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AbelianGroup Class Reference

#include <AbelianGroup.h>

Inheritance diagram for AbelianGroup::

ObjectOf List of all members.

Public Methods

 AbelianGroup (const FPGroup &G, bool makeFile=false)
void computeCyclicDecomposition ()
void findPrimaryBasis ()
bool haveCyclicDecomposition () const
bool havePrimaryDecomposition () const
Chars getFileName () const
Chars getFileNameOfPDGens () const
const FPGroup getFPGroup () const
SetOf<WordgetAllRelators () const
AbelianWord oldInAbelianForm (const Word &w) const
int rankOfFreeAbelianFactor () const
VectorOf<Integer> invariants () const
VectorOf<AbelianWordoldToNewGens () const
VectorOf<AbelianWordnewToOldGens () const
AbelianGroup getCanonicalSmithPresentation () const
Integer order () const
bool isTrivial () const
bool isFinite () const
bool isInfinite () const
bool isFree () const
bool isomorphicTo (const AbelianGroup &G) const
AbelianGroup computeIntegralHomology (int n) const
Integer orderOfTheTorsionSubgroup () const
AbelianSGPresentation makeSubgroupPresentation (const VectorOf< Word > &vG) const
VectorOf<WordfindSubgroupIsolator (const VectorOf< Word > &vG) const
VectorOf<WordfindVirtFreeComplementOfSG (const VectorOf< Word > &vG) const
VectorOf<WordjoinSubgroups (const VectorOf< Word > &vG1, const VectorOf< Word > &vG2) const
VectorOf<WordfindSubgIntersection (const VectorOf< Word > &vG1, const VectorOf< Word > &vG2, File &file) const
bool isPureCyclSubgroup (const Word &w) const
bool areEqual (const Word &u, const Word &v) const
bool isTrivial (const Word &w) const
Integer orderOfElt (const Word &w) const
AbelianWord newToOldGens (const AbelianWord &w) const
AbelianWord oldToNewGens (const AbelianWord &w) const
AbelianWord findEltPrimeForm (const Word &w) const
AbelianWord pBlockOfElt (const AbelianWord &w, Integer p) const
AbelianWord pBlockOfElt (const Word &w, Integer p) const
Integer pHeightOfElt (const Word &w, const Integer &p, Integer orderofElt=-1) const
Integer powerOfEltInSubgroup (const Word &w, const VectorOf< Word > &sGroup) const
bool isEltProperPower (const Word &w) const
void abelianMaximalRoot (const Word &w, Word &maxRoot, Integer &maxExp) const
AbelianWord primeFormInOldGens (const AbelianWord &w) const
int isPowerOfSecond (const Word &word1, const Word &word2) const
Bool isEpimorphism (const VectorOf< Word > &V) const
int orderOfAuto (const VectorOf< Word > &V) const
VectorOf<WordinverseAuto (const VectorOf< Word > &V) const
VectorOf<WordfixedPointsOfAuto (const VectorOf< Word > &v) const
void printWordInNewGens (ostream &ostr, const AbelianWord &w) const
void printInPrimaryForm (ostream &ostr, const AbelianWord &aw) const
void printPrimaryDec (ostream &ostr) const

Protected Methods

 AbelianGroup (AbelianGroupRep *newrep)

Friends

ostream& operator<< (ostream &ostr, const AbelianGroup &G)
ostream& operator< (ostream &ostr, const AbelianGroup &G)
istream& operator> (istream &istr, AbelianGroup &G)
AbelianSGPresentationRep AbelianGroupRep::makeSubgroupPresentation (const VectorOf< Word > &vG) const
AbelianSGPresentationRep AbelianGroupRep::buildTorsionFreePresentation (Matrix< Integer > &gensTransformation, const VectorOf< Word > &vG) const

Constructor & Destructor Documentation

AbelianGroup::AbelianGroup ( const FPGroup & G,
bool makeFile = false ) [inline]
 

Definition at line 52 of file AbelianGroup.h.

AbelianGroup::AbelianGroup ( AbelianGroupRep * newrep ) [inline, protected]
 

Definition at line 435 of file AbelianGroup.h.


Member Function Documentation

void AbelianGroup::computeCyclicDecomposition ( ) [inline]
 

Definition at line 72 of file AbelianGroup.h.

void AbelianGroup::findPrimaryBasis ( ) [inline]
 

Definition at line 78 of file AbelianGroup.h.

bool AbelianGroup::haveCyclicDecomposition ( ) const [inline]
 

Definition at line 84 of file AbelianGroup.h.

bool AbelianGroup::havePrimaryDecomposition ( ) const [inline]
 

Definition at line 89 of file AbelianGroup.h.

Chars AbelianGroup::getFileName ( ) const [inline]
 

Definition at line 94 of file AbelianGroup.h.

Chars AbelianGroup::getFileNameOfPDGens ( ) const [inline]
 

Definition at line 100 of file AbelianGroup.h.

const FPGroup AbelianGroup::getFPGroup ( ) const [inline]
 

Definition at line 106 of file AbelianGroup.h.

SetOf< Word > AbelianGroup::getAllRelators<Word> ( ) const [inline]
 

Definition at line 112 of file AbelianGroup.h.

AbelianWord AbelianGroup::oldInAbelianForm ( const Word & w ) const [inline]
 

Definition at line 118 of file AbelianGroup.h.

int AbelianGroup::rankOfFreeAbelianFactor ( ) const [inline]
 

Definition at line 132 of file AbelianGroup.h.

VectorOf< Integer > AbelianGroup::invariants<Integer> ( ) const [inline]
 

Definition at line 138 of file AbelianGroup.h.

VectorOf< AbelianWord > AbelianGroup::oldToNewGens<AbelianWord> ( ) const [inline]
 

Definition at line 144 of file AbelianGroup.h.

VectorOf< AbelianWord > AbelianGroup::newToOldGens<AbelianWord> ( ) const [inline]
 

Definition at line 150 of file AbelianGroup.h.

AbelianGroup AbelianGroup::getCanonicalSmithPresentation ( ) const [inline]
 

Definition at line 156 of file AbelianGroup.h.

Integer AbelianGroup::order ( ) const [inline]
 

Definition at line 171 of file AbelianGroup.h.

Referenced by isFinite().

bool AbelianGroup::isTrivial ( ) const [inline]
 

Definition at line 177 of file AbelianGroup.h.

bool AbelianGroup::isFinite ( ) const [inline]
 

Definition at line 183 of file AbelianGroup.h.

Referenced by isInfinite().

bool AbelianGroup::isInfinite ( ) const [inline]
 

Definition at line 187 of file AbelianGroup.h.

bool AbelianGroup::isFree ( ) const [inline]
 

Definition at line 191 of file AbelianGroup.h.

bool AbelianGroup::isomorphicTo ( const AbelianGroup & G ) const [inline]
 

Definition at line 197 of file AbelianGroup.h.

AbelianGroup AbelianGroup::computeIntegralHomology ( int n ) const [inline]
 

Definition at line 203 of file AbelianGroup.h.

Integer AbelianGroup::orderOfTheTorsionSubgroup ( ) const [inline]
 

Definition at line 214 of file AbelianGroup.h.

AbelianSGPresentation AbelianGroup::makeSubgroupPresentation ( const VectorOf< Word > & vG ) const
 

VectorOf< Word > AbelianGroup::findSubgroupIsolator<Word> ( const VectorOf< Word > & vG ) const [inline]
 

Definition at line 223 of file AbelianGroup.h.

VectorOf< Word > AbelianGroup::findVirtFreeComplementOfSG<Word> ( const VectorOf< Word > & vG ) const [inline]
 

Definition at line 229 of file AbelianGroup.h.

VectorOf< Word > AbelianGroup::joinSubgroups<Word> ( const VectorOf< Word > & vG1,
const VectorOf< Word > & vG2 ) const [inline]
 

Definition at line 235 of file AbelianGroup.h.

VectorOf< Word > AbelianGroup::findSubgIntersection<Word> ( const VectorOf< Word > & vG1,
const VectorOf< Word > & vG2,
File & file ) const [inline]
 

Definition at line 241 of file AbelianGroup.h.

bool AbelianGroup::isPureCyclSubgroup ( const Word & w ) const [inline]
 

Definition at line 249 of file AbelianGroup.h.

bool AbelianGroup::areEqual ( const Word & u,
const Word & v ) const [inline]
 

Definition at line 260 of file AbelianGroup.h.

bool AbelianGroup::isTrivial ( const Word & w ) const [inline]
 

Definition at line 266 of file AbelianGroup.h.

Integer AbelianGroup::orderOfElt ( const Word & w ) const [inline]
 

Definition at line 272 of file AbelianGroup.h.

AbelianWord AbelianGroup::newToOldGens ( const AbelianWord & w ) const [inline]
 

Definition at line 278 of file AbelianGroup.h.

AbelianWord AbelianGroup::oldToNewGens ( const AbelianWord & w ) const [inline]
 

Definition at line 283 of file AbelianGroup.h.

AbelianWord AbelianGroup::findEltPrimeForm ( const Word & w ) const [inline]
 

Definition at line 288 of file AbelianGroup.h.

Referenced by pBlockOfElt().

AbelianWord AbelianGroup::pBlockOfElt ( const AbelianWord & w,
Integer p ) const [inline]
 

Definition at line 294 of file AbelianGroup.h.

AbelianWord AbelianGroup::pBlockOfElt ( const Word & w,
Integer p ) const [inline]
 

Definition at line 299 of file AbelianGroup.h.

Integer AbelianGroup::pHeightOfElt ( const Word & w,
const Integer & p,
Integer orderofElt = -1 ) const [inline]
 

Definition at line 305 of file AbelianGroup.h.

Integer AbelianGroup::powerOfEltInSubgroup ( const Word & w,
const VectorOf< Word > & sGroup ) const [inline]
 

Definition at line 311 of file AbelianGroup.h.

bool AbelianGroup::isEltProperPower ( const Word & w ) const [inline]
 

Definition at line 316 of file AbelianGroup.h.

void AbelianGroup::abelianMaximalRoot ( const Word & w,
Word & maxRoot,
Integer & maxExp ) const [inline]
 

Definition at line 322 of file AbelianGroup.h.

AbelianWord AbelianGroup::primeFormInOldGens ( const AbelianWord & w ) const [inline]
 

Definition at line 330 of file AbelianGroup.h.

int AbelianGroup::isPowerOfSecond ( const Word & word1,
const Word & word2 ) const [inline]
 

Definition at line 335 of file AbelianGroup.h.

Bool AbelianGroup::isEpimorphism ( const VectorOf< Word > & V ) const [inline]
 

Definition at line 346 of file AbelianGroup.h.

int AbelianGroup::orderOfAuto ( const VectorOf< Word > & V ) const [inline]
 

Definition at line 354 of file AbelianGroup.h.

VectorOf< Word > AbelianGroup::inverseAuto<Word> ( const VectorOf< Word > & V ) const [inline]
 

Definition at line 362 of file AbelianGroup.h.

VectorOf< Word > AbelianGroup::fixedPointsOfAuto<Word> ( const VectorOf< Word > & v ) const [inline]
 

Definition at line 369 of file AbelianGroup.h.

void AbelianGroup::printWordInNewGens ( ostream & ostr,
const AbelianWord & w ) const [inline]
 

Definition at line 390 of file AbelianGroup.h.

void AbelianGroup::printInPrimaryForm ( ostream & ostr,
const AbelianWord & aw ) const [inline]
 

Definition at line 395 of file AbelianGroup.h.

void AbelianGroup::printPrimaryDec ( ostream & ostr ) const [inline]
 

Definition at line 400 of file AbelianGroup.h.


Friends And Related Function Documentation

ostream & operator<< ( ostream & ostr,
const AbelianGroup & G ) [friend]
 

Definition at line 382 of file AbelianGroup.h.

ostream & operator< ( ostream & ostr,
const AbelianGroup & G ) [friend]
 

Definition at line 411 of file AbelianGroup.h.

istream & operator> ( istream & istr,
AbelianGroup & G ) [friend]
 

Definition at line 417 of file AbelianGroup.h.

AbelianSGPresentationRep AbelianGroupRep::makeSubgroupPresentation ( const VectorOf< Word > & vG ) const [friend]
 

AbelianSGPresentationRep AbelianGroupRep::buildTorsionFreePresentation ( Matrix< Integer > & gensTransformation,
const VectorOf< Word > & vG ) const [friend]
 


The documentation for this class was generated from the following file:
Generated at Tue Jun 19 09:49:45 2001 for Magnus Classes by doxygen1.2.6 written by Dimitri van Heesch, © 1997-2001