FPGroup Class Reference

Class FPGroup (finitely presented group). More...

#include <FPGroup.h>

List of all members.

Public Member Functions
	FPGroup (int num=0)
	FPGroup (int numOfGen, const vector< Word > &relators)
	FPGroup (const FiniteAlphabet &a)
	FPGroup (const FiniteAlphabet &a, const vector< Word > &relators)
int	numberOfGenerators () const
	Get the number of generators.
const vector< string > &	getGeneratorsNames () const
	Get the names of the generators.
const FiniteAlphabet &	getAlphabet () const
	Get the alphabet.
const vector< Word > &	relators () const
Word	randomEqWord_Baltimore (const Word &w, int length, float conj_param) const
	Generate random equivalent word.
Word	randomIdentity_Stack (int length) const
	Generate random trivial word.
Word	randomIdentity_Classic (int length, float conj_param) const
	Generate random trivial word.
Word	randomIdentity_Baltimore (int length, float conj_param) const
	Generate random trivial word (using randomEqWord_Baltimore).
FPGroup	triangulatePresentation () const
	Triangulate the set of relations.
Static Public Member Functions
static vector< string >	initializeGenNames (int num)
Protected Attributes
int	numOfGenerators
vector< Word >	theRelators
FiniteAlphabet	theAlphabet
bool	useDefaultAlphabet
Friends
ostream &	operator<< (ostream &os, const FPGroup &group)
istream &	operator>> (istream &is, FPGroup &group)

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Detailed Description

Class FPGroup (finitely presented group).

Definition at line 32 of file FPGroup.h.

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Constructor & Destructor Documentation

FPGroup::FPGroup

(

int

num = 0

)

FPGroup::FPGroup	(	int	numOfGen,
		const vector< Word > &	relators
	)

FPGroup::FPGroup

(

const FiniteAlphabet &

a

)

FPGroup::FPGroup	(	const FiniteAlphabet &	a,
		const vector< Word > &	relators
	)

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Member Function Documentation

int FPGroup::numberOfGenerators

(

)

const [inline]

Get the number of generators.

Definition at line 59 of file FPGroup.h.

References numOfGenerators.

const vector< string >& FPGroup::getGeneratorsNames

(

)

const [inline]

Get the names of the generators.

Definition at line 61 of file FPGroup.h.

References theAlphabet.

const FiniteAlphabet& FPGroup::getAlphabet

(

)

const [inline]

Get the alphabet.

Definition at line 63 of file FPGroup.h.

References theAlphabet.

const vector< Word >& FPGroup::relators

(

)

const [inline]

Definition at line 65 of file FPGroup.h.

References theRelators.

Word FPGroup::randomEqWord_Baltimore	(	const Word &	w,
		int	length,
		float	conj_param
	)			const

Generate random equivalent word.

Function inserts into random positions in the given word relators (and their cyclic permutations and inverses) of the group conjugated by randomly chosen words. The lengths of conjugators is chosen using geometric distribution with parameter = conj_param. When the required length is reached the word is being reduced and output. So, the result often is shorter than the given parameter length.

Word FPGroup::randomIdentity_Stack

(

int

length

)

const

Generate random trivial word.

Function starts with a pair of trivial words , . On each iteration randomly takes a relators , takes a random cyclic permutation of it or its inverse, then randomly cuts in two pieces (one can be trivial) and multiplies on the right by and on the right by . When reaches the length output freely reduced .

Word FPGroup::randomIdentity_Classic	(	int	length,
		float	conj_param
	)			const

Generate random trivial word.

Function starts with a trivial word . On each iteration it multiplies on the right by a relator (and their cyclic permutations and inverses) of the group conjugated by randomly chosen words. Lengths of conjugators are chosen using geometric distribution with parameter = conj_param. When the required length is reached the word is being reduced and output. So, the result often is shorter than the given parameter length.

Word FPGroup::randomIdentity_Baltimore	(	int	length,
		float	conj_param
	)			const

Generate random trivial word (using randomEqWord_Baltimore).

FPGroup FPGroup::triangulatePresentation

(

)

const

Triangulate the set of relations.

Returns:

The result is a finite group presentation with all relators of length at most 3. Notice that the names of the original generators change to to avoid possible name collisions. New generator names are .

static vector< string > FPGroup::initializeGenNames

(

int

num

)

[static]

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Friends And Related Function Documentation

ostream& operator<<	(	ostream &	os,
		const FPGroup &	group
	)			[friend]

istream& operator>>	(	istream &	is,
		FPGroup &	group
	)			[friend]

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Member Data Documentation

int FPGroup::numOfGenerators [protected]

Definition at line 184 of file FPGroup.h.

Referenced by numberOfGenerators().

vector< Word > FPGroup::theRelators [protected]

Definition at line 187 of file FPGroup.h.

Referenced by relators().

FiniteAlphabet FPGroup::theAlphabet [protected]

Definition at line 189 of file FPGroup.h.

Referenced by getAlphabet(), and getGeneratorsNames().

bool FPGroup::useDefaultAlphabet [protected]

Definition at line 190 of file FPGroup.h.

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The documentation for this class was generated from the following file:

• Group/include/FPGroup.h