Main class for the work. More...

#include <coxiter.h>

Collaboration diagram for CoxIter:

[legend]

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

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

	~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	readGraphFromFile (const string &inputFilename)
	Read the graph from a file. More...

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

bool	writeGraph (const string &filename)
	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 ()

void	IS_computations (const string &t0, const string &s0)

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

void	growthSeries ()

int	isGraphCocompact ()
	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	checkCovolumeFiniteness ()

bool	canBeFiniteCovolume ()
	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 checkFiniteCovolume after that, most of the time). More...

vector< vector< short unsigned int > >	canBeFiniteCovolume_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	isVertexValid (const string &vertexLabel) const
	Test if a vertex exists in the graph. More...

unsigned int	get_vertexIndex (const string &vertexLabel) const
	Get the index of a vertex. More...

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

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

MPZ_rational	get_brEulerCaracteristic () const
	return brEulerCaracteristic More...

string	get_eulerCaracteristicString () const
	return Euler characteristic More...

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

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

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

vector< unsigned int >	get_infSeqFVectorsUnits () const
	Return the units of the f-vector after n-doubling. More...

vector< unsigned int >	get_infSeqFVectorsPowers () const

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

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

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

bool	get_debug () const
	Return get_debug. More...

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

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

int	get_isCocompact ()
	Return the value of isCompact. More...

int	get_isFiniteCovolume ()
	Return the value of isFiniteCovolume. More...

int	get_isArithmetic () const
	Arithmetic? More...

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

unsigned int	get_coxeterMatrixEntry (const unsigned int &i, const unsigned int &j) const
	Return the one entry of the Coxeter matrix. More...

map< unsigned int, string >	get_weights () const
	Return the weights of the dotted lines. More...

string	get_CoxeterMatrixString () const
	Return the Coxeter matrix as a string. More...

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

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

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

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

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

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

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

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

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

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

int	get_hasDottedLineWithoutWeight () 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_isArithmetic (const unsigned int &arithmetic)
	Update the member isArithmetic. More...

void	set_checkCocompactness (const bool &value)

void	set_checkCofiniteness (const bool &value)

void	set_debug (const bool &value)

void	set_useOpenMP (const bool &value)

void	set_outputFilename (const string &filename)

void	set_sdtOutToFile (const string &filename)

void	set_verticesToRemove (const vector< string > &verticesRemove_)

void	set_verticesToConsider (const vector< string > &verticesToConsider)

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

void	set_dimension (const unsigned int &dimension_)
	Update the member dimension. More...

GraphsList *	get_gl_graphsList_spherical () const

GraphsList *	get_gl_graphsList_euclidean () const

bool	get_hasSphericalGraphsOfRank (const unsigned int &rank) const

bool	get_hasEuclideanGraphsOfRank (const unsigned int &rank) const

void	get_growthSeries (vector< unsigned int > &cyclotomicNumerator, vector< mpz_class > &polynomialDenominator, bool &isReduced)

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

vector< mpz_class >	get_growthSeries_denominator ()

string	get_growthSeries ()

string	get_growthSeries_raw ()

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

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

void	set_ouputMathematicalFormat (const string &format)

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

void	map_vertices_labels_addReference (const string &label)
	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 root, unsigned int from)
	Look for all the An starting from a given vertex. More...

void	printPath ()
	Print the path 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 > &pathTemp, const vector< bool > &verticesLinkable)

void	AnToEn_AnToTEn (const vector< short unsigned int > &pathTemp, const vector< bool > &linkableVertices, const bool &isSpherical, const short unsigned int &iStart)

void	B3ToF4_B4ToTF4 (const vector< bool > &linkableVerticesStart, vector< short unsigned int > pathTemp, const short unsigned int &endVertex)
	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 &isSpherical, GraphsProduct &gp, vector< bool > &gpNonLinkableVertices)

void	computeGraphsProducts_IS (GraphsListIterator grIt, const bool &isSpherical, GraphsProduct &gp, vector< bool > &gpNonLinkableVertices)

void	canBeFiniteCovolume_computeGraphsProducts (GraphsListIterator grIt, GraphsProduct &gp, vector< bool > &gpNonLinkableVertices)

void	canBeFiniteCovolume_complete_computeGraphsProducts (GraphsListIterator grIt, GraphsProduct &gp, vector< bool > &gpNonLinkableVertices)

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

bool	isGraph_cocompact_finiteVolume_parallel (unsigned int index)
	Check whether the graph is cocompact or not or has finite covolume or not Called by: isGraphCocompact and isFiniteCovolume. More...

bool	isGraph_cocompact_finiteVolume_sequential (unsigned int index)
	Check whether the graph is cocompact or not or has finite covolume or not Called by: isGraphCocompact and isFiniteCovolume. More...

void	growthSeries_symbolExponentFromProduct (const vector< vector< short unsigned int >> &product, vector< unsigned int > &symbol, unsigned int &exponent) const

void	growthSeries_symbolExponentFromProduct (const vector< vector< short unsigned int >> &product, string &symbol, unsigned int &exponent) const

void	growthSeries_parallel ()

void	growthSeries_sequential ()

void	growthSeries_details ()

void	growthSeries_mergeTerms (vector< mpz_class > &polynomial, vector< unsigned int > &symbol, vector< mpz_class > tempPolynomial, const vector< unsigned int > &tempSymbol, mpz_class biTemp=1)

Private Attributes
string	error
	Error code. More...

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

bool	useOpenMP
	Use OpenMP. More...

bool	bWriteInfo

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	ouputMathematicalFormat

unsigned int	verticesCount
	Number of vertices. More...

unsigned int	maximalSubgraphRank
	Maximal rank of a subgraph. More...

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

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

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

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

bool	isGraphExplored

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

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

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

int	hasDottedLineWithoutWeight

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

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

bool	checkCofiniteness

int	isCocompact

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

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

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

map< string, unsigned int >	map_vertices_labelToIndex

vector< string >	map_vertices_indexToLabel

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

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

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

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

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

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

bool	isGramMatrixFieldKnown
	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...

unsigned int	infSeq_t0
	First reflecting hyperplane. More...

unsigned int	infSeq_s0

vector< unsigned int >	infSeqFVectorsUnits
	(ultra)parallel hyperplane, will be conjugate More...

vector< unsigned int >	infSeqFVectorsPowers
	Components of the f-vector. More...

vector< vector< GraphsProductSet > >	graphsProducts

vector< vector< GraphsProductSet > >	graphsProducts_canBeFiniteCovolume

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 >	factorials

vector< mpz_class >	powersOf2

MPZ_rational	brEulerCaracteristic
	Euler characteristic. More...

string	eulerCharacteristic_computations

int	fVectorAlternateSum
	Alternating sum of the components of thef-vector. More...

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

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

vector< mpz_class >	growthSeries_polynomialDenominator

vector< unsigned int >	growthSeries_cyclotomicNumerator

bool	growthSeries_isFractionReduced

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() [1/3]

CoxIter::CoxIter ( )

Default constructor. Initialize the default values.

◆ CoxIter() [2/3]

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

◆ ~CoxIter()

CoxIter::~CoxIter ( )

◆ CoxIter() [3/3]

CoxIter::CoxIter ( const CoxIter & )

private

We do not want to do this.

Member Function Documentation

◆ addGraphsFromPath()

CoxIter::addGraphsFromPath ( )

private

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

Based on the content of path

◆ AnToEn_AnToTEn() [1/2]

void CoxIter::AnToEn_AnToTEn	(	const vector< short unsigned int > &	pathTemp,
		const vector< bool > &	linkableVertices,
		const bool &	isSpherical,
		const short unsigned int &	iStart
	)

private

◆ AnToEn_AnToTEn() [2/2]

void CoxIter::AnToEn_AnToTEn	(	const vector< short unsigned int > &	pathTemp,
		const vector< bool > &	verticesLinkable
	)

private

◆ B3ToF4_B4ToTF4()

CoxIter::B3ToF4_B4ToTF4	(	const vector< bool > &	linkableVerticesStart,
		vector< short unsigned int >	pathTemp,
		const short unsigned int &	endVertex
	)

private

Essaie de construire un F4 depuis un B3.

Parameters

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

◆ bRunAllComputations()

CoxIter::bRunAllComputations ( )

Do all the computations.

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

Returns: True if success

◆ canBeFiniteCovolume()

CoxIter::canBeFiniteCovolume ( )

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 checkFiniteCovolume after that, most of the time).

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

◆ canBeFiniteCovolume_complete()

CoxIter::canBeFiniteCovolume_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.

◆ canBeFiniteCovolume_complete_computeGraphsProducts()

void CoxIter::canBeFiniteCovolume_complete_computeGraphsProducts	(	GraphsListIterator	grIt,
		GraphsProduct &	gp,
		vector< bool > &	gpNonLinkableVertices
	)

private

◆ canBeFiniteCovolume_computeGraphsProducts()

void CoxIter::canBeFiniteCovolume_computeGraphsProducts	(	GraphsListIterator	grIt,
		GraphsProduct &	gp,
		vector< bool > &	gpNonLinkableVertices
	)

private

◆ checkCovolumeFiniteness()

int CoxIter::checkCovolumeFiniteness ( )

◆ computeEulerCharacteristicFVector()

CoxIter::computeEulerCharacteristicFVector ( )

Conmpute the euler characteristic and f-vector.

Returns: True if success

◆ computeGraphsProducts() [1/2]

CoxIter::computeGraphsProducts ( )

Compute the possible products of the irreducible graphs.

◆ computeGraphsProducts() [2/2]

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

private

◆ computeGraphsProducts_IS()

CoxIter::computeGraphsProducts_IS	(	GraphsListIterator	grIt,
		const bool &	isSpherical,
		GraphsProduct &	gp,
		vector< bool > &	gpNonLinkableVertices
	)

private

sequence

\param grIt(GraphsListIterator): Iterator on the list
\param isSpherical(const bool&): True if spherical, false if euclidean
\param gp(GraphsProduct&) To store the product (for the cocompacity and

finite covolume tests)

Parameters

gpNonLinkableVertices(vector< bool >&) Vertices which cannot be linked to the current product

◆ DFS()

CoxIter::DFS	(	unsigned int	root,
		unsigned int	from
	)

private

Look for all the An starting from a given vertex.

Thie function calls addGraphsFromPath() for each maximal An found

Parameters

root	Starting point
from	Previous vertex (or root if first call)

◆ exploreGraph()

void CoxIter::exploreGraph ( )

\fn exploreGraph
\brief Explore the graph (via coxeterMatrix) to gind subgraphs

First, we find all the chains startings from every vertex. Then, we

expand the chains to spherical and euclidean graphs

◆ get_array_str_2_GramMatrix()

CoxIter::get_array_str_2_GramMatrix ( ) const

Return the entries of 2*G (string)

Returns: Entries of 2*G

◆ get_brEulerCaracteristic()

CoxIter::get_brEulerCaracteristic ( ) const

return brEulerCaracteristic

Returns: brEulerCaracteristic (MPZ_rational)

◆ get_bWriteInfo()

CoxIter::get_bWriteInfo ( ) const

Return bWriteInfo.

Returns: bWriteInfo

◆ get_coxeterGraph()

CoxIter::get_coxeterGraph ( ) const

Returns the Coxeter graph.

Returns: Gram graph (string)

◆ get_coxeterMatrix()

CoxIter::get_coxeterMatrix ( ) const

Return the Coxeter matrix.

Returns: Coxeter matrix

◆ get_coxeterMatrixEntry()

CoxIter::get_coxeterMatrixEntry	(	const unsigned int &	i,
		const unsigned int &	j
	)		const

Return the one entry of the Coxeter matrix.

Returns: Entry

◆ get_CoxeterMatrixString()

CoxIter::get_CoxeterMatrixString ( ) const

Return the Coxeter matrix as a string.

Returns: Coxeter matrix (string)

◆ get_debug()

CoxIter::get_debug ( ) const

Return get_debug.

Returns: get_debug

◆ get_dimension()

CoxIter::get_dimension ( ) const

Return the dimension.

Returns: Dimension (0 if not specified/guessed)

◆ get_dimensionGuessed()

CoxIter::get_dimensionGuessed ( ) const

Return true if the dimension was guessed.

Returns: True if the dimension was guessed

◆ get_error()

CoxIter::get_error ( ) const

Retourne le code d'erreur.

Returns: Code d'erreur (string)

◆ get_eulerCaracteristicString()

CoxIter::get_eulerCaracteristicString ( ) const

return Euler characteristic

Returns: Euler characteristic (string)

◆ get_eulerCharacteristic_computations()

CoxIter::get_eulerCharacteristic_computations ( ) const

Return the computations needed to determine Euler's characteristic.

Returns: eulerCharacteristic_computations (string)

◆ get_fVector()

CoxIter::get_fVector ( ) const

Return the f-vector.

Returns: f-vector

◆ get_fVectorAlternateSum()

CoxIter::get_fVectorAlternateSum ( ) const

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

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

◆ get_gl_graphsList_euclidean()

GraphsList* CoxIter::get_gl_graphsList_euclidean ( ) const

◆ get_gl_graphsList_spherical()

GraphsList* CoxIter::get_gl_graphsList_spherical ( ) const

◆ get_gramMatrix()

CoxIter::get_gramMatrix ( ) const

Returns the Gram matrix.

Returns: Gram matrix (string)

◆ get_gramMatrix_GAP()

CoxIter::get_gramMatrix_GAP ( ) const

Returns the Gram matrix (format GAP)

Returns: Gram matrix (string)

◆ get_gramMatrix_LaTeX()

CoxIter::get_gramMatrix_LaTeX ( ) const

Returns the Gram matrix (format LaTeX)

Returns: Gram matrix (string)

◆ get_gramMatrix_Mathematica()

CoxIter::get_gramMatrix_Mathematica ( ) const

Returns the Gram matrix (format Mathematica)

Returns: Gram matrix (string)

◆ get_gramMatrix_PARI()

CoxIter::get_gramMatrix_PARI ( ) const

Returns the Gram matrix (format PARI)

Returns: Gram matrix (string)

◆ get_gramMatrixField()

CoxIter::get_gramMatrixField ( ) const

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

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

◆ get_growthSeries() [1/2]

string CoxIter::get_growthSeries ( )

◆ get_growthSeries() [2/2]

void CoxIter::get_growthSeries	(	vector< unsigned int > &	cyclotomicNumerator,
		vector< mpz_class > &	polynomialDenominator,
		bool &	isReduced
	)

\fn get_growthSeries
\brief Return the growth series of the group

\param cyclotomicNumerator(vector<unsigned int>&) Numerator (cyclotomic

factors)

Parameters

polynomialDenominator(vector<	mpz_class >&) Denominator
isReduced(bool&)	True if the fraction is reduced

◆ get_growthSeries_denominator()

vector<mpz_class> CoxIter::get_growthSeries_denominator ( )

◆ get_growthSeries_raw()

string CoxIter::get_growthSeries_raw ( )

◆ get_hasDottedLine()

CoxIter::get_hasDottedLine ( ) const

Does the graph have at least one dotted edge?

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

◆ get_hasDottedLineWithoutWeight()

CoxIter::get_hasDottedLineWithoutWeight ( ) const

Does the graph have dotted edges without weights?

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

◆ get_hasEuclideanGraphsOfRank()

bool CoxIter::get_hasEuclideanGraphsOfRank ( const unsigned int & rank ) const

◆ get_hasSphericalGraphsOfRank()

bool CoxIter::get_hasSphericalGraphsOfRank ( const unsigned int & rank ) const

◆ get_infSeqFVectorsPowers()

vector<unsigned int> CoxIter::get_infSeqFVectorsPowers ( ) const

◆ get_infSeqFVectorsUnits()

CoxIter::get_infSeqFVectorsUnits ( ) const

Return the units of the f-vector after n-doubling.

Return the powers of 2^{n-1} of the f-vector after n-doubling.

Returns: Units

◆ get_irreducibleSphericalGraphsCount()

CoxIter::get_irreducibleSphericalGraphsCount ( ) const

Return the number of irreducible spherical graphs.

Returns: Return the number of irreducible spherical graphs

◆ get_isArithmetic()

CoxIter::get_isArithmetic ( ) const

Arithmetic?

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

◆ get_isCocompact()

CoxIter::get_isCocompact ( )

Return the value of isCompact.

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

◆ get_isFiniteCovolume()

CoxIter::get_isFiniteCovolume ( )

Return the value of isFiniteCovolume.

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

◆ get_isGrowthSeriesReduced()

CoxIter::get_isGrowthSeriesReduced ( )

Return true if the fraction is reduced.

Returns: True if the fraction is reduced

◆ get_ptr_graphsProducts()

CoxIter::get_ptr_graphsProducts ( ) const

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

◆ get_str_map_vertices_indexToLabel()

CoxIter::get_str_map_vertices_indexToLabel ( ) const

Return the label of the vertices.

Returns: The labels of the vertices

◆ get_vertexIndex()

CoxIter::get_vertexIndex ( const string & vertexLabel ) const

Get the index of a vertex.

Parameters

vertexLabel(const string&) Label of the vertex

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

◆ get_vertexLabel()

CoxIter::get_vertexLabel ( const unsigned int & vertex ) const

Get the label of a vertex.

Parameters

vertex(const unsigned int&) Index of the vertex

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

◆ get_verticesAtInfinityCount()

CoxIter::get_verticesAtInfinityCount ( ) const

Return the number of vertices at infinity.

Returns: Return the number of vertices at infinity

◆ get_verticesCount()

CoxIter::get_verticesCount ( ) const

Retourne le nombre de sommets du graphe.

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

◆ get_weights()

CoxIter::get_weights ( ) const

Return the weights of the dotted lines.

Returns: Weights of the dotted lines

◆ growthSeries()

CoxIter::growthSeries ( )

Compute the growth series

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

◆ growthSeries_details()

void CoxIter::growthSeries_details ( )

private

◆ growthSeries_mergeTerms()

CoxIter::growthSeries_mergeTerms	(	vector< mpz_class > &	polynomial,
		vector< unsigned int > &	symbol,
		vector< mpz_class >	tempPolynomial,
		const vector< unsigned int > &	tempSymbol,
		mpz_class	biTemp = `1`
	)

private

Given the parameters, compute polynomial/symbol += tempPolynomial/tempSymbol

\param polynomial(vector< mpz_class >&) First polynomial (by reference)
\param symbol(vector<short unsigned int>&) First symbol (by reference)
\param tempPolynomial(vector< mpz_class >) Second polynomial
\param tempSymbol(const vector<short unsigned int>&) Second symbol
\param biTemp(mpz_class) Eventually, some coefficient for the second

polynomial

\return Nothing but the first two parameters are modified

◆ growthSeries_parallel()

CoxIter::growthSeries_parallel ( )

private

Compute the growth series

◆ growthSeries_sequential()

CoxIter::growthSeries_sequential ( )

private

Compute the growth series

◆ growthSeries_symbolExponentFromProduct() [1/2]

void CoxIter::growthSeries_symbolExponentFromProduct	(	const vector< vector< short unsigned int >> &	product,
		string &	symbol,
		unsigned int &	exponent
	)		const

private

◆ growthSeries_symbolExponentFromProduct() [2/2]

void CoxIter::growthSeries_symbolExponentFromProduct	(	const vector< vector< short unsigned int >> &	product,
		vector< unsigned int > &	symbol,
		unsigned int &	exponent
	)		const

private

◆ i_orderFiniteSubgraph()

CoxIter::i_orderFiniteSubgraph	(	const unsigned int &	type,
		const unsigned int &	dataSupp
	)

private

Order of a connected spherical graph.

Parameters

type	Type du graphe (0 = An, 1=Bn, ...)
dataSupp	Valeur du n pour presque tous les graphes, poids pour un G_2^n \return Ordre (unsigned long int)

◆ initializations()

CoxIter::initializations ( )

private

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

◆ IS_computations()

void CoxIter::IS_computations	(	const string &	t0,
		const string &	s0
	)

\fn IS_computations
\brief Do some computations related to the infinite sequence
Remark: It is suppose that both t0, s0 are admissible vertices whose

corresponding hyperplanes are (ultra)parallel

Parameters

t0(const	string&) t0 Reflecting hyperplane
t0(const	string&) s0 Other hyperplane

◆ isGraph_cocompact_finiteVolume_parallel()

CoxIter::isGraph_cocompact_finiteVolume_parallel ( unsigned int index )

private

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

Parameters

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

Returns: True or false

◆ isGraph_cocompact_finiteVolume_sequential()

CoxIter::isGraph_cocompact_finiteVolume_sequential ( unsigned int index )

private

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

Parameters

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

Returns: True or false

◆ isGraphCocompact()

CoxIter::isGraphCocompact ( )

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 isCocompact

◆ isVertexValid()

CoxIter::isVertexValid ( const string & vertexLabel ) const

Test if a vertex exists in the graph.

Parameters

vertexLabel(const string&) Label of the vertex

Returns: True if the vertex exists, false otherwise

◆ map_vertices_labels_addReference()

CoxIter::map_vertices_labels_addReference ( const string & label )

Add a references for a new vertex.

Parameters

label(const string&) Label of the vertec

◆ map_vertices_labels_create()

CoxIter::map_vertices_labels_create ( )

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

◆ map_vertices_labels_reinitialize()

CoxIter::map_vertices_labels_reinitialize ( )

Create labels if there with int.

◆ map_vertices_labels_removeReference()

CoxIter::map_vertices_labels_removeReference ( const unsigned int & index )

Remove the references to a vertex (for the label)

Parameters

index(const unsigned int&) index of the vertex

◆ parseGraph()

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

◆ printCoxeterGraph()

CoxIter::printCoxeterGraph ( )

Print Coxeter graph.

◆ printCoxeterMatrix()

CoxIter::printCoxeterMatrix ( )

Print Coxeter matrix.

◆ printEdgesVisitedMatrix()

CoxIter::printEdgesVisitedMatrix ( )

Display the visited edges.

◆ printEuclideanGraphsProducts()

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

◆ printGramMatrix()

CoxIter::printGramMatrix ( )

Print the Gram matrix.

◆ printGramMatrix_GAP()

CoxIter::printGramMatrix_GAP ( )

Print the Gram matrix (format: GAP)

◆ printGramMatrix_LaTeX()

CoxIter::printGramMatrix_LaTeX ( )

Print the Gram matrix (format: LaTeX)

◆ printGramMatrix_Mathematica()

CoxIter::printGramMatrix_Mathematica ( )

Print the Gram matrix (format: Mathematica)

◆ printGramMatrix_PARI()

CoxIter::printGramMatrix_PARI ( )

Print the Gram matrix (format: PARI)

◆ printGrowthSeries()

CoxIter::printGrowthSeries ( )

Display the growth series.

◆ printPath()

CoxIter::printPath ( )

private

Print the path vector.

◆ readGraphFromFile()

CoxIter::readGraphFromFile ( const string & inputFilename )

Read the graph from a file.

Parameters

inputFilename(const string&) Path to the file

Returns: True if success

◆ set_bWriteInfo()

CoxIter::set_bWriteInfo ( const bool & newValue )

Set bWriteInfo.

Parameters

newValue(const bool&) The new value

Returns: void

◆ set_checkCocompactness()

void CoxIter::set_checkCocompactness ( const bool & value )

◆ set_checkCofiniteness()

void CoxIter::set_checkCofiniteness ( const bool & value )

◆ set_coxeterMatrix()

CoxIter::set_coxeterMatrix ( const vector< vector< unsigned int >> & matrix )

Set the Coxeter matrix.

Parameters

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

◆ set_debug()

void CoxIter::set_debug ( const bool & value )

◆ set_dimension()

CoxIter::set_dimension ( const unsigned int & dimension_ )

Update the member dimension.

◆ set_isArithmetic()

CoxIter::set_isArithmetic ( const unsigned int & arithmetic )

Update the member isArithmetic.

This is used by the Arithmeticity class

◆ set_ouputMathematicalFormat()

void CoxIter::set_ouputMathematicalFormat ( const string & format )

◆ set_outputFilename()

void CoxIter::set_outputFilename ( const string & filename )

◆ set_sdtOutToFile()

void CoxIter::set_sdtOutToFile ( const string & filename )

◆ set_useOpenMP()

void CoxIter::set_useOpenMP ( const bool & value )

◆ set_verticesToConsider()

void CoxIter::set_verticesToConsider ( const vector< string > & verticesToConsider )

◆ set_verticesToRemove()

void CoxIter::set_verticesToRemove ( const vector< string > & verticesRemove_ )

◆ writeGraph()

CoxIter::writeGraph ( const string & filename )

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

Parameters

filename(const string &)

Returns: True if success, false otherwise

◆ writeGraphToDraw()

CoxIter::writeGraphToDraw ( const string & outFilenameBasis )

Write the graph in a file for GraphViz.

The graph is written in outputGraphFilename + ".graphviz"

Parameters

outFilenameBasis(const string&) Filename

Returns: True if OK, false otherwise

Friends And Related Function Documentation

◆ operator<<

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

friend

Member Data Documentation

◆ bCoutFile

bool CoxIter::bCoutFile

private

True if we want to redirect cout to a file.

◆ brEulerCaracteristic

MPZ_rational CoxIter::brEulerCaracteristic

private

Euler characteristic.

◆ bWriteInfo

bool CoxIter::bWriteInfo

private

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

◆ checkCocompactness

bool CoxIter::checkCocompactness

private

True if we want to check the cocompacity.

◆ checkCofiniteness

bool CoxIter::checkCofiniteness

private

True if we want to check the finite covolume condition

◆ coxeterMatrix

vector<vector<unsigned int> > CoxIter::coxeterMatrix

private

Coxeter matrix.

◆ debug

bool CoxIter::debug

private

If true, prints additionnal information.

◆ dimension

unsigned int CoxIter::dimension

private

Dimension (or 0)

◆ error

string CoxIter::error

private

Error code.

◆ euclideanMaxRankFound

unsigned int CoxIter::euclideanMaxRankFound

private

Maximal rank for an euclidean graph.

◆ eulerCharacteristic_computations

string CoxIter::eulerCharacteristic_computations

private

Euler characteristic (without the computations done)

◆ factorials

vector<mpz_class> CoxIter::factorials

private

◆ fVector

vector<unsigned int> CoxIter::fVector

private

F-vector.

◆ fVectorAlternateSum

int CoxIter::fVectorAlternateSum

private

Alternating sum of the components of thef-vector.

◆ gramMatrixField

string CoxIter::gramMatrixField

private

Field generated by the entries of the Gram matrix.

◆ graphsList_euclidean

GraphsList* CoxIter::graphsList_euclidean

private

Pointer to the list of euclidean graphs.

◆ graphsList_spherical

GraphsList* CoxIter::graphsList_spherical

private

Pointer to the list of spherical graphs.

◆ graphsProducts

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 canBeFiniteCovolume_complete)

◆ graphsProducts_canBeFiniteCovolume

CoxIter::graphsProducts_canBeFiniteCovolume

private

Euclidean products of codimension 0

OR

[i] => Euclidean products of rank i

◆ graphsProductsCount_euclidean

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

◆ graphsProductsCount_spherical

CoxIter::graphsProductsCount_spherical

private

◆ growthSeries_cyclotomicNumerator

vector<unsigned int> CoxIter::growthSeries_cyclotomicNumerator

private

Contains a list oif cyclotomic polynomials

◆ growthSeries_isFractionReduced

bool CoxIter::growthSeries_isFractionReduced

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))

◆ growthSeries_polynomialDenominator

vector<mpz_class> CoxIter::growthSeries_polynomialDenominator

private

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

◆ growthSeries_raw

string CoxIter::growthSeries_raw

private

Row series, not simplified.

◆ hasBoldLine

bool CoxIter::hasBoldLine

private

True if the graph has a bold line.

◆ hasDottedLine

bool CoxIter::hasDottedLine

private

True if the graph has a dotted line.

◆ hasDottedLineWithoutWeight

int CoxIter::hasDottedLineWithoutWeight

private

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

◆ infSeq_s0

unsigned int CoxIter::infSeq_s0

private

◆ infSeq_t0

unsigned int CoxIter::infSeq_t0

private

First reflecting hyperplane.

◆ infSeqFVectorsPowers

vector<unsigned int> CoxIter::infSeqFVectorsPowers

private

Components of the f-vector.

◆ infSeqFVectorsUnits

vector<unsigned int> CoxIter::infSeqFVectorsUnits

private

(ultra)parallel hyperplane, will be conjugate

Components of the f-vector

◆ isArithmetic

int CoxIter::isArithmetic

private

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

◆ isCocompact

int CoxIter::isCocompact

private

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

◆ isDimensionGuessed

bool CoxIter::isDimensionGuessed

private

If the dimension was not specified but guessed.

◆ isFiniteCovolume

CoxIter::isFiniteCovolume

private

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.

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

Returns: Value of isFiniteCovolume

◆ isGramMatrixFieldKnown

bool CoxIter::isGramMatrixFieldKnown

private

True if the field was determined.

◆ isGraphExplored

bool CoxIter::isGraphExplored

private

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

◆ isGraphsProductsComputed

bool CoxIter::isGraphsProductsComputed

private

True if we computed the graphs products.

◆ isGrowthSeriesComputed

bool CoxIter::isGrowthSeriesComputed

private

True if we computed the growth series.

◆ map_vertices_indexToLabel

vector<string> CoxIter::map_vertices_indexToLabel

private

For the correspondance: label <-> indexes of vertices

◆ map_vertices_labelToIndex

map<string, unsigned int> CoxIter::map_vertices_labelToIndex

private

For the correspondance: label <-> indexes of vertices

◆ maximalSubgraphRank

unsigned int CoxIter::maximalSubgraphRank

private

Maximal rank of a subgraph.

◆ ouputMathematicalFormat

string CoxIter::ouputMathematicalFormat

private

Format for mathematical output (generic, mathematica)

◆ outCout

ofstream* CoxIter::outCout

private

Flow to the file.

◆ path

vector<short unsigned int> CoxIter::path

private

chemin en cours (pour le DFS)

◆ powersOf2

vector<mpz_class> CoxIter::powersOf2

private

◆ sBufOld

streambuf* CoxIter::sBufOld

private

To reset the cout, at the end.

◆ sphericalMaxRankFound

unsigned int CoxIter::sphericalMaxRankFound

private

Maximal rank for a spherical graph.

◆ useOpenMP

bool CoxIter::useOpenMP

private

Use OpenMP.

◆ vertices

vector<string> CoxIter::vertices

private

Vertices to be taken.

◆ verticesAtInfinityCount

unsigned int CoxIter::verticesAtInfinityCount

private

Number of vertices at infinity.

◆ verticesCount

unsigned int CoxIter::verticesCount

private

Number of vertices.

◆ verticesToRemove

vector<string> CoxIter::verticesToRemove

private

Vertices to be removed.

◆ visitedEdges

vector<vector<bool> > CoxIter::visitedEdges

private

For the DFS: traversed edges.

◆ visitedVertices

vector<bool> CoxIter::visitedVertices

private

For the DFS: traversed vertices.

◆ weightsDotted

map<unsigned int, string> CoxIter::weightsDotted

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

◆ CoxIter() [1/3]

◆ CoxIter() [2/3]

◆ ~CoxIter()

◆ CoxIter() [3/3]

Member Function Documentation

◆ addGraphsFromPath()

◆ AnToEn_AnToTEn() [1/2]

◆ AnToEn_AnToTEn() [2/2]

◆ B3ToF4_B4ToTF4()

◆ bRunAllComputations()

◆ canBeFiniteCovolume()

◆ canBeFiniteCovolume_complete()

◆ canBeFiniteCovolume_complete_computeGraphsProducts()

◆ canBeFiniteCovolume_computeGraphsProducts()

◆ checkCovolumeFiniteness()

◆ computeEulerCharacteristicFVector()

◆ computeGraphsProducts() [1/2]

◆ computeGraphsProducts() [2/2]

◆ computeGraphsProducts_IS()

◆ DFS()

◆ exploreGraph()

◆ get_array_str_2_GramMatrix()

◆ get_brEulerCaracteristic()

◆ get_bWriteInfo()

◆ get_coxeterGraph()

◆ get_coxeterMatrix()

◆ get_coxeterMatrixEntry()

◆ get_CoxeterMatrixString()

◆ get_debug()

◆ get_dimension()

◆ get_dimensionGuessed()

◆ get_error()

◆ get_eulerCaracteristicString()

◆ get_eulerCharacteristic_computations()

◆ get_fVector()

◆ get_fVectorAlternateSum()

◆ get_gl_graphsList_euclidean()

◆ get_gl_graphsList_spherical()

◆ get_gramMatrix()

◆ get_gramMatrix_GAP()

◆ get_gramMatrix_LaTeX()

◆ get_gramMatrix_Mathematica()

◆ get_gramMatrix_PARI()

◆ get_gramMatrixField()

◆ get_growthSeries() [1/2]

◆ get_growthSeries() [2/2]

◆ get_growthSeries_denominator()

◆ get_growthSeries_raw()

◆ get_hasDottedLine()

◆ get_hasDottedLineWithoutWeight()

◆ get_hasEuclideanGraphsOfRank()

◆ get_hasSphericalGraphsOfRank()

◆ get_infSeqFVectorsPowers()

◆ get_infSeqFVectorsUnits()

◆ get_irreducibleSphericalGraphsCount()

◆ get_isArithmetic()

◆ get_isCocompact()

◆ get_isFiniteCovolume()

◆ get_isGrowthSeriesReduced()

◆ get_ptr_graphsProducts()

◆ get_str_map_vertices_indexToLabel()

◆ get_vertexIndex()

◆ get_vertexLabel()

◆ get_verticesAtInfinityCount()

◆ get_verticesCount()

◆ get_weights()

◆ growthSeries()

◆ growthSeries_details()

◆ growthSeries_mergeTerms()

◆ growthSeries_parallel()

◆ growthSeries_sequential()

◆ growthSeries_symbolExponentFromProduct() [1/2]

◆ growthSeries_symbolExponentFromProduct() [2/2]

◆ i_orderFiniteSubgraph()