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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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1
<?xml version="1.0" encoding="UTF-8"?>

2


3


4
<!DOCTYPE Book SYSTEM "gapdoc.dtd"

5
 [ <!ENTITY see '<Alt Only="LaTeX">$\to$</Alt><Alt Not="LaTeX">&#8594;</Alt>'>

6
 ]>

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8
<Book Name="GAPDoc Example">

9


10
<TitlePage>

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  <Title>A Complete Example (&see; <Ref Sect="One"/>)</Title>

12
  <Subtitle>Every element shows up</Subtitle>

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  <Version>Version <#Include SYSTEM "../version"></Version>

14
  <TitleComment>

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  If the subtitle is not sufficient, this &lt;TitleComment> 

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  element can be used for a slightly longer text on the front page.

17
  </TitleComment>

18
  <Author>Frank Lübeck 

19
          <Email>[email protected]</Email> 

20
  </Author>

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  <Author> Max Neunhöffer 

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          <Email>neunhoef at mcs.st-and.ac.uk</Email>

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  </Author>

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  <Date>November 2017</Date>

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  <Address>

26
  Lehrstuhl D für Mathematik<Br/>  Pontdriesch

27
  14/16<Br/> 52062 Aachen<Br/> (Germany)

28
  </Address>

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  <Abstract>This document tries to use all elements that exist in &GAPDoc;.

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            In addition, the final output not only contains the usual

31
            content, but also an appendix with the source text. There

32
            are also links from the usual content to the corresponding

33
            source text. This should enable new users to learn &GAPDoc;

34
            quickly.

35
  </Abstract>

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  <Copyright>&copyright; 2000-2017 by Frank Lübeck and Max Neunhöffer

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  </Copyright>

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  <Acknowledgements>We thank Lehrstuhl D für Mathematik.

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  </Acknowledgements>

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  <Colophon>This is the Colophon page.

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  </Colophon>

42
</TitlePage>

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44
<TableOfContents/>

45


46
<Body>

47
  Text before chapter <Ref Chap="First"/>. (&see; <Ref Sect="Two"/>)

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49
<Chapter Label="First"><Heading>Sectioning Elements</Heading>

50


51
  Text before the section <Ref Sect="FirstSect"/>. (&see; <Ref Sect="Two"/>)

52


53
 <Label Name="ThreeBack"/>

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 <Section Label="FirstSect"><Heading>Normal subsections</Heading>

55
  

56
  [&see; <Ref Sect="Three"/>]

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  <Subsection Label="Asub"><Heading>A subsection</Heading>

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   This is text in the first subsection.

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62
  </Subsection>

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  <Subsection Label="Another"><Heading>Another subsection</Heading>

65
  

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   This is text in the second subsection. This subsection 

67
   has a label, such that one can reference it.

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69
  </Subsection>

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71
 </Section>

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73
 <Section><Heading>ManSections</Heading>

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 <Label Name="FourBack"/>

75
 

76
  [&see; <Ref Sect="Four"/>]

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78
  <ManSection>

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   <Func Name="f" Arg="x[,y]" Comm="calculates something"/>

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   <Returns>an element in <Ref Filt="IsBlubb" /> or <K>fail</K>.</Returns>

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   <Description>

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    This function calculates something.

83
   </Description>

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  </ManSection>

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86
  <ManSection>

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   <Meth Name="\^\{\}\[\]\&lt;\&amp;" Arg="c" 

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         Label="for nothing" Comm="tricky name"/>

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   <Description>

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    This method is for an operation with a tricky name.

91
   </Description>

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  </ManSection>

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94
  <ManSection>

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   <Oper Name="MyOperation" Arg="x" Comm="calculates something"/>

96
   <Description>

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    The operation <Ref Oper="MyOperation"/> operates on <Arg>x</Arg>.

98
   </Description>

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  </ManSection>

100
   

101
  <ManSection>

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   <Meth Name="MyOperation" Label="First" Arg="x" 

103
         Comm="generic method"/>

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   <Description>

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    This method calculates something by the generic method.

106
   </Description>

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  </ManSection>

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109
  <ManSection>

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   <Meth Name="MyOperation" Label="for bla" Arg="x[, good_hint]"

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         Comm="for bla arguments"/>

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   <Description>

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    This is the super-fast method for the operation

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    <Ref Oper="MyOperation"/> if the argument <A>x</A> is in the

115
    representation <Ref Filt="IsBla"/>. It will become even faster if

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    the optional argument <A>good_hint</A> is given.

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   </Description>

118
  </ManSection>

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120
  <ManSection>

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   <Constr Name="MyConstructor" Arg="filt, x" Comm="constructs something"/>

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   <Description>

123
    The constructor <Ref Oper="MyConstructor"/> constructs from <Arg>x</Arg>

124
    an object in <A>filt</A>.

125
   </Description>

126
  </ManSection>

127


128
  <ManSection>

129
   <Filt Name="IsBla" Arg="obj" Comm="representation bla"

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         Type="representation"/>

131
   <Description>

132
    For objects in this representation there is a super-fast method

133
    (see <Ref Meth="MyOperation" Label="for bla"/>) for the operation

134
    <Ref Oper="MyOperation"/>.

135
   </Description>

136
  </ManSection>

137


138
  <ManSection>

139
   <Prop Name="IsBlubb" Arg="obj" Comm="property, whether object is blubb"/>

140
   <Description>

141
    A property.

142
   </Description>

143
  </ManSection>

144


145
  <ManSection>

146
   <Attr Name="NumberBlobbs" Arg="obj" Comm="number of blobbs"/>

147
   <Description>

148
    An attribute. Number of blobbs.

149
   </Description>

150
  </ManSection>

151


152
  <ManSection>

153
   <Var Name="AllBlibbs" Comm="list of all blibbs in the system"/>

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   <Description>

155
    This global variable holds a list of all blibbs.

156
   </Description>

157
  </ManSection>

158


159
  <ManSection>

160
   <Fam Name="BlibbsFamily" Comm="family of blibbs"/>

161
   <Description>

162
    Family of all blibbs.

163
   </Description>

164
  </ManSection>

165


166
  <ManSection>

167
   <InfoClass Name="InfoBlibbs" Comm="InfoClass for the library of blibbs"/>

168
   <Description>

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    This info class is used throughout the library of blibbs.

170
   </Description>

171
  </ManSection>

172
    

173
 </Section>

174


175
</Chapter>

176


177


178
<Chapter><Heading>Other Markup</Heading>

179
<Label Name="FiveBack"/>

180


181
<Section><Heading>Various types of text</Heading>

182


183
[&see; <Ref Sect="Five"/>]<P/>

184


185
In this section we present examples for all the various types of text

186
that are possible in &GAPDoc;: 

187
<List>

188
 <Item>

189
  <Emph>This</Emph> is <E>emphasized</E>.</Item>

190
 <Item>

191
  <E>Keywords</E> are typeset like <Keyword>this</Keyword> and <K>that</K>.

192
  </Item>

193
 <Item>

194
  <E>Arguments</E> of functions have an element. They look like this: 

195
    <Arg>x</Arg> and <A>y</A>.</Item>

196
 <Item> 

197
  <E>Code</E> can be written with the Code element: 

198
    <Code>if x = y then Print("Equal"); fi;</Code> or

199
    <C>while true do Print("Hello"); od;</C>.</Item> 

200
 <Item>

201
  <E>Filenames</E> have their own element:

202
    <File>/usr/local/ca/gap4r2</File> or <F>pkg/xgap/doc</F>.</Item>

203
 <Item>

204
  <E>Buttons</E>, <E>menus</E>, <E>menu entries</E>, and such things

205
    are also supported: <B>OK</B> or <Button>Cancel</Button>.</Item>

206
 <Item>

207
  <E>Packages</E> are typeset like this: 

208
    <Package>Small Groups Library</Package>

209
 </Item>

210
 <Item>

211
  <E>Quoted</E> text: <Q>This is a text in quotes.</Q>

212
 </Item>

213
</List>

214


215
<E>Paragraphs</E> are separated by the empty <C>Par</C> or <C>P</C> element.

216
<Par/><E>Alternatives</E> for different output formats:

217


218
<Alt Only="LaTeX">This is &LaTeX; output.</Alt>

219
<Alt Not="LaTeX">This is other than &LaTeX; output, namely:

220
<Alt Only="HTML"><![CDATA[<b>HTML</b>]]></Alt>

221
<Alt Only="Text">Text</Alt> output.</Alt>

222


223
<P/>

224


225
<Label Name="SixBack"/>

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There are also three elements to typeset <Q>verbatim-like</Q> text.

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(&see; <Ref Sect="Six"/>)<P/>

228
The first is a <E>Listing</E>:

229


230
<Listing Type="GAP code">

231
<![CDATA[Sieve := function(n)

232
  # Returns the primes less than n

233
  local l,p,i;

234
  l := [1..n]; Unbind(l[1]);

235
  p := 2;

236
  while p^2 <= n do

237
      if IsBound(l[p]) then

238
          i := 2 * p;

239
          while i <= n do Unbind(l[i]); i := i + p; od;

240
      fi;

241
      p := p + 1;

242
  od;

243
  return Compacted(l);

244
end;]]>

245
</Listing>

246


247
Here is a <E>Log</E> of a &GAP; session using this function:

248


249
<Log>

250
gap&gt; Sieve(100);

251
[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,

252
  67, 71, 73, 79, 83, 89, 97 ]

253
gap&gt; Length(last);

254
25

255
</Log>

256


257
Here is a &GAP; <E>Example</E> session that is automatically tested:

258


259
<Example>

260
gap&gt; s := Size(CharacterTable("M"));

261
808017424794512875886459904961710757005754368000000000

262
gap&gt; s &lt; 10^53;                     

263
false

264
gap&gt; s &lt; 10^54;

265
true

266
</Example>

267


268
</Section>

269


270
<Section><Heading>Formulae</Heading>

271
<Label Name="SevenBack"/>

272
 

273
 [&see; <Ref Sect="Seven"/>]<P/>

274


275
There are three types of formulae. <P/>

276
The first is the <E>normal math mode</E> of &LaTeX;: 

277


278
<Math>b_i \cdot b_j = \sum_{k=1}^d h_{ijk} b_k</Math>. 

279


280
Then there are <E>displayed formulae</E>:

281
<Display>

282
   \Longrightarrow \quad \left(\sum_{i=1}^d x_i b_i \right) \cdot

283
   \left(\sum_{j=1}^d y_j b_j \right) =

284
   \sum_{k=1}^d \left( \sum_{i,j} x_i y_j h_{ijk} \right) b_k 

285
</Display>

286


287
If possible,  use the <C>Alt</C> element  to specify a better  readable text

288
version of such a formula as in the following example:<P/>

289


290
<Alt Not="Text,HTML"><Display>

291
   \Longrightarrow \quad \left(\sum_{i=1}^d x_i b_i \right) \cdot

292
   \left(\sum_{j=1}^d y_j b_j \right) =

293
   \sum_{k=1}^d \left( \sum_{i,j} x_i y_j h_{ijk} \right) b_k 

294
</Display></Alt>

295
<Alt Only="Text,HTML"><Verb>

296
         d                d                 d   

297
       -----            -----             -----  -----                 

298
        \                \                 \      \                    

299
 ==> (   )  x_i b_i )(    )  y_j b_j ) =    )  (   )  x_i y_j h_ijk ) b_k

300
        /                /                 /      /                    

301
       -----            -----             -----  -----                

302
       i = 1            j = 1             k = 1   i,j                

303
</Verb><P/></Alt>

304


305
For small formulae without <Q>difficult</Q> parts use the <C>M</C>

306
element: <M>b_i</M>,

307
<M>x^2</M>, <M>x^2 + 2x + 1 = (x + 1)^2</M>. Note that here whitespace 

308
matters for text (or HTML) output.<P/>

309


310
Here are two formulae containing less than characters which are special 

311
characters for XML: 

312
<M><![CDATA[a < b < c < d]]></M> and  <M>e &lt; f</M>.

313
<P/>

314


315
Using the <C>Mode</C> attribute of a <C>Display</C> element formulae 

316
like

317
<Display Mode="M">a \longrightarrow a \bmod m\prime</Display>

318
can also be displayed nicely in text and HTML output.

319
</Section>

320


321


322
<Section Label="Cross"><Heading>Crossreferencing</Heading>

323
<Label Name="EightBack"/>

324


325
[&see; <Ref Sect="Eight"/>]<P/>

326


327
<Label Name="there"/>

328


329
In this section we demonstrate various references to parts of this

330
document. Here is a reference to this section: <Ref Sect="Cross"/>.

331
Here is a reference to chapter <Ref Chap="First"/>, to appendix

332
<Ref Appendix="Appendix"/>, and to subsection <Ref Subsect="Asub"/>. 

333
<P/>

334


335
We distinguish among others references 

336
 to functions (see <Ref Func="f"/>), 

337
 to methods with tricky name (see 

338
                 <Ref Meth="\^\{\}\[\]\&lt;\&amp;" Label="for nothing"/>),

339
 to operations (see <Ref Oper="MyOperation"/>), 

340
 to methods (see <Ref Meth="MyOperation" Label="First"/> or 

341
                 <Ref Meth="MyOperation" Label="for bla"/>), 

342
 to filters (see <Ref Filt="IsBla"/>), 

343
 to properties (see <Ref Prop="IsBlubb"/>),

344
 to attributes (see <Ref Attr="NumberBlobbs"/>), 

345
 to variables (<Ref Var="AllBlibbs"/>), 

346
 to families (see <Ref Fam="BlibbsFamily"/>),

347
 and to info classes (see <Ref InfoClass="InfoBlibbs"/>).

348
<P/>

349


350
There are also references to labels: see <Ref Text="here" Label="there"/>,

351
to other books: see <Ref Sect="What is a DTD" BookName="GAPDoc"/> or

352
<Ref Oper="IsSubgroup" BookName="ref"/> in the &GAP; reference

353
manual.

354
<P/>

355


356
References to sections come in two styles: 

357
<Ref Chap="First" Style="Number"/>

358
or <Ref Chap="First" Style="Text"/>.

359
<P/>

360


361
Another type of cross referencing is bibliography. Here is a 

362
citation: <Cite Key="CR1" Where="(5.22)"/> is an interesting lemma.

363
<P/>

364


365
There are also URLs:<P/>

366


367
<URL>http://www.math.rwth-aachen.de/</URL><P/>

368


369
Email addresses have a special element:

370
<Email>[email protected]</Email>

371
<P/>

372


373
and Homepages another one:

374
<Homepage>http://www-groups.mcs.st-and.ac.uk/~neunhoef/</Homepage>

375
<P/>

376
And here is a link to the <URL>

377
<Link>http://www.math.rwth-aachen.de/~Frank.Luebeck/gap/EDIM/index.html#ARCHS</Link>

378
<LinkText><Package>EDIM</Package> 

379
archives</LinkText></URL>.

380
<P/>

381


382
One can generate index entries as follows (look up the words 

383
<Q>&TeX;-UserGroup</Q>, <Q>RWTH</Q>, <Q>Aachen, Hauptbahnhof</Q>, and

384
<Q><Package>GAPDoc</Package>, for &GAP; programmers</Q>).

385
<Index Key="TeX-Usergroup">&TeX;-UserGroup</Index>

386
<Index>RWTH</Index>

387
<Index>Aachen <Subkey>Hauptbahnhof</Subkey></Index>

388
<Index Key="GAPDoc" Subkey="for GAP programmers"><Package>GAPDoc</Package> 

389
<Subkey>for &GAP; programmers</Subkey></Index>

390


391
</Section>

392


393


394
<Section><Heading>Lists and Tables</Heading>

395
<Label Name="NineBack"/>

396


397
[&see; <Ref Sect="Nine"/>]<P/>

398


399
There are

400
<List>

401
 <Item>lists</Item>

402
 <Item>enumerations, and</Item>

403
 <Item>tables</Item>

404
</List>

405
or:

406
<Enum>

407
 <Item>lists</Item>

408
 <Item>enumerations, and</Item>

409
 <Item>tables</Item>

410
</Enum>

411
or with marks:

412
<List>

413
 <Mark>lists:</Mark><Item> not numbered</Item>

414
 <Mark>enumerations:</Mark><Item> numbered</Item>

415
 <Mark>tables:</Mark><Item> two-dimensional</Item>

416
</List>

417


418
Lists can also be nested:

419
<Enum>

420
 <Item>

421
   <Enum>

422
     <Item>first item of inner enumeration </Item>

423
     <Item>second item of inner enumeration </Item>

424
   </Enum>

425
 </Item>

426
 <Item>

427
   <List>

428
     <Item>first item of inner list </Item>

429
     <Item>second item of inner list </Item>

430
   </List>

431
  </Item>

432
</Enum>

433


434
Here is a <E>table</E>:

435


436
<Table Align="|r|c|l|">

437
 <Caption>Prices</Caption>

438
 <HorLine/>

439
  <Row>

440
   <Item>Object</Item><Item>Price</Item><Item>available</Item>

441
  </Row>

442
 <HorLine/>

443
 <HorLine/>

444
  <Row>

445
   <Item>Shoe</Item><Item>$1,00</Item><Item>there</Item>

446
  </Row>

447
 <HorLine/>

448
  <Row>

449
   <Item>Hat</Item><Item>$2,00</Item><Item>not there</Item>

450
  </Row>

451
 <HorLine/>

452
</Table>

453


454
</Section>

455


456


457
<Section><Heading>Entities and Special Characters</Heading>

458
<Label Name="TenBack"/>

459


460
[&see; <Ref Sect="Ten"/>]<P/>

461


462
Here is a table of special characters, the first two are special for

463
XML and must be typed in by entities in &GAPDoc; documents. The other 

464
characters are special for &LaTeX; but in &GAPDoc; they can be typed

465
directly. 

466


467
<Table Align="|c|c|c|c|c|c|c|c|c|c|c|c|c|" Label="charsInCDATA"> 

468
 <Caption>Special characters in character data</Caption>

469
 <HorLine/> <Row> 

470
  <Item><C>&amp;</C></Item>

471
  <Item><C>&lt;</C></Item>

472
  <Item><C>></C></Item>

473
  <Item><C>#</C></Item>

474
  <Item><C>$</C></Item>

475
  <Item><C>%</C></Item>

476
  <Item><C>~</C></Item>

477
  <Item><C>\</C></Item>   

478
  <Item><C>{</C></Item>

479
  <Item><C>}</C></Item>

480
  <Item><C>_</C></Item>

481
  <Item><C>^</C></Item>

482
  <Item><C>&nbsp;</C></Item>

483
 </Row> <HorLine/>

484
</Table>

485


486
And here are the predefined entities in &GAPDoc;:

487


488
<Table Align="|l|l|">

489
<Caption>Predefined Entities in the &GAPDoc; system</Caption>

490
<HorLine/>

491
<Row> <Item><C>&amp;GAP;</C></Item>       <Item>&GAP;</Item> </Row>

492
<HorLine/>

493
<Row> <Item><C>&amp;GAPDoc;</C></Item>    <Item>&GAPDoc;</Item> </Row>

494
<HorLine/>

495
<Row> <Item><C>&amp;TeX;</C></Item>       <Item>&TeX;</Item> </Row>

496
<HorLine/>

497
<Row> <Item><C>&amp;LaTeX;</C></Item>     <Item>&LaTeX;</Item> </Row>

498
<HorLine/>

499
<Row> <Item><C>&amp;BibTeX;</C></Item>    <Item>&BibTeX;</Item> </Row>

500
<HorLine/>

501
<Row> <Item><C>&amp;MeatAxe;</C></Item>   <Item>&MeatAxe;</Item> </Row>

502
<HorLine/>

503
<Row> <Item><C>&amp;XGAP;</C></Item>      <Item>&XGAP;</Item> </Row>

504
<HorLine/>

505
<Row> <Item><C>&amp;copyright;</C></Item> <Item>&copyright;</Item> </Row>

506
<HorLine/>

507
</Table>

508


509
And some more for mathematical symbols: 

510
&CC;, &ZZ;, &NN;, &PP;, &QQ;, &HH;, &RR;.

511


512
</Section>

513


514
</Chapter>

515


516
</Body>

517


518
<Appendix Label="Appendix">

519
<Heading>An Appendix</Heading>

520
<Label Name="ElevenBack"/>

521


522
[&see; <Ref Sect="Eleven"/>]<P/>

523


524
This is an appendix. 

525
</Appendix>

526


527
<Appendix Label="Source"><Heading>The Source</Heading>

528


529
<Section Label="One"><Heading>TitlePage (Source)</Heading>

530


531
<Listing>

532
<![CDATA[<TitlePage>

533
  <Title>A Complete Example (&see; <Ref Sect="One"/>)</Title>

534
  <Subtitle>Every element shows up</Subtitle>

535
  <Version>Version <#Include SYSTEM "../version"></Version>

536
  <TitleComment>

537
  If the subtitle ist not sufficient, this &lt;TitleComment> 

538
  element can be used for a slightly longer text on the front page.

539
  </TitleComment>

540
  <Author>Frank Lübeck 

541
          <Email>[email protected]</Email> 

542
  </Author>

543
  <Author> Max Neunhöffer 

544
          <Email>neunhoef at mcs.st-and.ac.uk</Email>

545
  </Author>

546
  <Date>September 2011</Date>

547
  <Address>

548
  Lehrstuhl D für Mathematik<Br/> Templergraben 

549
  64<Br/> 52062 Aachen<Br/> (Germany)

550
  </Address>

551
  <Abstract>This document tries to use all elements that exist in &GAPDoc;.

552
            In addition, the final output not only contains the usual

553
            content, but also an appendix with the source text. There

554
            are also links from the usual content to the corresponding

555
            source text. This should enable new users to learn &GAPDoc;

556
            quickly.

557
  </Abstract>

558
  <Copyright>&copyright; 2000-2011 by Frank Lübeck and Max Neunhöffer

559
  </Copyright>

560
  <Acknowledgements>We thank Lehrstuhl D für Mathematik.

561
  </Acknowledgements>

562
  <Colophon>This is the Colophon page.

563
  </Colophon>

564
</TitlePage>]]>

565
</Listing>

566


567
</Section>

568


569


570
<Section Label="Two"><Heading>Before First Chapter (Source)</Heading>

571


572
<Listing>

573
<![CDATA[<TableOfContents/>

574


575
<Body>

576


577
  Text before chapter <Ref Chap="First"/>.

578


579
<Chapter Label="First"><Heading>Sectioning Elements</Heading>

580


581
  Text before the section <Ref Sect="FirstSect"/>.]]>

582
</Listing>

583


584
</Section>

585


586


587
<Section Label="Three">

588
<Heading>First Chapter (Source)</Heading>

589


590
[<Ref  Label="ThreeBack"/>]

591


592
<Listing>

593
<![CDATA[<Section Label="FirstSect"><Heading>Normal subsections</Heading>

594


595
  <Subsection Label="Asub"><Heading>A subsection</Heading>

596


597
   This is text in the first subsection.

598


599
  </Subsection>

600


601
  <Subsection Label="Another"><Heading>Another subsection</Heading>

602
   

603
   This is text in the second subsection. This subsection 

604
   has a label, such that one can reference it.

605


606
  </Subsection>

607


608
 </Section>]]>

609
</Listing>

610


611
</Section>

612


613


614
<Section Label="Four"><Heading>ManSections (Source)</Heading>

615


616
[<Ref Label="FourBack"/>]

617


618
<Listing>

619
<![CDATA[<Section><Heading>ManSections</Heading>

620


621
  <ManSection>

622
   <Func Name="f" Arg="x[,y]" Comm="calculates something"/>

623
   <Returns>an element in <Ref Filt="IsBlubb" /> or <K>fail</K>.</Returns>

624
   <Description>

625
    This function calculates something.

626
   </Description>

627
  </ManSection>

628


629
  <ManSection>

630
   <Meth Name="\^\{\}\[\]\&lt;\&amp;" Arg="c" 

631
         Label="for nothing" Comm="tricky name"/>

632
   <Description>

633
    This method is for an operation with a tricky name.

634
   </Description>

635
  </ManSection>

636


637
  <ManSection>

638
   <Oper Name="MyOperation" Arg="x" Comm="calculates something"/>

639
   <Description>

640
    The operation <Ref Oper="MyOperation"/> operates on <Arg>x</Arg>.

641
   </Description>

642
  </ManSection>

643
   

644
  <ManSection>

645
   <Meth Name="MyOperation" Label="First" Arg="x" 

646
         Comm="generic method"/>

647
   <Description>

648
    This method calculates something by the generic method.

649
   </Description>

650
  </ManSection>

651


652
  <ManSection>

653
   <Meth Name="MyOperation" Label="for bla" Arg="x[, good_hint]"

654
         Comm="for bla arguments"/>

655
   <Description>

656
    This is the super-fast method for the operation

657
    <Ref Oper="MyOperation"/> if the argument <A>x</A> is in the

658
    representation <Ref Filt="IsBla"/>. It will become even faster if

659
    the optional argument <A>good_hint</A> is given.

660
   </Description>

661
  </ManSection>

662


663
  <ManSection>

664
   <Constr Name="MyConstructor" Arg="filt, x" Comm="constructs something"/>

665
   <Description>

666
    The constructor <Ref Oper="MyConstructor"/> constructs from <Arg>x</Arg>

667
    an object in <A>filt</A>.

668
   </Description>

669
  </ManSection>

670


671
  <ManSection>

672
   <Filt Name="IsBla" Arg="obj" Comm="representation bla"

673
         Type="representation"/>

674
   <Description>

675
    For objects in this representation there is a super-fast method

676
    (see <Ref Meth="MyOperation" Label="for bla"/>) for the operation

677
    <Ref Oper="MyOperation"/>.

678
   </Description>

679
  </ManSection>

680


681
  <ManSection>

682
   <Prop Name="IsBlubb" Arg="obj" Comm="property, whether object is blubb"/>

683
   <Description>

684
    A property.

685
   </Description>

686
  </ManSection>

687


688
  <ManSection>

689
   <Attr Name="NumberBlobbs" Arg="obj" Comm="number of blobbs"/>

690
   <Description>

691
    An attribute. Number of blobbs.

692
   </Description>

693
  </ManSection>

694


695
  <ManSection>

696
   <Var Name="AllBlibbs" Comm="list of all blibbs in the system"/>

697
   <Description>

698
    This global variable holds a list of all blibbs.

699
   </Description>

700
  </ManSection>

701


702
  <ManSection>

703
   <Fam Name="BlibbsFamily" Comm="family of blibbs"/>

704
   <Description>

705
    Family of all blibbs.

706
   </Description>

707
  </ManSection>

708


709
  <ManSection>

710
   <InfoClass Name="InfoBlibbs" Comm="InfoClass for the library of blibbs"/>

711
   <Description>

712
    This info class is used throughout the library of blibbs.

713
   </Description>

714
  </ManSection>

715
    

716
 </Section>]]>

717
</Listing>

718


719
</Section>

720


721


722
<Section Label="Five"><Heading>Various Types of Text (Source)</Heading>

723


724
[<Ref Label="FiveBack"/>]

725


726
<Listing>

727
<![CDATA[<Chapter><Heading>Other Markup</Heading>

728


729
<Section><Heading>Various types of text</Heading>

730


731
In this section we present examples for all the various types of text

732
that are possible in &GAPDoc;: 

733
<List>

734
 <Item>

735
  <Emph>This</Emph> is <E>emphasized</E>.</Item>

736
 <Item>

737
  <E>Keywords</E> are typeset like <Keyword>this</Keyword> and <K>that</K>.

738
  </Item>

739
 <Item>

740
  <E>Arguments</E> of functions have an element. They look like this: 

741
    <Arg>x</Arg> and <A>y</A>.</Item>

742
 <Item> 

743
  <E>Code</E> can be written with the Code element: 

744
    <Code>if x = y then Print("Equal"); fi;</Code> or

745
    <C>while true do Print("Hello"); od;</C>.</Item> 

746
 <Item>

747
  <E>Filenames</E> have their own element:

748
    <File>/usr/local/ca/gap4r2</File> or <F>pkg/xgap/doc</F>.</Item>

749
 <Item>

750
  <E>Buttons</E>, <E>menus</E>, <E>menu entries</E>, and such things

751
    are also supported: <B>OK</B> or <Button>Cancel</Button>.</Item>

752
 <Item>

753
  <E>Packages</E> are typeset like this: 

754
    <Package>Small Groups Library</Package>

755
 </Item>

756
 <Item>

757
  <E>Quoted</E> text: <Q>This is a text in quotes.</Q>

758
 </Item>

759
</List>

760


761
<E>Paragraphs</E> are separated by the empty <C>Par</C> or <C>P</C> element.

762
<Par/><E>Alternatives</E> for different output formats:

763


764
<Alt Only="LaTeX">This is &LaTeX; output.</Alt>

765
<Alt Not="LaTeX">This is other than &LaTeX; output, namely:

766
<Alt Only="HTML"><![CDATA[<b>HTML</b>]]>]<![CDATA[]></Alt>

767
<Alt Only="Text">Text</Alt> output.</Alt>

768


769
<P/>]]>

770
</Listing>

771


772
</Section>

773


774


775
<Section Label="Six"><Heading>Verbatim-like text (Source)</Heading>

776


777
[<Ref Label="SixBack"/>]

778


779
<Listing>

780
<![CDATA[There are also three elements to typeset <Q>verbatim-like</Q> text.

781
<P/>

782
The first is a <E>Listing</E>:

783


784
<Listing Type="GAP code">

785
<![CDATA[Sieve := function(n)

786
  # Returns the primes less than n

787
  local l,p,i;

788
  l := [1..n]; Unbind(l[1]);

789
  p := 2;

790
  while p^2 <= n do

791
      if IsBound(l[p]) then

792
          i := 2 * p;

793
          while i <= n do Unbind(l[i]); i := i + p; od;

794
      fi;

795
      p := p + 1;

796
  od;

797
  return Compacted(l);

798
end;]]>]<![CDATA[]>

799
</Listing>

800


801
Here is a <E>Log</E> of a &GAP; session using this function:

802


803
<Log>

804
gap&gt; Sieve(100);

805
[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,

806
  67, 71, 73, 79, 83, 89, 97 ]

807
gap&gt; Length(last);

808
25

809
</Log>

810


811
Here is a &GAP; <E>Example</E> session that is automatically tested:

812


813
<Example>

814
gap&gt; s := Size(CharacterTable("M"));

815
808017424794512875886459904961710757005754368000000000

816
gap&gt; s &lt; 10^53;                     

817
false

818
gap&gt; s &lt; 10^54;

819
true

820
</Example>

821


822
</Section>]]>

823
</Listing>

824


825
</Section>

826


827


828
<Section Label="Seven"><Heading>Formulae (Source)</Heading>

829


830
[<Ref Label="SevenBack"/>]

831


832
<Listing>

833
<![CDATA[<Section><Heading>Formulae</Heading>

834


835
There are three types of formulae. <P/>

836
The first is the <E>normal math mode</E> of &LaTeX;: 

837


838
<Math>b_i \cdot b_j = \sum_{k=1}^d h_{ijk} b_k</Math>. 

839


840
Then there are <E>displayed formulae</E>:

841
<Display>

842
   \Longrightarrow \quad \left(\sum_{i=1}^d x_i b_i \right) \cdot

843
   \left(\sum_{j=1}^d y_j b_j \right) =

844
   \sum_{k=1}^d \left( \sum_{i,j} x_i y_j h_{ijk} \right) b_k 

845
</Display>

846


847
If possible,  use the <C>Alt</C> element  to specify a better  readable text

848
version of such a formula as in the following example:<P/>

849


850
<Alt Not="Text,HTML"><Display>

851
   \Longrightarrow \quad \left(\sum_{i=1}^d x_i b_i \right) \cdot

852
   \left(\sum_{j=1}^d y_j b_j \right) =

853
   \sum_{k=1}^d \left( \sum_{i,j} x_i y_j h_{ijk} \right) b_k 

854
</Display></Alt>

855
<Alt Only="Text,HTML"><Verb>

856
         d                d                 d   

857
       -----            -----             -----  -----                 

858
        \                \                 \      \                    

859
 ==> (   )  x_i b_i )(    )  y_i b_i ) =    )  (   )  x_i y_j h_ijk ) b_k

860
        /                /                 /      /                    

861
       -----            -----             -----  -----                

862
       i = 1            i = 1             k = 1   i,j                

863
</Verb><P/></Alt>

864


865
For small formulae without <Q>difficult</Q> parts use the <C>M</C>

866
element: <M>b_i</M>,

867
<M>x^2</M>, <M>x^2 + 2x + 1 = (x + 1)^2</M>. Note that here whitespace 

868
matters for text (or HTML) output).<P/>

869


870
Here are two formulae containing less than characters which are special

871
characters for XML:

872
<M><![CDATA[a < b < c < d]]]]>&gt;<![CDATA[</M> and  <M>e &lt; f</M>.

873
</Section>]]>

874
</Listing>

875


876
</Section>

877


878


879
<Section Label="Eight"><Heading>Crossreferencing (Source)</Heading>

880


881
[<Ref Label="EightBack"/>]

882


883
<Listing>

884
<![CDATA[<Section Label="Cross"><Heading>Crossreferencing</Heading>

885


886
<Label Name="there"/>

887


888
In this section we demonstrate various references to parts of this

889
document. Here is a reference to this section: <Ref Sect="Cross"/>.

890
Here is a reference to chapter <Ref Chap="First"/>, to appendix

891
<Ref Appendix="Appendix"/>, and to subsection <Ref Subsect="Asub"/>. 

892
<P/>

893


894
We distinguish among others references 

895
 to functions (see <Ref Func="f"/>), 

896
 to methods with tricky name (see 

897
                 <Ref Meth="\^\{\}\[\]\&lt;\&amp;" Label="for nothing"/>),

898
 to operations (see <Ref Oper="MyOperation"/>), 

899
 to methods (see <Ref Meth="MyOperation" Label="First"/> or 

900
                 <Ref Meth="MyOperation" Label="for bla"/>), 

901
 to filters (see <Ref Filt="IsBla"/>), 

902
 to properties (see <Ref Prop="IsBlubb"/>),

903
 to attributes (see <Ref Attr="NumberBlobbs"/>), 

904
 to variables (<Ref Var="AllBlibbs"/>), 

905
 to families (see <Ref Fam="BlibbsFamily"/>),

906
 and to info classes (see <Ref InfoClass="InfoBlibbs"/>).

907
<P/>

908


909
There are also references to labels: see <Ref Text="here" Label="there"/>,

910
to other books: see <Ref Sect="syntaxXML" BookName="gapdoc"/> or

911
<Ref Oper="IsSubgroup" BookName="ref"/> in the &GAP; reference

912
manual.

913
<P/>

914


915
References to sections come in two styles: 

916
<Ref Chap="First" Style="Number"/>

917
or <Ref Chap="First" Style="Text"/>.

918
<P/>

919


920
Another type of cross referencing is bibliography. Here is a 

921
citation: <Cite Key="CR1" Where="(5.22)"/> is an interesting lemma.

922
<P/>

923


924
There are also URLs:<P/>

925


926
<URL>http://www.math.rwth-aachen.de/LDfM/</URL><P/>

927


928
Email addresses have a special element:

929
<Email>[email protected]</Email>

930
<P/>

931


932
and Homepages another one:

933
<Homepage>http://www-groups.mcs.st-and.ac.uk/~neunhoef/</Homepage>

934
<P/>

935


936
One can generate index entries as follows (look up the words 

937
<Q>&TeX;-UserGroup</Q>, <Q>RWTH</Q>, and <Q>Aachen, Hauptbahnhof</Q>).

938
<Index Key="TeX-Usergroup">&TeX;-UserGroup</Index>

939
<Index>RWTH</Index>

940
<Index>Aachen <Subkey>Hauptbahnhof</Subkey></Index>

941
<Index Key="GAPDoc" Subkey="for GAP programmers">&GAPDoc; 

942
<Subkey>for &GAP; programmers</Subkey></Index>

943


944
</Section>]]>

945
</Listing>

946


947
</Section>

948


949


950
<Section Label="Nine"><Heading>Lists and Tables (Source)</Heading>

951


952
[<Ref Label="NineBack"/>]

953


954
<Listing>

955
<![CDATA[<Section><Heading>Lists and Tables</Heading>

956


957
There are

958
<List>

959
 <Item>lists</Item>

960
 <Item>enumerations, and</Item>

961
 <Item>tables</Item>

962
</List>

963
or:

964
<Enum>

965
 <Item>lists</Item>

966
 <Item>enumerations, and</Item>

967
 <Item>tables</Item>

968
</Enum>

969
or with marks:

970
<List>

971
 <Mark>lists:</Mark><Item> not numbered</Item>

972
 <Mark>enumerations:</Mark><Item> numbered</Item>

973
 <Mark>tables:</Mark><Item> two-dimensional</Item>

974
</List>

975


976
Lists can also be nested:

977
<Enum>

978
 <Item>

979
   <Enum>

980
     <Item>first item of inner enumeration </Item>

981
     <Item>second item of inner enumeration </Item>

982
   </Enum>

983
 </Item>

984
 <Item>

985
   <List>

986
     <Item>first item of inner list </Item>

987
     <Item>second item of inner list </Item>

988
   </List>

989
  </Item>

990
</Enum>

991


992
Here is a <E>table</E>:

993


994
<Table Align="|r|c|l|">

995
 <Caption>Prices</Caption>

996
 <HorLine/>

997
  <Row>

998
   <Item>Object</Item><Item>Price</Item><Item>available</Item>

999
  </Row>

1000
 <HorLine/>

1001
 <HorLine/>

1002
  <Row>

1003
   <Item>Shoe</Item><Item>$1,00</Item><Item>there</Item>

1004
  </Row>

1005
 <HorLine/>

1006
  <Row>

1007
   <Item>Hat</Item><Item>$2,00</Item><Item>not there</Item>

1008
  </Row>

1009
 <HorLine/>

1010
</Table>

1011


1012
</Section>]]>

1013
</Listing>

1014


1015
</Section>

1016


1017


1018
<Section Label="Ten">

1019
<Heading>Entities and Special Characters (Source)</Heading>

1020


1021
[<Ref Label="TenBack"/>]

1022


1023
<Listing>

1024
<![CDATA[<Section><Heading>Entities and Special Characters</Heading>

1025
<Label Name="TenBack"/>

1026


1027
[&see; <Ref Sect="Ten"/>]<P/>

1028


1029
Here is a table of special characters, the first two are special for

1030
XML and must be typed in by entities in &GAPDoc; documents. The other 

1031
characters are special for &LaTeX; but in &GAPDoc; they can be typed

1032
directly. 

1033


1034
<Table Align="|c|c|c|c|c|c|c|c|c|c|c|c|c|" Label="charsInCDATA"> 

1035
 <Caption>Special characters in character data</Caption>

1036
 <HorLine/> <Row> 

1037
  <Item><C>&amp;</C></Item>

1038
  <Item><C>&lt;</C></Item>

1039
  <Item><C>></C></Item>

1040
  <Item><C>#</C></Item>

1041
  <Item><C>$</C></Item>

1042
  <Item><C>%</C></Item>

1043
  <Item><C>~</C></Item>

1044
  <Item><C>\</C></Item>   

1045
  <Item><C>{</C></Item>

1046
  <Item><C>}</C></Item>

1047
  <Item><C>_</C></Item>

1048
  <Item><C>^</C></Item>

1049
  <Item><C>&nbsp;</C></Item>

1050
 </Row> <HorLine/>

1051
</Table>

1052


1053
And here are the predefined entities in &GAPDoc;:

1054


1055
<Table Align="|l|l|">

1056
<Caption>Predefined Entities in the &GAPDoc; system</Caption>

1057
<HorLine/>

1058
<Row> <Item><C>&amp;GAP;</C></Item>       <Item>&GAP;</Item> </Row>

1059
<HorLine/>

1060
<Row> <Item><C>&amp;GAPDoc;</C></Item>    <Item>&GAPDoc;</Item> </Row>

1061
<HorLine/>

1062
<Row> <Item><C>&amp;TeX;</C></Item>       <Item>&TeX;</Item> </Row>

1063
<HorLine/>

1064
<Row> <Item><C>&amp;LaTeX;</C></Item>     <Item>&LaTeX;</Item> </Row>

1065
<HorLine/>

1066
<Row> <Item><C>&amp;BibTeX;</C></Item>    <Item>&BibTeX;</Item> </Row>

1067
<HorLine/>

1068
<Row> <Item><C>&amp;MeatAxe;</C></Item>   <Item>&MeatAxe;</Item> </Row>

1069
<HorLine/>

1070
<Row> <Item><C>&amp;XGAP;</C></Item>      <Item>&XGAP;</Item> </Row>

1071
<HorLine/>

1072
<Row> <Item><C>&amp;copyright;</C></Item> <Item>&copyright;</Item> </Row>

1073
<HorLine/>

1074
</Table>

1075


1076
And some more for mathematical symbols: 

1077
&CC;, &ZZ;, &NN;, &PP;, &QQ;, &HH;, &RR;.

1078


1079
</Section>

1080


1081
</Chapter>

1082


1083
</Body>]]>

1084
</Listing>

1085


1086
</Section>

1087


1088


1089
<Section Label="Eleven"><Heading>Appendix (Source)</Heading>

1090


1091
[<Ref Label="ElevenBack"/>]

1092


1093
<Listing Type="GAPDoc source">

1094
<![CDATA[<Appendix><Heading>An Appendix</Heading>

1095


1096
This is an appendix.

1097
</Appendix>]]>

1098
</Listing>

1099


1100
</Section>

1101


1102
</Appendix>

1103


1104
<Bibliography Databases="examplebib.xml" Style="alpha"/>

1105
<TheIndex/>

1106


1107
</Book>

1108


1109


1110