style{}##$\hfil}\eqa@preamble} |
1299 | \eqa@def x{\eqa@add{\hfil$\eqa@style##$\hfil}\eqa@preamble} |
1300 | % \end{macrocode} |
1301 | % |
1302 | % Now for the textual ones. This is also fairly easy. |
1303 | % |
1304 | % \begin{macrocode} |
1305 | \eqa@def T#1{% |
1306 | \eqa@add{}% |
1307 | \if#1l\else\eqa@addraw{\hfil}\fi% |
1308 | \eqa@addraw{##}% |
1309 | \if#1r\else\eqa@addraw{\hfil}\fi% |
1310 | \eqa@preamble% |
1311 | } |
1312 | % \end{macrocode} |
1313 | % |
1314 | % Sort of split types of equations. I mustn't use |\rlap| here, or |
1315 | % everything goes wrong -- |\\| doesn't get noticed by \TeX\ in the same way |
1316 | % as |\cr| does. |
1317 | % |
1318 | % \begin{macrocode} |
1319 | \eqa@def L{\eqa@add{\hb@xt@\z@{$\eqa@style##$\hss}\qquad}\eqa@preamble} |
1320 | % \end{macrocode} |
1321 | % |
1322 | % The \lit{:} column type is fairly simple. We set |\tabskip| up to make |
1323 | % lots of space and close the current column, because there must be one.^^A |
1324 | % \footnote{This is an assumption.} |
1325 | % |
1326 | % \begin{macrocode} |
1327 | \eqa@def :{% |
1328 | \eqa@addraw{\tabskip\eqacolskip&}\@tempswafalse\eqa@preamble% |
1329 | } |
1330 | \eqa@def q{\eqa@add{\quad}\@tempswafalse\eqa@preamble} |
1331 | % \end{macrocode} |
1332 | % |
1333 | % The other column types just insert given text in an appropriate way. |
1334 | % |
1335 | % \begin{macrocode} |
1336 | \eqa@def >#1{\eqa@add{#1}\@tempswafalse\eqa@preamble} |
1337 | \eqa@def <#1{\eqa@addraw{#1}\eqa@preamble} |
1338 | % \end{macrocode} |
1339 | % |
1340 | % Finally, the magical \lit{!} column type, which sets the equation number. |
1341 | % We set up the |\tabskip| glue properly, tab on, and set the flag which |
1342 | % marks the final column. |
1343 | % |
1344 | % \begin{macrocode} |
1345 | \eqa@def !#1{% |
1346 | \eqa@addraw{\tabskip\eqacloseskip&\@eqalasttrue#1}\eqa@preamble% |
1347 | } |
1348 | % \end{macrocode} |
1349 | % |
1350 | % \subsubsection{Newline codes} |
1351 | % |
1352 | % Newline sequences (|\\|) get turned into calls of |\@eqncr|. The job is |
1353 | % fairly simple, really. However, to avoid reading `|&|' characters |
1354 | % prematurely, we set up a magic brace (from the \package{array} package -- |
1355 | % this avoids creating ord atoms and other nastyness). |
1356 | % |
1357 | % \begin{macrocode} |
1358 | \def\@eqncr{% |
1359 | \iffalse{\fi\ifnum0=`}\fi% |
1360 | \@ifstar{\eqacr@i{\@M}}{\eqacr@i{\interdisplaylinepenalty}}% |
1361 | } |
1362 | \def\eqacr@i#1{\@ifnextchar[{\eqacr@ii{#1}}{\eqacr@ii{#1}[\z@]}} |
1363 | \def\eqacr@ii#1[#2]{% |
1364 | \ifnum0=`{}\fi% |
1365 | \eqa@eqnum% |
1366 | \noalign{\penalty#1\vskip#2\relax}% |
1367 | } |
1368 | % \end{macrocode} |
1369 | % |
1370 | % \subsubsection{Setting equation numbers} |
1371 | % |
1372 | % Before we start, we need to generalise the flush-left number handling bits. |
1373 | % The macro |\eqa@eqpos| will put its argument in the right place. |
1374 | % |
1375 | % \begin{macrocode} |
1376 | \if@leqno |
1377 | \def\eqa@eqpos#1{% |
1378 | \hb@xt@.01\p@{}\rlap{\normalfont\normalcolor\hskip-\displaywidth#1}% |
1379 | } |
1380 | \else |
1381 | \def\eqa@eqpos#1{\normalfont\normalcolor#1} |
1382 | \fi |
1383 | % \end{macrocode} |
1384 | % |
1385 | % First we need to move into the right column. Then we just set the equation |
1386 | % number appropriately. There is some subtlety here, ish. The |\relax| is |
1387 | % important, to delay expansion of the |\if|\dots\ until the new column has |
1388 | % been started. The two helper macros are important too, to hide `|&|'s and |
1389 | % `|\cr|'s from \TeX's scanner until the right time. |
1390 | % |
1391 | % \begin{macrocode} |
1392 | \def\eqa@eqnum{% |
1393 | \relax% |
1394 | \if@eqalast\expandafter\eqa@eqnum@i\else\expandafter\eqa@eqnum@ii\fi% |
1395 | } |
1396 | \def\eqa@eqnum@i{% |
1397 | \if@eqnsw% |
1398 | \eqa@eqpos{(\theequation)}\stepcounter{equation}% |
1399 | \else% |
1400 | \eqa@eqpos\eqa@number% |
1401 | \fi% |
1402 | \global\@eqnswtrue% |
1403 | \cr% |
1404 | } |
1405 | \def\eqa@eqnum@ii{&\eqa@eqnum} |
1406 | % \end{macrocode} |
1407 | % |
1408 | % \subsubsection{Numbering control} |
1409 | % |
1410 | % This is trivial. We set the |\if@eqnsw| flag to be |false| and store the |
1411 | % text in a macro. |
1412 | % |
1413 | % \begin{macrocode} |
1414 | \let\nonumber\relax |
1415 | \newcommand\nonumber[1][]{\global\@eqnswfalse\global\def\eqa@number{#1}} |
1416 | % \end{macrocode} |
1417 | % |
1418 | % \subsubsection{Closing the environments off} |
1419 | % |
1420 | % This is really easy. Set the final equation number, close the |\halign|, |
1421 | % tidy up the equation counter (it's been stepped once too many times) and |
1422 | % close the display. |
1423 | % |
1424 | % \begin{macrocode} |
1425 | \def\endeqnarray{% |
1426 | \eqa@eqnum% |
1427 | \egroup% |
1428 | \global\advance\c@equation\m@ne% |
1429 | $$% |
1430 | \global\@ignoretrue% |
1431 | } |
1432 | \expandafter\let\csname endeqnarray*\endcsname\endeqnarray |
1433 | % \end{macrocode} |
1434 | % |
1435 | % Now start up the other package again. |
1436 | % |
1437 | % \begin{macrocode} |
1438 | %</oldeqnarray> |
1439 | %<*package> |
1440 | % \end{macrocode} |
1441 | % |
1442 | % \end{old-eqnarray} |
1443 | % |
1444 | % That's all there is. Byebye. |
1445 | % |
1446 | % \begin{macrocode} |
1447 | %</package> |
1448 | % \end{macrocode} |
1449 | % |
1450 | % \hfill Mark Wooding, \today |
1451 | % |
1452 | % \Finale |
1453 | \endinput |