FPGroup Class Reference

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

#include <FPGroup.h>

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)

Detailed Description

Class FPGroup (finitely presented group).

Definition at line 32 of file FPGroup.h.

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
	)

Member Function Documentation

const FiniteAlphabet& FPGroup::getAlphabet ( ) const [inline]

Get the alphabet.

Definition at line 63 of file FPGroup.h.

References theAlphabet.

const vector< string >& FPGroup::getGeneratorsNames ( ) const [inline]

Get the names of the generators.

Definition at line 61 of file FPGroup.h.

References theAlphabet.

static vector< string > FPGroup::initializeGenNames ( int num ) [static]

int FPGroup::numberOfGenerators ( ) const [inline]

Get the number of generators.

Definition at line 59 of file FPGroup.h.

References numOfGenerators.

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 $w$ 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_Baltimore	(	int	length,
		float	conj_param
	)			const

Generate random trivial word (using randomEqWord_Baltimore).

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

Generate random trivial word.

Function starts with a trivial word $w = \varepsilon$ . On each iteration it multiplies $w$ 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_Stack ( int length ) const

Generate random trivial word.

Function starts with a pair of trivial words $w_1 = \varepsilon$ , $w_2 = \varepsilon$ . On each iteration randomly takes a relators $r$ , takes a random cyclic permutation $r'$ of it or its inverse, then randomly cuts in two pieces $r' = r_1 \circ r_2$ (one can be trivial) and multiplies $w_1$ on the right by $r_1$ and $w_2$ on the right by $r_2^{-1}$ . When $|w_1|+|w_2|$ reaches the length output freely reduced $w_1 w_2^{-1}$ .

const vector< Word >& FPGroup::relators ( ) const [inline]

Definition at line 65 of file FPGroup.h.

References theRelators.

FPGroup FPGroup::triangulatePresentation ( ) const

Triangulate the set of relations.

Returns:: The result is a finite group presentation $\langle Y;S \rangle$ with all relators of length at most 3. Notice that the names of the original generators change to $x_1,\ldots,x_n$ to avoid possible name collisions. New generator names are $x_{n+1},\ldots$ .