FreeMetabelianGroupAlgorithms Class Reference

Static class FreeMetabelianGroupAlgorithms encapsulates algorithms for FreeMetabelianGroup groups. More...

#include <FreeMetabelianGroupAlgorithms.h>

List of all members.

Public Member Functions

FreeMetabelianGroupAlgorithms ()

Default constructor is not instantiated to protect from creating the obects of this class.

Static Public Member Functions

static bool trivial (int N, const Word &w)

Decide if a word represents the identity of a free metabelian group.

static pair< bool, Word > conjugate (int N, Word w1, Word w2)

Decide if words represent conjugate elements in a free metabelian group.

static Word getWordFromEdgeMap (int N, const map< vector< int >, int > &EM)

Compute a word (not a shortest) defining the same edge map as EM.

Detailed Description

Static class FreeMetabelianGroupAlgorithms encapsulates algorithms for FreeMetabelianGroup groups.

The class FreeMetabelianGroupAlgorithms is static, i.e., all member functions are static and there is no constructor defined.

Definition at line 36 of file FreeMetabelianGroupAlgorithms.h.

Constructor & Destructor Documentation

FreeMetabelianGroupAlgorithms::FreeMetabelianGroupAlgorithms ( )

Default constructor is not instantiated to protect from creating the obects of this class.

Member Function Documentation

static bool FreeMetabelianGroupAlgorithms::trivial	(	int	N,
		const Word &	w
	)			`[static]`

Decide if a word represents the identity of a free metabelian group.

$N$ is the rank of the corresponding metabelian group, $w$ is the given word.

static pair< bool , Word > FreeMetabelianGroupAlgorithms::conjugate	(	int	N,
		Word	w1,
		Word	w2
	)			`[static]`

Decide if words represent conjugate elements in a free metabelian group.

$N$ is the rank of the corresponding metabelian group, $w1, w2$ are the given word. The function returns a pair $(A,B)$ where $A$ is true if and only if words are conjugate and $B$ is a conjugator, i.e., $B^{-1} w1 B = w2$ holds.

static Word FreeMetabelianGroupAlgorithms::getWordFromEdgeMap	(	int	N,
		const map< vector< int >, int > &	EM
	)			`[static]`

Compute a word (not a shortest) defining the same edge map as EM.

It is assumed here that EM defines an element of $M_r'$ .

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

FreeMetabelianGroup/include/FreeMetabelianGroupAlgorithms.h


Public Member Functions
	FreeMetabelianGroupAlgorithms ()
	Default constructor is not instantiated to protect from creating the obects of this class.
Static Public Member Functions
static bool	trivial (int N, const Word &w)
	Decide if a word represents the identity of a free metabelian group.
static pair< bool, Word >	conjugate (int N, Word w1, Word w2)
	Decide if words represent conjugate elements in a free metabelian group.
static Word	getWordFromEdgeMap (int N, const map< vector< int >, int > &EM)
	Compute a word (not a shortest) defining the same edge map as EM.