Arithmeticity Class Reference

This class tests the arithmeticity of a graph which has no dotted edge and which is non-cocompact. It uses Vinberg's criteria. More...

#include <arithmeticity.h>

Collaboration diagram for Arithmeticity:

Public Member Functions
	Arithmeticity ()
	Basic constructor. More...
	~Arithmeticity ()
	Destructor. More...
void	test (CoxIter &ci, const bool &bListCycles_)
	Test the arithmeticity of a graph. More...
vector< string >	get_strListCycles ()
	Return the list of cycles. More...
string	get_strError ()
	Return the error code. More...

Private Member Functions
unsigned int	collapseQueues ()
	Try to collapse queues of the graph. More...
void	testCycles ()
	Test the cycles. More...
void	findCycles (const unsigned int &iRoot, const unsigned int &iFrom)
	Look for cycles. More...
void	testCycle ()
	Test the cycle in iPath. More...

Private Attributes
string	strError
	If an error occured, small text. More...
CoxIter *	ci
	Pointer to the CoxIter object. More...
unsigned int	iVerticesCount
	Number of generators of the group. More...
vector< vector< unsigned int > >	iCoxeterMatrix
	Coxeter matrix of the group. More...
vector< unsigned int >	iReferencesToLabels
	Correspondence for the new indices to the old ones. More...
vector< vector< bool > >	bEdgesVisited
	Traversed edges. More...
vector< bool >	bVerticesVisited
	Taversed vertices. More...
vector< unsigned int >	iPath
	Current path. More...
bool	bNotArithmetic
	True if not arithmetic (i.e. we have to quit the algorithm) More...
bool	bListCycles
	If true, will list the cycles to be manually tested. More...
vector< string >	strListCycles
	The list. More...

Detailed Description

This class tests the arithmeticity of a graph which has no dotted edge and which is non-cocompact. It uses Vinberg's criteria.

Constructor & Destructor Documentation

Arithmeticity::Arithmeticity

(

)

Basic constructor.

Arithmeticity::~Arithmeticity

(

)

Destructor.

Member Function Documentation

Arithmeticity::collapseQueues ( )

private

Try to collapse queues of the graph.

Returns

Number of vertices removed

Arithmeticity::findCycles ( const unsigned int &  iRoot, const unsigned int &  iFrom  )

private

Look for cycles.

Update the vector iPath to find cycles

Parameters

iRoot(	unsigned int& ) Starting vertex
iFrom(	unsigned int& ) Previoud vertex (if recursive call); iRoot otherwise

Arithmeticity::get_strError

(

)

Return the error code.

Returns

Error code (string)

Arithmeticity::get_strListCycles

(

)

Return the list of cycles.

Returns

List (vector<string>)

Arithmeticity::test	(	CoxIter &	ci,
		const bool &	bListCycles_
	)

Test the arithmeticity of a graph.

Parameters

ci(	CoxIter& ) The graph
bListCycles_(	const bool& ) If true, will list the cycles to be manually tested

Returns

True if success, false otherwise. Then, use ci.get_iIsArithmetic( )

Arithmeticity::testCycle ( )

private

Test the cycle in iPath.

This function is called by findCycles. Eventually, set bNotArithmetic to true

Arithmeticity::testCycles ( )

private

Test the cycles.

Member Data Documentation

vector< vector< bool > > Arithmeticity::bEdgesVisited

private

Traversed edges.

bool Arithmeticity::bListCycles

private

If true, will list the cycles to be manually tested.

bool Arithmeticity::bNotArithmetic

private

True if not arithmetic (i.e. we have to quit the algorithm)

vector< bool > Arithmeticity::bVerticesVisited

private

Taversed vertices.

CoxIter* Arithmeticity::ci

private

Pointer to the CoxIter object.

vector< vector< unsigned int > > Arithmeticity::iCoxeterMatrix

private

Coxeter matrix of the group.

vector< unsigned int > Arithmeticity::iPath

private

Current path.

vector< unsigned int > Arithmeticity::iReferencesToLabels

private

Correspondence for the new indices to the old ones.

unsigned int Arithmeticity::iVerticesCount

private

Number of generators of the group.

string Arithmeticity::strError

private

If an error occured, small text.

vector< string > Arithmeticity::strListCycles

private

The list.

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

• arithmeticity.h
• arithmeticity.cpp