summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/tex/context/third/mathsets/t-mathsets.tex
blob: 38d3a23fbd544d5cdf3c3a665f1fa33d526b2754 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
%D \module
%D   [       file=t-mathsets,
%D        version=2011-01-22,
%D          title=Math Sets,
%D       subtitle=\CONTEXT\ port of \filename{braket.sty},
%D         author={Aditya Mahajan},
%D          email={adityam [at] umich [dot] edu},
%D           date=\currentdate,
%D        license=Simplified BSD License]
%D
  
%M \usemodule[mathsets] 
%M \setuphead[section]  [page=]
%M \setupbodyfontenvironment[default][em=italic]
%M \loadsetups[t-mathsets.xml]

%D \section {Introduction}
%D
%D I write a lot of probability expressions which look like this.
%D \startbuffer
%D \startformula
%D \mfunction{E} \left\{ \sum_{y} f(X,y) \,\middle|\, Z \right\}
%D \stopformula
%D \stopbuffer
%D \getbuffer 
%D
%D The usual way to input them is as follows
%D \typebuffer
%D
%D We need to ensure that the delimiters and the {\em conditional} sign \type{|}
%D scale properly, and the spacing around the conditional sign is correct. As a
%D result, the input is markup heavy, and consequently difficult to read.
%D
%D In \LATEX, Donald Arseneau's \filename{braket.sty} can be used to input such
%D expressions in a natural manner, and automatically takes care of the scaling
%D of delimiters and the conditional signs. (The actual package only provides
%D this functionality of bra and ket notation, hence the name, but can be easily
%D extended to probability expressions also. This module is a partial port of
%D \filename{braket.sty} to \CONTEXT.

%D \section {Usage}
%D
%D To use this module add
%D
%D \starttyping
%D \usemodule[mathsets]
%D \stoptyping
%D 
%D on the top of your file. This module defines one command
%D \type{\definemathset} for defining new math-sets. The syntax of this command
%D is:
%D
%D \setup{definemathset}
%D
%D The first argument is the name of the set to be defined. Thus, after 
%D
%D \starttyping
%D \definemathset[mathset]
%D \stoptyping
%D
%D \type{\mathset} is available as a command. The second argument to
%D \type{\definemathset} are optional assignments \type{text}, \type{left},
%D \type{middle}, \type{right}. For example, if we can use \type{text} to
%D specify what comes at the beginning of the math-set. By default,
%D \type{text=no} which causes no text to appear, but we can change that to any
%D text that we want (Note that \type{\mfunction} tells \CONTEXT\ to use the
%D current math text font)
%D
%D \startbuffer[EXP]
%D \definemathset[EXP] [text=\mfunction{E}]
%D \stopbuffer
%D
%D \typebuffer[EXP] \getbuffer[EXP]
%D
%D We can use \type{\EXP{X}} to get $\EXP{X}$ and \type{\EXP{X|Y}} to get
%D $\EXP{X|Y}$. Scaling of the delimiters and conditional sign are take care
%D automatically. For example
%D
%D \startbuffer
%D \startformula
%D  \EXP{\sum_y f(X,y) | Z }
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer
%D
%D gives
%D
%D \getbuffer
%D
%D Compare the above input with the one used in the first example.
%D
%D By default, the contents of the set are surrounded by curly brackets (or
%D braces); we can change them by using \type{left} and \type{right} keys. For
%D example.
%D
%D \startbuffer[PR]
%D \definemathset[PR]  [text={\mfunction{Pr}},left=(,right=)]
%D \stopbuffer
%D \startbuffer
%D \startformula
%D    \EXP{ \sum_y f(X,y) | Z = z } = \sum_{x,y} \PR{x,y | Z=z}
%D \stopformula
%D \stopbuffer
%D 
%D \typebuffer[PR] \typebuffer
%D
%D  gives
%D
%D \getbuffer[PR] \getbuffer
%D
%D We also provide a mechanism for changing the conditional bar using the
%D \type{middle} key, although I am not sure if this is needed by anyone. For
%D example, consider the following contrived example
%D
%D \startbuffer
%D \definemathset[VAR][text={\mfunction{Var}}, left=(, right=), middle=\Vert]
%D \startformula
%D    \VAR{f(X,Y) | Y = y }
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer
%D
%D gives
%D
%D \getbuffer
%D
%D This module also takes care of correct nesting of math-sets, so 
%D \startbuffer
%D \startformula
%D   \EXP{ \sum_{Y} \EXP { \frac{1}{f(X)} | Y } } 
%D \stopformula
%D \stopbuffer
%D \typebuffer gives
%D \getbuffer[EXP] \getbuffer
%D
%D If you do not want some \type{|} to be considered as conditional signs, nest
%D them inside a group \type{{}}. For example, to get 
%D \startbuffer
%D \startformula
%D   \mathset{ x\in {\bf R}^2 | 0<{|x|}<\frac {3}{16} }
%D \stopformula
%D \stopbuffer
%D \getbuffer
%D we typed
%D \typebuffer
%D
%D We can also use limits after the command, for example:
%D
%D \startbuffer
%D \startformula
%D   \EXP_X{F(X, Y) | Y = y } 
%D \stopformula
%D \stopbuffer
%D \typebuffer gives \getbuffer
%D
%D Only one set, \type{\mathset}, is predefined. It is relatively simple
%D to define sets equivalent to those defined in \filename{braket.sty}.
%D
%D \startbuffer
%D \definemathset[BRAKET][left=\langle,right=\rangle]
%D
%D \startformula
%D   \BRAKET{ \phi | \frac{\partial^2}{\partial t^2} | \psi }
%D \stopformula
%D \stopbuffer
%D \typebuffer \getbuffer

%D \section {Implementation}
%D
%D Most of the ideas are simply a \CONTEXT ified version of the code in
%D \filename{braket.sty}. I mostly used \filename{bracket.sty} to define
%D commands for probability and expectation. So, I have also added the
%D option of declaring such operators using \type{text=no} option for
%D \type|\definemathset|.

\writestatus  {loading}   {ConTeXt Math Sets Module}

\startmodule[mathsets]

\unprotect

%D Since two letter codes are reserved for system modules, and \CONTEXT\
%D seems to be running out of those, I choose a more verbose variable to
%D store options.

\definesystemvariable {mathset}   % Math Set

%D \macros{setupmathset}
%D To specify the default values of text, left, middle, and right delimiters

\def\setupmathset
  {\dosingleargument\getparameters[\??mathset]}

%D \macros
%D    {definemathset}
%D
%D To define a new math set.

\def\definemathset
  {\dodoubleargument\dodefinemathset}


%D Now we define internal macros to take care of the formatting

\let\currentmathset\empty
\let\currentmathsetgrouplevel\empty

\def\mathsetmiddle
  {\ifnum\currentmathsetgrouplevel=\currentgrouplevel
      \expandafter\firstoftwoarguments
    \else
      \expandafter\secondoftwoarguments
    \fi
   {\egroup\,\middle\mathsetparameter\c!middle\,\bgroup}
   {\mathsetparameter\c!middle}}

\def\mathsetparameter#1%
  {\executeifdefined{\??mathset\currentmathset#1}{\executeifdefined{\??mathset#1}\empty}}

\def\dodefinemathset[#1][#2]%
  {\getparameters[\??mathset#1][#2]
   \setvalue{#1}{\dododefinemathset[#1]}}

%D Since \type{|} is already active, we do not have to make it active
%D again.

\def\dododefinemathset[#1]%
  {\begingroup
   \def\currentmathset{#1}
   \edef\currentmathsetgrouplevel{\the\numexpr\currentgrouplevel+2\relax}
   % Not here, else messes subscripts
   % \mathcode`\|32768
   % \let|\mathsetmiddle
   \doifelsenothing{\mathsetparameter\c!text}
      {\dodododefinemathset!notext}
      {\doifelse{\mathsetparameter\c!text}{\v!no}
      {\dodododefinemathset!notext}
      {\docapturemathoplimits\dodododefinemathset!text}}}


\def\setmathmiddle
  {\mathcode`\|32768
   \let|\mathsetmiddle}


%D \type|\docapturemathoplimits| is to capture limits that may follow
%D the text command. This allows the following to work
%D
%D \startbuffer
%D \startformula
%D    \PR^{f,g} {f(X) | g(Y)}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer
%D
%D \getbuffer[PR] \getbuffer
%D We need to be a bit careful not to activate \type{|} to soon, as it can also
%D occur in sub- and superscripts. For example
%D \startbuffer
%D \startformula
%D    \EXP_{X|Y}{f(X) | Y = y}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer
%D
%D gives
%D
%D \getbuffer[EXP] \getbuffer

\def\dodododefinemathset!notext#1%
  {\setmathmiddle
   \mathopen{}\left\mathsetparameter\c!left
   {#1}%
   \right\mathsetparameter\c!right\mathclose{}%
   \endgroup}
  
%D TODO. Keep the \type|\nolimits| to be configurable.

\def\dodododefinemathset!text#1#2%
    {\mathop{\kern\zeropoint\mathsetparameter\c!text}\nolimits#1%
     \setmathmiddle
     \left\mathsetparameter\c!left
     {#2}%
     \right\mathsetparameter\c!right%
     \endgroup}

%D The extra group in the definition of \type{dodododefinemathset!} is
%D so that such expressions turn out correct
%D \getbuffer[EXP]
%D \startformula
%D \EXP{ \left(\frac {a}{b}\right) | 
%D      \left( \frac{a} {\frac{b}{\sum c}} \right) }
%D \stopformula


%D The \type{\left} and \type{\right} generate a math atom of type inner,
%D while for math sets, we want a math math open atom. To see the difference,
%D consider
%D
%D \startbuffer
%D \startformula
%D  2\left(\frac {3}{4} \right) \qquad \hbox{ vs } \qquad  
%D  2\biggl( \frac {3}{4} \biggr)
%D \stopformula
%D
%D and
%D 
%D \startformula
%D  \Pr\left(\frac {3}{4} \right) \qquad \hbox{ vs } \qquad  
%D  \Pr\biggl( \frac {3}{4} \biggr)
%D \stopformula
%D \stopbuffer
%D \typebuffer 
%D
%D which gives (notice the spacing before the parenthesis)
%D
%D \getbuffer 
%D
%D I will assume that if \type{text} is something, then
%D the default behaviour is desirable, if \type{text} is empty, then I add
%D \type{\mathopen} and \type{\mathclose}.  Using \type{\mathopen} to correct
%D the spacing is due to Frank Mittelbach, see
%D \hyphenatedurl{http://www.latex-project.org/cgi-bin/ltxbugs2html?pr=latex/3853}
%D
%D Mathset module ensures that we get the correct spacing in both cases
%D \startbuffer
%D \definemathset[SET][left=(,right=)]
%D \startformula
%D  2\SET{\frac{3}{4}} \qquad \hbox{ and } \qquad 
%D  \PR{ \frac{3}{4} }
%D \stopformula
%D \stopbuffer
%D \getbuffer[PR] \getbuffer which was typed as \typebuffer
%D
%D Also, if its argument is a single character, \type{\mathop} centers it to
%D with respect to the math||axis. Compare the outputs of
%D
%D \startbuffer
%D \ruledhbox{$\mathop{y}\nolimits_x\left\{A\,\middle|\,B\right\}$}
%D \ruledhbox{$\mathop{\kern\zeropoint y}\nolimits_x\left\{A\,\middle|\,B\right\}$}
%D \stopbuffer
%D
%D \typebuffer
%D \getbuffer
%D
%D I have added a \type{\kern\zeropoint} to prevent that.


%D \macros
%D    {docapturemathoplimits}
%D
%D The next macro captures math limits. This should probably go to some
%D general purpose module. There are three different valid inputs
%D \startitemize[n,packed]
%D   \item An operator with neither subscript nor superscript.
%D   \item An operator with one subscript or superscript.
%D   \item An operator with both subscript and superscript.
%D \stopitemize
%D So we scan for four arguments, to capture the following situations
%D \startitemize[packed]
%D   \item \type|_{sub}^{sup}|
%D   \item \type|^{sup}_{sub}|
%D   \item \type|_{sub}|
%D   \item \type|^{sup}|
%D   \item \type|<empty>|
%D \stopitemize

\def\docapturemathoplimits#1%
  {\doifnextcharelse _%
    {\dodocapturemathoplimits{#1}}
    {\doifnextcharelse ^%
      {\dodocapturemathoplimits{#1}}
      {#1{}}}}

\def\dodocapturemathoplimits#1#2#3%
  {\doifnextcharelse _%
    {\redocapturemathoplimits{#1}{#2}{#3}}
    {\doifnextcharelse ^%
        {\redocapturemathoplimits{#1}{#2}{#3}}
        {#1{#2{#3}}}}}

\def\redocapturemathoplimits#1#2#3#4#5%
  {#1{#2{#3}#4{#5}}}

\setupmathset
  [  \c!left={\{},
    \c!right={\}},
   \c!middle=\vert,
     \c!text=no,]

\definemathset[mathset]

%D \section {Change log}
%D
%D \startitemize[n, reverse][headstyle=bold]
%D
%D \head \date[d=22,m=1,y=2011]
%D
%D  Changed license to BSD
%D
%D \head \date[d=6,m=12,y=2008]
%D
%D Defined a new macro \type{setmathmiddle}. Now \type{|} is made active after
%D the subscripts, so that things still work when \type{|} is used in the
%D subscripts.
%D
%D \head \date[d=3,m=7,y=2008] 
%D
%D Added \type{text=no} option, included an interface file, and cleaned up the
%D documentation for \TEX live 2008.
%D
%D \head \date[d=17,m=6,y=2007] 
%D       
%D Added \type|\docapturemathoplimits| macro. This prevents a
%D serious bug in the previous version, due to which things like
%D \type{\mathset_{...}} did not work.
%D
%D \head \date[d=11,m=4,y=2007]
%D
%D This version provides some fine tuning of how the sets are displayed
%D by working around two mis|-|features of \TEX\ math: \type|\left|
%D \unknown \type|\right| always create a math inner atom and
%D \type|\mathop| centers its argument if the argument is a single
%D letter. 
%D
%D \head \date[d=25,m=2,y=2007]
%D
%D First version of the module.
%D  
%D \stopitemize

\protect
\stopmodule