Main class for the work. More...

#include <coxiter.h>

Collaboration diagram for CoxIter:

Public Member Functions
	CoxIter ()
	Default constructor. Initialize the default values. More...

	CoxIter (const vector< vector< unsigned int > > &iMatrix, const unsigned int &iDimension)
	Constructor. More...

	~CoxIter ()

bool	bRunAllComputations ()
	Do all the computations. More...

void	printCoxeterMatrix ()
	Print Coxeter matrix. More...

void	printCoxeterGraph ()
	Print Coxeter graph. More...

void	printGramMatrix ()
	Print the Gram matrix. More...

void	printGramMatrix_GAP ()
	Print the Gram matrix (format: GAP) More...

void	printGramMatrix_Mathematica ()
	Print the Gram matrix (format: Mathematica) More...

void	printGramMatrix_PARI ()
	Print the Gram matrix (format: PARI) More...

void	printGramMatrix_LaTeX ()
	Print the Gram matrix (format: LaTeX) More...

void	printEdgesVisitedMatrix ()
	Display the visited edges. More...

bool	bReadGraphFromFile (const string &strInputFilename)
	Read the graph from a file. More...

bool	bWriteGraphToDraw (const string &strOutFilenameBasis)
	Write the graph in a file for GraphViz. More...

bool	bWriteGraph (const string &strFilename)
	Write the graph in a file (so that it can be read by CoxIter) More...

bool	parseGraph (istream &streamIn)
	Read and parse graph from stream. More...

void	exploreGraph ()
	Explore the graph (via iCoxeterMatrix) to gind subgraphs. More...

bool	bEulerCharacteristicFVector ()
	Conmpute the euler characteristic and f-vector. More...

void	growthSeries ()

int	iIsGraphCocompact ()
	Check whether the graph is cocompact or not Remark: If the programm was not called with the -compacity flag, the function does nothing. More...

int	isFiniteCovolume ()
	Check whether the graph is of finite covolume or not Remark: If the programm was not called with the -fv flag, the function does nothing. More...

bool	bCanBeFiniteCovolume ()
	Check whether the group can be of finite covolume or no Remark: If true, it does not mean that the group is of finite covolume. The function only provides a faster test if we think that the group is of infinite covolume. We also suppose that this function is called alone most of the time (i.e. that we won't call bCheckFiniteCovolume after that, most of the time). More...

vector< vector< short unsigned int > >	bCanBeFiniteCovolume_complete ()
	Check whether the group can be of finite covolume or no. More...

void	computeGraphsProducts ()
	Compute the possible products of the irreducible graphs. More...

void	printGrowthSeries ()
	Display the growth series. More...

void	printEuclideanGraphsProducts (vector< map< vector< vector< short unsigned int > >, unsigned int > > *graphsProductsCount)
	Display the euclidean graph products found. More...

bool	bIsVertexValid (const string &strVertexLabel) const
	Test if a vertex exists in the graph. More...

unsigned int	get_iVertexIndex (const string &strVertexLabel) const
	Get the index of a vertex. More...

string	get_strVertexLabel (const unsigned int &iVertex) const
	Get the label of a vertex. More...

string	get_strError () const
	Retourne le code d'erreur. More...

MPZ_rational	get_brEulerCaracteristic () const
	return brEulerCaracteristic More...

string	get_strEulerCaracteristic () const
	return brEulerCaracteristic More...

string	get_strEulerCharacteristic_computations () const
	Return the computations needed to determine Euler's characteristic. More...

int	get_iFVectorAlternateSum () const
	Return the alternating sum of the componenents of the f-vector. More...

vector< unsigned int >	get_iFVector () const
	Return the f-vector. More...

unsigned int	get_iVerticesAtInfinityCount () const
	Return the number of vertices at infinity. More...

unsigned int	get_iIrreducibleSphericalGraphsCount () const
	Return the number of irreducible spherical graphs. More...

bool	get_bWriteInfo () const
	Return bWriteInfo. More...

bool	get_bDebug () const
	Return get_bDebug. More...

unsigned int	get_iDimension () const
	Return the dimension. More...

bool	get_bDimensionGuessed () const
	Return true if the dimension was guessed. More...

int	get_iIsCocompact ()
	Return the value of iIsCompact. More...

int	get_iIsFiniteCovolume ()
	Return the value of iIsFiniteCovolume. More...

int	get_iIsArithmetic () const
	Arithmetic? More...

vector< vector< unsigned int > >	get_iCoxeterMatrix () const
	Return the Coxeter matrix. More...

map< unsigned int, string >	get_strWeights () const

string	get_strCoxeterMatrix () const
	Return the Coxeter matrix. More...

vector< vector< string > >	get_array_str_2_GramMatrix () const
	Return the entries of 2*G (string) More...

string	get_strGramMatrix () const
	Returns the Gram matrix. More...

string	get_strCoxeterGraph () const
	Returns the Coxeter graph. More...

string	get_strGramMatrix_GAP () const
	Returns the Gram matrix (format GAP) More...

string	get_strGramMatrix_LaTeX () const
	Returns the Gram matrix (format LaTeX) More...

string	get_strGramMatrix_Mathematica () const
	Returns the Gram matrix (format Mathematica) More...

string	get_strGramMatrix_PARI () const
	Returns the Gram matrix (format PARI) More...

string	get_strGramMatrixField () const
	Field generated by the entries of the Gram matrix (string) More...

unsigned int	get_iVerticesCount () const
	Retourne le nombre de sommets du graphe. More...

bool	get_bHasDottedLine () const
	Does the graph have at least one dotted edge? More...

int	get_iHasDottedLineWithoutWeight () const
	Does the graph have dotted edges without weights? More...

vector< string >	get_str_map_vertices_indexToLabel () const
	Return the label of the vertices. More...

void	set_iIsArithmetic (const unsigned int &iArithmetic)
	Update the member iIsArithmetic. More...

void	set_bCheckCocompactness (const bool &bValue)

void	set_bCheckCofiniteness (const bool &bValue)

void	set_bDebug (const bool &bValue)

void	set_bUseOpenMP (const bool &bValue)

void	set_strOutputFilename (const string &strValue)

void	set_sdtoutToFile (const string &strFilename)

void	set_strVerticesToRemove (const vector< string > &strVerticesRemove_)

void	set_strVerticesToConsider (const vector< string > &strVerticesToConsider)

void	set_bWriteInfo (const bool &bNewValue)
	Set bWriteInfo. More...

void	set_iDimension (const unsigned int &iDimension_)
	Update the member iDimension. More...

GraphsList *	get_gl_graphsList_spherical () const

GraphsList *	get_gl_graphsList_euclidean () const

bool	get_b_hasSphericalGraphsOfRank (const unsigned int &iRank) const

bool	get_b_hasEuclideanGraphsOfRank (const unsigned int &iRank) const

void	get_iGrowthSeries (vector< unsigned int > &iCyclotomicNumerator, vector< mpz_class > &iPolynomialDenominator, bool &bReduced)
	Return the growth series of the group. More...

bool	get_bGrowthSeriesReduced ()
	Return true if the fraction is reduced. More...

vector< mpz_class >	get_iGrowthSeries_denominator ()

string	get_strGrowthSeries ()

string	get_strGrowthSeries_raw ()

const vector< vector< GraphsProductSet > > *	get_ptr_graphsProducts () const
	Return the list of graphs products Remark: there is absolutely no verification. More...

void	set_iCoxeterMatrix (const vector< vector< unsigned int > > &iMat)
	Set the Coxeter matrix. More...

void	set_strOuputMathematicalFormat (const string &strO)

void	map_vertices_labels_removeReference (const unsigned int &iIndex)
	Remove the references to a vertex (for the label) More...

void	map_vertices_labels_addReference (const string &strLabel)
	Add a references for a new vertex. More...

void	map_vertices_labels_create ()
	Create labels if there is none (int –> string) More...

void	map_vertices_labels_reinitialize ()
	Create labels if there with int. More...

Private Member Functions
	CoxIter (const CoxIter &)
	We do not want to do this. More...

void	initializations ()
	Une fois le nombre de sommets du graphe connu (via inputRead( ) ), fait divers initialisations de variables. More...

void	DFS (unsigned int iRoot, unsigned int iFrom)
	Look for all the An starting from a given vertex. More...

void	printPath ()
	Print the iPath vector. More...

void	addGraphsFromPath ()
	Find the different type of graphs (An, Bn, Dn, En, Hn, F4) from any An. More...

void	AnToEn_AnToTEn (const vector< short unsigned int > &iPathTemp, const vector< bool > &bVerticesLinkable)
	Essaie de construire des En depuis un An. More...

void	AnToEn_AnToTEn (const vector< short unsigned int > &iPathTemp, const vector< bool > &bVerticesLinkable, const bool &bSpherical, const short unsigned int &iStart)
	Try to foind an En from an An. More...

void	B3ToF4_B4ToTF4 (const vector< bool > &bVerticesBeginLinkable, vector< short unsigned int > iPathTemp, const short unsigned int &iVEnd)
	Essaie de construire un F4 depuis un B3. More...

void	computeGraphsProducts (GraphsListIterator grIt, vector< map< vector< vector< short unsigned int > >, unsigned int > > *graphsProductsCount, const bool &bSpherical, GraphsProduct &gp, vector< bool > &bGPVerticesNonLinkable)
	Try to find products of connected graphs. More...

void	bCanBeFiniteCovolume_computeGraphsProducts (GraphsListIterator grIt, GraphsProduct &gp, vector< bool > &bGPVerticesNonLinkable)

void	bCanBeFiniteCovolume_complete_computeGraphsProducts (GraphsListIterator grIt, GraphsProduct &gp, vector< bool > &bGPVerticesNonLinkable)

mpz_class	i_orderFiniteSubgraph (const unsigned int &iType, const unsigned int &iDataSupp)
	Order of a connected spherical graph. More...

bool	b_isGraph_cocompact_finiteVolume_parallel (unsigned int iIndex)
	Check whether the graph is cocompact or not or has finite covolume or not Called by: iIsGraphCocompact and iIsFiniteCovolume. More...

bool	b_isGraph_cocompact_finiteVolume_sequential (unsigned int iIndex)
	Check whether the graph is cocompact or not or has finite covolume or not Called by: iIsGraphCocompact and iIsFiniteCovolume. More...

void	growthSeries_symbolExponentFromProduct (const vector< vector< short unsigned int > > &iProduct, vector< unsigned int > &iSymbol, unsigned int &iExponent) const

void	growthSeries_symbolExponentFromProduct (const vector< vector< short unsigned int > > &iProduct, string &strSymbol, unsigned int &iExponent) const

void	growthSeries_parallel ()

void	growthSeries_sequential ()

void	growthSeries_details ()

void	growthSeries_mergeTerms (vector< mpz_class > &iPolynomial, vector< unsigned int > &iSymbol, vector< mpz_class > iTemp_polynomial, const vector< unsigned int > &iTemp_symbol, mpz_class biTemp=1)

Private Attributes
string	strError
	Error code. More...

bool	bDebug
	If true, prints additionnal information. More...

bool	bUseOpenMP
	Use OpenMP. More...

bool	bWriteInfo
	If we want to write informations (false if CoxIter is used "as a plugin") More...

bool	bWriteProgress
	If we want to display the progress // TODO: option. More...

bool	bCoutFile
	True if we want to redirect cout to a file. More...

ofstream *	outCout
	Flow to the file. More...

streambuf *	sBufOld
	To reset the cout, at the end. More...

string	strOuputMathematicalFormat
	Format for mathematical output (generic, mathematica) More...

unsigned int	iVerticesCount
	Number of vertices. More...

unsigned int	iDimension
	Dimension (or 0) More...

unsigned int	iSphericalMaxRankFound
	Maximal rank for a spherical graph. More...

unsigned int	iEuclideanMaxRankFound
	Maximal rank for an euclidean graph. More...

bool	bDimension_guessed
	If the dimension was not specified but guessed. More...

bool	bGraphExplored
	True if we looked for connected subgraphs (affine and spherical) More...

bool	bGraphsProductsComputed
	True if we computed the graphs products. More...

bool	bGrowthSeriesComputed
	True if we computed the growth series. More...

bool	bHasDottedLine
	True if the graph has a dotted line. More...

int	iHasDottedLineWithoutWeight
	If the graph dotted lines without weight (-1: maybe, 0: no, 1: yes) More...

bool	bHasBoldLine
	True if the graph has a bold line. More...

bool	bCheckCocompactness
	True if we want to check the cocompacity. More...

bool	bCheckCofiniteness
	True if we want to check the finite covolume condition. More...

int	iIsCocompact
	1 If cocompact, 0 if not, -1 if don't know, -2 if not tested More...

int	iIsArithmetic
	1 If arithmetic, 0 if non-arithmetic, -1 if don't know More...

int	iIsFiniteCovolume
	1 If finite covolume, 0 if not, -1 if don't know (or cannot know), -2 if not tested More...

vector< string >	strVerticesRemove
	Vertices to be removed. More...

vector< string >	strVertices
	Vertices to be taken. More...

map< string, unsigned int >	map_vertices_labelToIndex
	For the correspondance: label <-> indexes of vertices. More...

vector< string >	map_vertices_indexToLabel
	For the correspondance: label <-> indexes of vertices. More...

vector< vector< unsigned int > >	iCoxeterMatrix
	Coxeter matrix. More...

map< unsigned int, string >	strWeights
	Weights of the dotted lines (via linearization) More...

vector< vector< bool > >	bEdgesVisited
	For the DFS: traversed edges. More...

vector< bool >	bVerticesVisited
	For the DFS: traversed vertices. More...

vector< short unsigned int >	iPath
	chemin en cours (pour le DFS) More...

string	strGramMatrixField
	Field generated by the entries of the Gram matrix. More...

bool	bGramMatrixField
	True if the field was determined. More...

GraphsList *	graphsList_spherical
	Pointer to the list of spherical graphs. More...

GraphsList *	graphsList_euclidean
	Pointer to the list of euclidean graphs. More...

vector< vector< GraphsProductSet > >	graphsProducts

vector< vector< GraphsProductSet > >	graphsProducts_bCanBeFiniteCovolume

vector< map< vector< vector< short unsigned int > >, unsigned int > >	graphsProductsCount_spherical

vector< map< vector< vector< short unsigned int > >, unsigned int > >	graphsProductsCount_euclidean
	Count graphs products (with their multiplicities) More...

vector< mpz_class >	iFactorials

vector< mpz_class >	iPowersOf2
	Some factorials and powers of two. More...

MPZ_rational	brEulerCaracteristic
	Euler characteristic. More...

string	strEulerCharacteristic_computations
	Euler characteristic (without the computations done) More...

int	iFVectorAlternateSum
	Alternating sum of the components of the f-vector. More...

vector< unsigned int >	iFVector
	F-vector. More...

unsigned int	iVerticesAtInfinityCount
	Number of vertices at infinity. More...

vector< mpz_class >	growthSeries_iPolynomialDenominator
	(i-1)th term contains the coefficient of x^i More...

vector< unsigned int >	growthSeries_iCyclotomicNumerator
	Contains a list oif cyclotomic polynomials. More...

bool	growthSeries_bFractionReduced
	True if the fraction has been reduced (it is always the case when the cyclotomic terms are <= 60, which is... always (except if we find an hyperbolic group in H^31)) More...

string	growthSeries_raw
	Row series, not simplified. More...

Friends
ostream &	operator<< (ostream &, CoxIter const &)

Detailed Description

Main class for the work.

Remarks: This must be compiled with C++11 and a few other stuff (see documentation)

Constructor & Destructor Documentation

CoxIter::CoxIter ( )

Default constructor. Initialize the default values.

CoxIter::CoxIter	(	const vector< vector< unsigned int > > &	iMatrix,
		const unsigned int &	iDimension
	)

Constructor.

Parameters

iMatrix(	const vector< vector<unsigned int> >& ) Coxeter matrix
iDimension(	const unsigned int & ) Dimension

CoxIter does not verification on iMatrix. Especially, it is assumed that iMatrix is symmetric

CoxIter::~CoxIter ( )

CoxIter::CoxIter ( const CoxIter & )

private

We do not want to do this.

Member Function Documentation

CoxIter::addGraphsFromPath ( )

private

Find the different type of graphs (An, Bn, Dn, En, Hn, F4) from any An.

Based on the content of iPath

CoxIter::AnToEn_AnToTEn	(	const vector< short unsigned int > &	iPathTemp,
		const vector< bool > &	bVerticesLinkable
	)

private

Essaie de construire des En depuis un An.

Parameters

iPathTemp(	vector<short unsigned int>& ) Chemin actuel composant le An
bVerticesLinkable(	const vector< bool >& ) Ce qui est liable ou non au graphe

CoxIter::AnToEn_AnToTEn	(	const vector< short unsigned int > &	iPathTemp,
		const vector< bool > &	bVerticesLinkable,
		const bool &	bSpherical,
		const short unsigned int &	iStart
	)

private

Try to foind an En from an An.

Parameters

iPathTemp	( const vector<unsigned int>& ) Vertices of the An
bVerticesLinkable(	const vector<bool> & ) Linkable vertices
bSpherical(	const bool& ) True if spherical, false if euclidean
iStart(	const unsigned int& ) Starting point

CoxIter::B3ToF4_B4ToTF4	(	const vector< bool > &	bVerticesBeginLinkable,
		vector< short unsigned int >	iPathTemp,
		const short unsigned int &	iVEnd
	)

private

Essaie de construire un F4 depuis un B3.

Parameters

bVerticesBeginLinkable(	const vector<bool> & ) What's linkable to the B3
iPathTemp	(vector<unsigned int>) Vertices of the B3
iVEnd	Index of the vertex connected by a 4

CoxIter::b_isGraph_cocompact_finiteVolume_parallel ( unsigned int iIndex )

private

Check whether the graph is cocompact or not or has finite covolume or not Called by: iIsGraphCocompact and iIsFiniteCovolume.

Parameters

iIndex( unsigned int ): 1 if test for compacity, 2 if test for the finite covolume

Returns: True or false

CoxIter::b_isGraph_cocompact_finiteVolume_sequential ( unsigned int iIndex )

private

Check whether the graph is cocompact or not or has finite covolume or not Called by: iIsGraphCocompact and iIsFiniteCovolume.

Parameters

iIndex( unsigned int ): 1 if test for compacity, 2 if test for the finite covolume

Returns: True or false

CoxIter::bCanBeFiniteCovolume ( )

Check whether the group can be of finite covolume or no Remark: If true, it does not mean that the group is of finite covolume. The function only provides a faster test if we think that the group is of infinite covolume. We also suppose that this function is called alone most of the time (i.e. that we won't call bCheckFiniteCovolume after that, most of the time).

Returns: True is the group can be of finite covolume, false if the group is of infinite covolume

< Current graphs product

CoxIter::bCanBeFiniteCovolume_complete ( )

Check whether the group can be of finite covolume or no.

Returns: The list of affine graphs which cannot be extended to an affine graph of rank n-1. If the list is empty, then it is possible that the group has finite covolume.

< Current graphs product

void CoxIter::bCanBeFiniteCovolume_complete_computeGraphsProducts	(	GraphsListIterator	grIt,
		GraphsProduct &	gp,
		vector< bool > &	bGPVerticesNonLinkable
	)

private

void CoxIter::bCanBeFiniteCovolume_computeGraphsProducts	(	GraphsListIterator	grIt,
		GraphsProduct &	gp,
		vector< bool > &	bGPVerticesNonLinkable
	)

private

CoxIter::bEulerCharacteristicFVector ( )

Conmpute the euler characteristic and f-vector.

Returns: True if success

CoxIter::bIsVertexValid ( const string & strVertexLabel ) const

Test if a vertex exists in the graph.

Parameters

strVertexLabel( const string& ) Label of the vertex

Returns: True if the vertex exists, false otherwise

CoxIter::bReadGraphFromFile ( const string & strInputFilename )

Read the graph from a file.

Parameters

strInputFilename( const string& ) Path to the file

Returns: True if success

CoxIter::bRunAllComputations ( )

Do all the computations.

Call the followings functions:
readGraph( )
exploreGraph( )
computeGraphsProducts( )
euler( )
isFiniteCovolume( )
iIsGraphCocompact( )

Returns: True if success

CoxIter::bWriteGraph ( const string & strFilename )

Write the graph in a file (so that it can be read by CoxIter)

Parameters

strFilename( const string & )

Returns: True if success, false otherwise

CoxIter::bWriteGraphToDraw ( const string & strOutFilenameBasis )

Write the graph in a file for GraphViz.

The graph is written in szOutputGraphFilename + ".graphviz"

Parameters

strOutFilenameBasis( const string& ) Filename

Returns: True if OK, false otherwise

CoxIter::computeGraphsProducts ( )

Compute the possible products of the irreducible graphs.

< Current graphs product

CoxIter::computeGraphsProducts	(	GraphsListIterator	grIt,
		vector< map< vector< vector< short unsigned int > >, unsigned int > > *	graphsProductsCount,
		const bool &	bSpherical,
		GraphsProduct &	gp,
		vector< bool > &	bGPVerticesNonLinkable
	)

private

Try to find products of connected graphs.

Parameters

grIt(	GraphsListIterator ): Iterator on the list
graphsProductsCount(	vector< map<vector< vector<short unsigned int> >, unsigned int> >* ) Point to the list of graphs
bSpherical(	const bool& ): True if spherical, false if euclidean
gp(	GraphsProduct& ) To store the product (for the cocompacity and finite covolume tests)
bGPVerticesNonLinkable(	vector< bool >& ) Vertices which cannot be linked to the current product

CoxIter::DFS	(	unsigned int	iRoot,
		unsigned int	iFrom
	)

private

Look for all the An starting from a given vertex.

Thie function calls addGraphsFromPath() for each maximal An found

Parameters

iRoot	Starting point
iFrom	Previous vertex (or iRoot if first call)

CoxIter::exploreGraph ( )

Explore the graph (via iCoxeterMatrix) to gind subgraphs.

First, we find all the chains startings from every vertex. Then, we wxpand the chains to spherical and euclidean graphs

CoxIter::get_array_str_2_GramMatrix ( ) const

Return the entries of 2*G (string)

Returns: Entries of 2*G

bool CoxIter::get_b_hasEuclideanGraphsOfRank ( const unsigned int & iRank ) const

bool CoxIter::get_b_hasSphericalGraphsOfRank ( const unsigned int & iRank ) const

CoxIter::get_bDebug ( ) const

Return get_bDebug.

Returns: get_bDebug

CoxIter::get_bDimensionGuessed ( ) const

Return true if the dimension was guessed.

Returns: True if the dimension was guessed

CoxIter::get_bGrowthSeriesReduced ( )

Return true if the fraction is reduced.

Returns: True if the fraction is reduced

CoxIter::get_bHasDottedLine ( ) const

Does the graph have at least one dotted edge?

Returns: Yes if the graph has at least one dotted edge

CoxIter::get_brEulerCaracteristic ( ) const

return brEulerCaracteristic

Returns: brEulerCaracteristic (MPZ_rational)

CoxIter::get_bWriteInfo ( ) const

Return bWriteInfo.

Returns: bWriteInfo

GraphsList * CoxIter::get_gl_graphsList_euclidean ( ) const

GraphsList * CoxIter::get_gl_graphsList_spherical ( ) const

CoxIter::get_iCoxeterMatrix ( ) const

Return the Coxeter matrix.

Return the weights of the dotted lines.

Returns: Coxeter matrix; Weights of the dotted lines

CoxIter::get_iDimension ( ) const

Return the dimension.

Returns: Dimension (0 if not specified/guessed)

CoxIter::get_iFVector ( ) const

Return the f-vector.

Returns: f-vector

CoxIter::get_iFVectorAlternateSum ( ) const

Return the alternating sum of the componenents of the f-vector.

Returns: Alternating sum of the componenents of the f-vector (int)

CoxIter::get_iGrowthSeries	(	vector< unsigned int > &	iCyclotomicNumerator,
		vector< mpz_class > &	iPolynomialDenominator,
		bool &	bReduced
	)

Return the growth series of the group.

Parameters

iCyclotomicNumerator(	vector<unsigned int>& ) Numerator (cyclotomic factors)
iPolynomialDenominator(	vector< mpz_class >& ) Denominator
bReduced(	bool& ) True if the fraction is reduced

vector< mpz_class > CoxIter::get_iGrowthSeries_denominator ( )

CoxIter::get_iHasDottedLineWithoutWeight ( ) const

Does the graph have dotted edges without weights?

Returns: -1: maybe, 0: no, 1: yes

CoxIter::get_iIrreducibleSphericalGraphsCount ( ) const

Return the number of irreducible spherical graphs.

Returns: Return the number of irreducible spherical graphs

CoxIter::get_iIsArithmetic ( ) const

Arithmetic?

Returns: 1 if arithmetic, 0 if not, -1 if not known

CoxIter::get_iIsCocompact ( )

Return the value of iIsCompact.

Returns: 1 if cocompact, 0 if not, -1 if not tested

CoxIter::get_iIsFiniteCovolume ( )

Return the value of iIsFiniteCovolume.

Returns: 1 if finite covolume, 0 if not, -1 if not tested

CoxIter::get_iVertexIndex ( const string & strVertexLabel ) const

Get the index of a vertex.

Parameters

strVertexLabel( const string& ) Label of the vertex

Returns: Index of the vertex (throw an exception if the vertex does not exist)

CoxIter::get_iVerticesAtInfinityCount ( ) const

Return the number of vertices at infinity.

Returns: Return the number of vertices at infinity

CoxIter::get_iVerticesCount ( ) const

Retourne le nombre de sommets du graphe.

Returns: Retourne le nombre de sommets du graphe (int)

CoxIter::get_ptr_graphsProducts ( ) const

Return the list of graphs products Remark: there is absolutely no verification.

CoxIter::get_str_map_vertices_indexToLabel ( ) const

Return the label of the vertices.

Returns: The labels of the vertices

CoxIter::get_strCoxeterGraph ( ) const

Returns the Coxeter graph.

Returns: Gram graph (string)

CoxIter::get_strCoxeterMatrix ( ) const

Return the Coxeter matrix.

Returns: Coxeter matrix (string)

CoxIter::get_strError ( ) const

Retourne le code d'erreur.

Returns: Code d'erreur (string)

CoxIter::get_strEulerCaracteristic ( ) const

return brEulerCaracteristic

Returns: Euler characteristic (string)

CoxIter::get_strEulerCharacteristic_computations ( ) const

Return the computations needed to determine Euler's characteristic.

Returns: strEulerCharacteristic_computations (string)

CoxIter::get_strGramMatrix ( ) const

Returns the Gram matrix.

Returns: Gram matrix (string)

CoxIter::get_strGramMatrix_GAP ( ) const

Returns the Gram matrix (format GAP)

Returns: Gram matrix (string)

CoxIter::get_strGramMatrix_LaTeX ( ) const

Returns the Gram matrix (format LaTeX)

Returns: Gram matrix (string)

CoxIter::get_strGramMatrix_Mathematica ( ) const

Returns the Gram matrix (format Mathematica)

Returns: Gram matrix (string)

CoxIter::get_strGramMatrix_PARI ( ) const

Returns the Gram matrix (format PARI)

Returns: Gram matrix (string)

CoxIter::get_strGramMatrixField ( ) const

Field generated by the entries of the Gram matrix (string)

Returns: Field generated by the entries of the Gram matrix (string)

string CoxIter::get_strGrowthSeries ( )

string CoxIter::get_strGrowthSeries_raw ( )

CoxIter::get_strVertexLabel ( const unsigned int & iVertex ) const

Get the label of a vertex.

Parameters

iVertex( const unsigned int& ) Index of the vertex

Returns: Label of the vertex (throw an exception if the vertex does not exist)

std::map< unsigned int, string > CoxIter::get_strWeights ( ) const

CoxIter::growthSeries ( )

Compute the growth series

Remarks: The only purpose of this function is to call growthSeries_parallel or growthSeries_sequential

void CoxIter::growthSeries_details ( )

private

CoxIter::growthSeries_mergeTerms	(	vector< mpz_class > &	iPolynomial,
		vector< unsigned int > &	iSymbol,
		vector< mpz_class >	iTemp_polynomial,
		const vector< unsigned int > &	iTemp_symbol,
		mpz_class	biTemp = `1`
	)

private

Given the parameters, compute iPolynomial/iSymbol += iTemp_polynomial/iTemp_symbol

Parameters

iPolynomial(	vector< mpz_class >& ) First polynomial (by reference)
iSymbol(	vector<short unsigned int>& ) First symbol (by reference)
iTemp_polynomial(	vector< mpz_class > ) Second polynomial
iTemp_symbol(	const vector<short unsigned int>& ) Second symbol
biTemp(	mpz_class ) Eventually, some coefficient for the second polynomial

Returns: Nothing but the first two parameters are modified

CoxIter::growthSeries_parallel ( )

private

Compute the growth series

CoxIter::growthSeries_sequential ( )

private

Compute the growth series

CoxIter::growthSeries_symbolExponentFromProduct	(	const vector< vector< short unsigned int > > &	iProduct,
		vector< unsigned int > &	iSymbol,
		unsigned int &	iExponent
	)		const

private

From a product of graphs, compute the corresponding symbol [n1, n2, ..., nk] together with the exponent.

Parameters

iProduct(	const vector< vector<short unsigned int> >& ) The product of graphs
iSymbol(	vector<short unsigned int>& ) [i] = j means [i, ..., i] j times (parameter by reference)
iExponent(	unsigned int& ) The exponent

CoxIter::growthSeries_symbolExponentFromProduct	(	const vector< vector< short unsigned int > > &	iProduct,
		string &	strSymbol,
		unsigned int &	iExponent
	)		const

private

From a product of graphs, compute the corresponding symbol [n1, n2, ..., nk] together with the exponent.

Parameters

iProduct(	const vector< vector<unsigned int> >& ) The product of graphs
strSymbol(	string& )
iExponent	(u nsigned int& ) The exponent

CoxIter::i_orderFiniteSubgraph	(	const unsigned int &	iType,
		const unsigned int &	iDataSupp
	)

private

Order of a connected spherical graph.

Parameters

iType	Type du graphe (0 = An, 1=Bn, ...)
iDataSupp	Valeur du n pour presque tous les graphes, poids pour un G_2^n

Returns: Ordre (unsigned long int)

CoxIter::iIsGraphCocompact ( )

Check whether the graph is cocompact or not Remark: If the programm was not called with the -compacity flag, the function does nothing.

Returns: Value of iIsCocompact

CoxIter::initializations ( )

private

Une fois le nombre de sommets du graphe connu (via inputRead( ) ), fait divers initialisations de variables.

CoxIter::isFiniteCovolume ( )

Check whether the graph is of finite covolume or not Remark: If the programm was not called with the -fv flag, the function does nothing.

Returns: Value of iIsFiniteCovolume

CoxIter::map_vertices_labels_addReference ( const string & strLabel )

Add a references for a new vertex.

Parameters

strLabel( const string& ) Label of the vertec

CoxIter::map_vertices_labels_create ( )

Create labels if there is none (int –> string)

CoxIter::map_vertices_labels_reinitialize ( )

Create labels if there with int.

CoxIter::map_vertices_labels_removeReference ( const unsigned int & iIndex )

Remove the references to a vertex (for the label)

Parameters

iIndex( const unsigned int& ) iIndex of the vertex

CoxIter::parseGraph ( istream & streamIn )

Read and parse graph from stream.

Parameters

streamIn( const ifstream& ) Stream to the content (file or std::cin)

Returns: True if success

CoxIter::printCoxeterGraph ( )

Print Coxeter graph.

CoxIter::printCoxeterMatrix ( )

Print Coxeter matrix.

CoxIter::printEdgesVisitedMatrix ( )

Display the visited edges.

CoxIter::printEuclideanGraphsProducts ( vector< map< vector< vector< short unsigned int > >, unsigned int > > * graphsProductsCount )

Display the euclidean graph products found.

Parameters

graphsProductsCount( vector< map<vector< vector<short unsigned int> >, unsigned int> >* ) Pointer to the vector contaitning the results

CoxIter::printGramMatrix ( )

Print the Gram matrix.

CoxIter::printGramMatrix_GAP ( )

Print the Gram matrix (format: GAP)

CoxIter::printGramMatrix_LaTeX ( )

Print the Gram matrix (format: LaTeX)

CoxIter::printGramMatrix_Mathematica ( )

Print the Gram matrix (format: Mathematica)

CoxIter::printGramMatrix_PARI ( )

Print the Gram matrix (format: PARI)

CoxIter::printGrowthSeries ( )

Display the growth series.

CoxIter::printPath ( )

private

Print the iPath vector.

void CoxIter::set_bCheckCocompactness ( const bool & bValue )

void CoxIter::set_bCheckCofiniteness ( const bool & bValue )

void CoxIter::set_bDebug ( const bool & bValue )

void CoxIter::set_bUseOpenMP ( const bool & bValue )

CoxIter::set_bWriteInfo ( const bool & bNewValue )

Set bWriteInfo.

Parameters

bNewValue( const bool& ) The new value

Returns: void

CoxIter::set_iCoxeterMatrix ( const vector< vector< unsigned int > > & iMat )

Set the Coxeter matrix.

Parameters

iMat( const vector< vector<short unsigned int> >& ) The matrix

CoxIter::set_iDimension ( const unsigned int & iDimension_ )

Update the member iDimension.

CoxIter::set_iIsArithmetic ( const unsigned int & iArithmetic )

Update the member iIsArithmetic.

This is used by the Arithmeticity class

void CoxIter::set_sdtoutToFile ( const string & strFilename )

void CoxIter::set_strOuputMathematicalFormat ( const string & strO )

void CoxIter::set_strOutputFilename ( const string & strValue )

void CoxIter::set_strVerticesToConsider ( const vector< string > & strVerticesToConsider )

void CoxIter::set_strVerticesToRemove ( const vector< string > & strVerticesRemove_ )

Friends And Related Function Documentation

ostream& operator<<	(	ostream &	,
		CoxIter const &
	)

friend

Member Data Documentation

bool CoxIter::bCheckCocompactness

private

True if we want to check the cocompacity.

bool CoxIter::bCheckCofiniteness

private

True if we want to check the finite covolume condition.

bool CoxIter::bCoutFile

private

True if we want to redirect cout to a file.

bool CoxIter::bDebug

private

If true, prints additionnal information.

bool CoxIter::bDimension_guessed

private

If the dimension was not specified but guessed.

vector< vector<bool> > CoxIter::bEdgesVisited

private

For the DFS: traversed edges.

bool CoxIter::bGramMatrixField

private

True if the field was determined.

bool CoxIter::bGraphExplored

private

True if we looked for connected subgraphs (affine and spherical)

bool CoxIter::bGraphsProductsComputed

private

True if we computed the graphs products.

bool CoxIter::bGrowthSeriesComputed

private

True if we computed the growth series.

bool CoxIter::bHasBoldLine

private

True if the graph has a bold line.

bool CoxIter::bHasDottedLine

private

True if the graph has a dotted line.

MPZ_rational CoxIter::brEulerCaracteristic

private

Euler characteristic.

bool CoxIter::bUseOpenMP

private

Use OpenMP.

vector< bool > CoxIter::bVerticesVisited

private

For the DFS: traversed vertices.

bool CoxIter::bWriteInfo

private

If we want to write informations (false if CoxIter is used "as a plugin")

bool CoxIter::bWriteProgress

private

If we want to display the progress // TODO: option.

GraphsList* CoxIter::graphsList_euclidean

private

Pointer to the list of euclidean graphs.

GraphsList* CoxIter::graphsList_spherical

private

Pointer to the list of spherical graphs.

CoxIter::graphsProducts

private

[0] Spherical products of codimension 1 [1] Spherical products of codimension 0 [2] Euclidean products of codimension 0

OR

[i] => Euclidean products of rank i (for bCanBeFiniteCovolume_complete)

CoxIter::graphsProducts_bCanBeFiniteCovolume

private

Used in bCanBeFiniteCovolume and bCanBeFiniteCovolume_complete [0] Euclidean products of codimension 0

OR

[i] => Euclidean products of rank i

CoxIter::graphsProductsCount_euclidean

private

Count graphs products (with their multiplicities)

External vectors: products of graphs by their number of total vertices
map< vector< vector<short unsigned int> >, unsigned int>
The key is "vector< vector<short unsigned int> >": For each type of graph and each rank, how many times it occurs in the product
For example, the vector [ 0 => [2, 3], 3 => [ 1 ] ] corresponds to: A1 x A1 x A2 x A2 X A2 x D3
la valeur est le nombre de fois que le produit apparait

CoxIter::graphsProductsCount_spherical

private

bool CoxIter::growthSeries_bFractionReduced

private

True if the fraction has been reduced (it is always the case when the cyclotomic terms are <= 60, which is... always (except if we find an hyperbolic group in H^31))

vector<unsigned int> CoxIter::growthSeries_iCyclotomicNumerator

private

Contains a list oif cyclotomic polynomials.

vector< mpz_class > CoxIter::growthSeries_iPolynomialDenominator

private

(i-1)th term contains the coefficient of x^i

string CoxIter::growthSeries_raw

private

Row series, not simplified.

vector< vector <unsigned int > > CoxIter::iCoxeterMatrix

private

Coxeter matrix.

unsigned int CoxIter::iDimension

private

Dimension (or 0)

unsigned int CoxIter::iEuclideanMaxRankFound

private

Maximal rank for an euclidean graph.

vector< mpz_class > CoxIter::iFactorials

private

vector<unsigned int> CoxIter::iFVector

private

F-vector.

int CoxIter::iFVectorAlternateSum

private

Alternating sum of the components of the f-vector.

int CoxIter::iHasDottedLineWithoutWeight

private

If the graph dotted lines without weight (-1: maybe, 0: no, 1: yes)

int CoxIter::iIsArithmetic

private

1 If arithmetic, 0 if non-arithmetic, -1 if don't know

int CoxIter::iIsCocompact

private

1 If cocompact, 0 if not, -1 if don't know, -2 if not tested

int CoxIter::iIsFiniteCovolume

private

1 If finite covolume, 0 if not, -1 if don't know (or cannot know), -2 if not tested

vector<short unsigned int> CoxIter::iPath

private

chemin en cours (pour le DFS)

vector< mpz_class > CoxIter::iPowersOf2

private

Some factorials and powers of two.

unsigned int CoxIter::iSphericalMaxRankFound

private

Maximal rank for a spherical graph.

unsigned int CoxIter::iVerticesAtInfinityCount

private

Number of vertices at infinity.

unsigned int CoxIter::iVerticesCount

private

Number of vertices.

vector< string > CoxIter::map_vertices_indexToLabel

private

For the correspondance: label <-> indexes of vertices.

map< string, unsigned int > CoxIter::map_vertices_labelToIndex

private

For the correspondance: label <-> indexes of vertices.

ofstream* CoxIter::outCout

private

Flow to the file.

streambuf* CoxIter::sBufOld

private

To reset the cout, at the end.

string CoxIter::strError

private

Error code.

string CoxIter::strEulerCharacteristic_computations

private

Euler characteristic (without the computations done)

string CoxIter::strGramMatrixField

private

Field generated by the entries of the Gram matrix.

string CoxIter::strOuputMathematicalFormat

private

Format for mathematical output (generic, mathematica)

vector< string > CoxIter::strVertices

private

Vertices to be taken.

vector< string > CoxIter::strVerticesRemove

private

Vertices to be removed.

map< unsigned int, string > CoxIter::strWeights

private

Weights of the dotted lines (via linearization)

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

Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation