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
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
|
// Copyright (C) 1995 The New York Group Theory Cooperative
// See magnus/doc/COPYRIGHT for the full notice.
// Contents: Declaration of classes SMSubgroup, SIC, SCM
//
// Principal Author: Dmitry Bormotov
//
// Status: in progress
//
// Revision History:
//
#ifndef _SMSubgroup_H_
#define _SMSubgroup_H_
#include "AlgebraicObject.h"
#include "SMFPGroup.h"
#include "SGofFreeGroup.h"
#include "NGSubgroupProblems.h"
#include "AbelianSGPresentation.h"
#include "AbelianProblems.h"
#include "ToddCoxeter.h"
#include "HToddCoxeter.h"
#include "SGNilpotentQuotients.h"
class CyclicDecompositionOfFactorProperty : public AbelianGroupProperty {
public:
CyclicDecompositionOfFactorProperty( const AbelianGroup& data )
: AbelianGroupProperty(data) {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "CyclicDecompositionOfFactor"; }
protected:
GenericProperty* clone() const {
return new CyclicDecompositionOfFactorProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class AbelianSubgroupPresentationProperty
: public AbelianSGPresentationProperty {
public:
AbelianSubgroupPresentationProperty(const AbelianSGPresentation& data)
: AbelianSGPresentationProperty(data) {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "AbelianSubgroupPresentation"; }
protected:
GenericProperty* clone() const {
return new AbelianSubgroupPresentationProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class IsPureSubgroupProperty : public NoDataProperty {
public:
IsPureSubgroupProperty() : NoDataProperty() {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IsPureSubgroup"; }
protected:
GenericProperty* clone() const { return new IsPureSubgroupProperty(*this); }
private:
static const PropertyType theTypeID;
};
class IsCentralSubgroupProperty : public NoDataProperty {
public:
IsCentralSubgroupProperty() : NoDataProperty() {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IsCentralSubgroup"; }
protected:
GenericProperty* clone() const {
return new IsCentralSubgroupProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class IsNormalSubgroupProperty : public NoDataProperty {
public:
IsNormalSubgroupProperty() : NoDataProperty() {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IsNormalSubgroup"; }
protected:
GenericProperty* clone() const {
return new IsNormalSubgroupProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class IsAbelianSubgroupProperty : public NoDataProperty {
public:
IsAbelianSubgroupProperty() : NoDataProperty() {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IsAbelianSubgroup"; }
protected:
GenericProperty* clone() const { return new IsAbelianSubgroupProperty(*this); }
private:
static const PropertyType theTypeID;
};
class IsTrivialSubgroupProperty : public NoDataProperty {
public:
IsTrivialSubgroupProperty() : NoDataProperty() {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IsTrivialSubgroup"; }
protected:
GenericProperty* clone() const {
return new IsTrivialSubgroupProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class IndexOfSubgroupProperty : public IntProperty {
public:
IndexOfSubgroupProperty(const int& data) : IntProperty(data) {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "IndexOfSubgroup"; }
protected:
GenericProperty* clone() const { return new IndexOfSubgroupProperty(*this);}
private:
static const PropertyType theTypeID;
};
class SGNilpotentQuotientsProperty : public SGNilpGroupAssocProperty {
public:
SGNilpotentQuotientsProperty(
const AssociationsOf<int,SGOfNilpotentGroup*>& data
) : SGNilpGroupAssocProperty(data) {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "SGNilpotentQuotients"; }
protected:
GenericProperty* clone() const {
return new SGNilpotentQuotientsProperty(*this);
}
private:
static const PropertyType theTypeID;
};
class SubgroupOfNilpotentGroupProperty : public SGOfNilpotentGroupProperty {
public:
SubgroupOfNilpotentGroupProperty( const SGOfNilpotentGroup& data )
: SGOfNilpotentGroupProperty( data ) {}
PropertyType actualType() const { return type(); }
static PropertyType type() { return theTypeID; }
Chars propertyName() const { return "SubgroupOfNilpotentGroup"; }
protected:
GenericProperty* clone() const {
return new SubgroupOfNilpotentGroupProperty(*this);
}
private:
static const PropertyType theTypeID;
};
// ------------------------------ SIC ------------------------------------- //
class SIC : public InformationCenter, protected FEData
{
public:
/////////////////////////////////////////////////////////////////////////
// //
// Constructors: //
// //
/////////////////////////////////////////////////////////////////////////
SIC( OID subgroup_oid );
~SIC( );
/////////////////////////////////////////////////////////////////////////
// //
// Abelianization of the factor group //
// //
/////////////////////////////////////////////////////////////////////////
void putHaveCyclicDecompositionOfFactor( const AbelianGroup& );
bool haveCyclicDecompositionOfFactor( ) const;
const AbelianGroup& getCyclicDecompositionOfFactor( ) const;
void putHaveCyclicDecomposition( const AbelianSGPresentation& );
void putHavePrimaryDecomposition( const AbelianSGPresentation& );
bool haveCyclicDecomposition( ) const;
bool havePrimaryDecomposition( ) const;
const AbelianSGPresentation& getSGPresentation( ) const;
// Methods for nilpotent subgroups
void putHaveSGOfNGPreimageInitialized( const SGOfNilpotentGroup& );
bool haveSGOfNGPreimageInitialized( ) const;
void putHaveSGOfNGinitialized( const SGOfNilpotentGroup& );
bool haveSGOfNGinitialized( ) const;
const SGOfNilpotentGroup& getSGOfNilpotentGroup( ) const;
// Methods for subgroup nilpotent quotients
void putHaveSGNilpotentQuotInited( const SGOfNilpotentGroup& theQuot,
int theClass );
bool haveSGNilpotentQuotInited(int theClass) const;
const SGOfNilpotentGroup& getSGNilpotentQuotInited(int theClass) const;
void putHaveCompleteCayleyGraph( const SubgroupGraph& S );
bool haveCompleteCayleyGraph( ) const;
const SubgroupGraph& getCompleteCayleyGraph( ) const;
// Methods for word decomposer.
void putHaveWordDecomposer( const DecomposeInSubgroupOfFPGroup& D );
bool haveWordDecomposer( ) const;
const DecomposeInSubgroupOfFPGroup& getWordDecomposer( ) const;
//////////////////////////////////////////////////////////
//
// Schreier Transversal
//
/////////////////////////////////////////////////////////
void putHaveSchreierTransvl(const PermutationRepresentation&);
bool haveSchreierTransvl()const;
const PermutationRepresentation& getSchreierTransvl()const;
Trichotomy isPure() const;
void putIsPure(bool ispure);
Trichotomy isCentral() const;
void putIsCentral( bool iscentral);
Trichotomy isNormal() const;
void putIsNormal( bool isnormal);
Trichotomy isAbelian() const;
void putIsAbelian( bool isabelian);
Trichotomy isTrivial() const;
void putIsTrivial( bool istrivial);
int index() const;
bool haveIndex() const;
void putIndex(const int& index);
/////////////////////////////////////////////////////////////////////////
// //
// Data Members: //
// //
/////////////////////////////////////////////////////////////////////////
private:
OID subgroupOID;
// Need this for composing messages about what has been found.
AssociationsOf<int,SGOfNilpotentGroup*>& getSGNilpotentQuotients() const;
//AbelianGroup* theAbelianGroup;
//AbelianSGPresentation* theAbelianSGPresentation;
//SGOfNilpotentGroup* theSGOfNilpotentGroup;
//Trichotomy isPureSubgroup;
//Trichotomy isCentralSubgroup;
//Trichotomy isNormalSubgroup;
//Trichotomy isAbelianSubgroup;
//Trichotomy isTrivialSubgroup;
//int theIndex;
//PermutationRepresentation* permutationRepresentation;
//AssociationsOf<int, SGOfNilpotentGroup*> theSGNilpotentQuotients;
//SubgroupGraph *theCompleteCayleyGraph;
//DecomposeInSubgroupOfFPGroup *theWordDecomposer;
};
// ------------------------------- SCM ------------------------------------- //
class SCM : public Supervisor
{
public:
/////////////////////////////////////////////////////////////////////////
// //
// Constructors: //
// //
/////////////////////////////////////////////////////////////////////////
SCM( class SMSubgroup& S );
/////////////////////////////////////////////////////////////////////////
// //
// Accessors: //
// //
/////////////////////////////////////////////////////////////////////////
SMSubgroup& getSubgroup( ) const { return theSubgroup; }
/////////////////////////////////////////////////////////////////////////
// //
// Front End Interfacing: //
// //
/////////////////////////////////////////////////////////////////////////
void viewStructure(ostream& ostr) const { }
/////////////////////////////////////////////////////////////////////////
// //
// Subordinate Computation Managers: //
// //
/////////////////////////////////////////////////////////////////////////
Subordinate<SCM,AbelianInvariantsOfFactor> abelianInvariantsOfFactor;
Subordinate<SCM,AbelianSGInvariants> abelianSGInvariants;
Subordinate<SCM,SGOfNGinitializeProblem> initializeSGOfNG;
Subordinate<SCM,SGOfNGinitPreimageProblem> initPreimageSGOfNG;
Subordinate<SCM,SGIndexToddCoxeter> sgToddCoxeter;
Subordinate<SCM,SGIndexToddCoxeter> sgGHToddCoxeter;
Subordinate<SCM,SGNilpotentQuotients> sgNilpotentQuotients;
Subordinate<SCM,NormalClosure> normalClosure;
/////////////////////////////////////////////////////////////////////////
// //
// Control: //
// //
/////////////////////////////////////////////////////////////////////////
void takeControl( ); // overrides ComputationManager
/////////////////////////////////////////////////////////////////////////
// //
// State Transitions: //
// //
/////////////////////////////////////////////////////////////////////////
void start( ) { } // overrides ComputationManager
void terminate( ) { } // overrides ComputationManager
private:
/////////////////////////////////////////////////////////////////////////
// //
// Data Members: //
// //
/////////////////////////////////////////////////////////////////////////
class SMSubgroup& theSubgroup;
bool didFastChecks;
// The takeControl method does some sneaky checks of obvious properties
// (this should be formalized, since they are not always that fast).
// This records the first call, so that they are not done over and over.
};
// ----------------------------- SMSubgroup -------------------------------- //
class SMSubgroup : public AlgebraicObject
{
public:
/////////////////////////////////////////////////////////////////////////
// //
// Constructors: //
// //
/////////////////////////////////////////////////////////////////////////
SMSubgroup(SMFPGroup& G, const SGofFreeGroup& S, const Chars heritage,
Chars def = Chars());
SMSubgroup(SMFPGroup& G)
: AlgebraicObject(""), theGroup(G), theSubgroup( *((SGofFreeGroup*)0) ),
sic( oid() ), theSCM( 0 )
{ }
//Bogus ctor; see `But no' comment in Menu.h
/////////////////////////////////////////////////////////////////////////
// //
// Accessors: //
// //
/////////////////////////////////////////////////////////////////////////
SGofFreeGroup getSubgroup( ) const { return theSubgroup; }
SMFPGroup& getParent( ) const { return theGroup; }
SCM& scm() const { return *theSCM; }
InformationCenter* infoCenter() { return &sic; }
const InformationCenter* infoCenter() const { return &sic; }
/////////////////////////////////////////////////////////////////////////
// //
// Front End Interfacing: //
// //
/////////////////////////////////////////////////////////////////////////
static const char* type( ) { return "SMSubgroup"; }
const char* typeID( ) const { return type(); } // overrides SMObject
const IconID iconID( ) const { return IconID::subgroup; }
// overrides SMObject
void viewStructure(ostream& ostr) const; // overrides SMObject
void printProperties(ostream& ostr) const; // overrides SMObject
void printDefinition(ostream& ostr) const; // overrides SMObject
protected:
/////////////////////////////////////////////////////////////////////////
// //
// Restricted Access: //
// //
/////////////////////////////////////////////////////////////////////////
void readMessage(istream&) { } // overrides SMObject
/////////////////////////////////////////////////////////////////////////
// //
// Data Members: //
// //
/////////////////////////////////////////////////////////////////////////
public:
SIC sic;
private:
const SGofFreeGroup theSubgroup;
SMFPGroup& theGroup;
SCM* theSCM; // TheObjects removes scm when this is removed.
Chars definition;
// This is a definition of the subgroup. If the string is empty, then
// printDefinition outputs some "standard" definition:
// gp(<list-of-generators>)
//
// The alternative definition can be put in the constructor.
};
#endif
|
