An interface for the computation of the Smith Normal Form of a series of a few rectangular matrices with coefficients in a Euclidean Domain. More...

#include <snfchomp.h>

Public Types
typedef CoefT	CoefType
	The type of coefficients in the chain. More...

typedef tAlgCell< int_t, unsigned char, CoefT >	CellType
	The type of an abstract algebraic cell that is used to carry the numbers of columns or rows in the matrix. More...

typedef tChain< CellType, CoefT >	ChainType
	The type of the corresponding image chain. More...

Public Member Functions
	tMatrixSNF ()
	The default constructor of a matrix. More...

	~tMatrixSNF ()
	The destructor of a matrix. More...

void	setSize (int q, int_t numRows, int_t numColumns)
	Sets the number of rows and columns in a given sub-matrix. More...

void	add (int q, int_t row, int_t column, const CoefT &element)
	Adds an element to the matrix whose SNF will be computed. More...

int_t	getNumRows (int q) const
	Returns the number of rows of the matrix. More...

int_t	getNumCols (int q) const
	Returns the number of columns of the matrix. More...

void	computeSNF (int numMatr)
	Computes the almost Smith Normal Form of all the matrices whose number is provided (indexing stats from 0 and ends at the given mumber minus 1). More...

CoefT	getColCoef (int q, int_t n) const
	Returns the coefficient in the given column of the given matrix in the SNF. More...

int_t	getColCell (int q, int_t n) const
	Returns the cell number in the given column of the given matrix in the SNF, or -1 if the column is zero. More...

CoefT	getRowCoef (int q, int_t n) const
	Returns the coefficient in the given row of the given matrix in the SNF. More...

int_t	getRowCell (int q, int_t n) const
	Returns the cell number in the given row of the given matrix in the SNF, or -1 if the row is zero. More...

ChainType	getNewChain (int q, int_t n) const
	For a cell in the original basis, returns the corresponding combination of elements in the new basis (the column of the change-of-basis matrix in this direction). More...

ChainType	getNewChainRow (int q, int_t n) const
	For a cell in the original basis, returns the given row of the change-of-basis matrix towards the new basis. More...

ChainType	getOldChain (int q, int_t n) const
	For a cell in the new basis, returns a combination of the original cells that correspond to this cell (the column of the change-of-basis matrix in this direction). More...

ChainType	getOldChainRow (int q, int_t n) const
	For a cell in the new basis, returns the given row of the change-of-basis matrix towards the original basis. More...

Private Member Functions
	tMatrixSNF (const tMatrixSNF< CoefT > &other)
	Copy constructor is not allowed. More...

tMatrixSNF< CoefT > &	operator= (const tMatrixSNF< CoefT > &other)
	Assignment operator is not allowed. More...

Static Private Member Functions
static ChainType	abstractChain (const chomp::homology::chain< tEuclWrap< CoefT > > &ch)
	Coverts a column of a matrix to an abstract algebraic chain. More...

Private Attributes
chomp::homology::multitable< chomp::homology::mmatrix< tEuclWrap< CoefT > > >	matrices
	The matrices whose Smith Normal Form will be computed. More...

chomp::homology::multitable< chomp::homology::mmatrix< tEuclWrap< CoefT > > >	chgBasisA
	Change of basis matrices from the original one to the SNF one. More...

chomp::homology::multitable< chomp::homology::mmatrix< tEuclWrap< CoefT > > >	chgBasisG
	Change of basis matrices from the SNF one to the original one. More...

bool	computedSNF
	Remembers if the SNF has already been computed. More...

Detailed Description

template<class CoefT>
class tMatrixSNF< CoefT >

An interface for the computation of the Smith Normal Form of a series of a few rectangular matrices with coefficients in a Euclidean Domain.

A Euclidean Domain is a commutative ring in which division with remainder is well defined; for example, the ring of integers, the ring of polynomials in one variable, or some field (like the rationals or the integers modulo a prime number p). In fact, what is to be computed, are the changes of bases in the complex such that each matrix in the series is in the SNF. The columns and rows of each matrix in the set are indexed by integer numbers starting at 0. In addition to the SNF, the change-of-basis matrices A and G are also computed, such that A is a change of basis from the original one to the new one, and G is a change of basis from the new basis back to the original one. In other words, if {M_q} is the original series of matrices and {S_q} is a series of its SNF then M_q = G_{q-1} S_q A_q, and G_q A_q = A_q G_q = identity. Please, note that it is not possible to make all the boundary matrices in the SNF with the non-zero entries starting at the 'diagonal', because the boundary of a boundary must be zero. Therefore, what is computed here, is a 'simple form' of the boundary matrices in which every column and every row has at most one nonzero entry. Please, note that the division condition required in the SNF is not satisfied either. As a consequence, the collection of coefficients that define a homology group may not be the same for isomorphic groups.

Definition at line 86 of file snfchomp.h.

Member Typedef Documentation

◆ CellType

template<class CoefT>

typedef tAlgCell<int_t,unsigned char,CoefT> tMatrixSNF< CoefT >::CellType

The type of an abstract algebraic cell that is used to carry the numbers of columns or rows in the matrix.

Please note that only the identifier of this cell is used, not its dimension, nor its boundary.

Definition at line 96 of file snfchomp.h.

◆ ChainType

template<class CoefT>

typedef tChain<CellType,CoefT> tMatrixSNF< CoefT >::ChainType

The type of the corresponding image chain.

Definition at line 99 of file snfchomp.h.

◆ CoefType

template<class CoefT>

typedef CoefT tMatrixSNF< CoefT >::CoefType

The type of coefficients in the chain.

Definition at line 90 of file snfchomp.h.

Constructor & Destructor Documentation

◆ tMatrixSNF() [1/2]

template<class CoefT >

tMatrixSNF< CoefT >::tMatrixSNF ( )

inline

The default constructor of a matrix.

Definition at line 195 of file snfchomp.h.

◆ ~tMatrixSNF()

template<class CoefT >

tMatrixSNF< CoefT >::~tMatrixSNF ( )

inline

The destructor of a matrix.

Definition at line 201 of file snfchomp.h.

◆ tMatrixSNF() [2/2]

template<class CoefT >

tMatrixSNF< CoefT >::tMatrixSNF ( const tMatrixSNF< CoefT > & other )

inlineprivate

Copy constructor is not allowed.

Definition at line 207 of file snfchomp.h.

Member Function Documentation

◆ abstractChain()

template<class CoefT >

tMatrixSNF< CoefT >::ChainType tMatrixSNF< CoefT >::abstractChain ( const chomp::homology::chain< tEuclWrap< CoefT > > & ch )

inlinestaticprivate

Coverts a column of a matrix to an abstract algebraic chain.

Definition at line 357 of file snfchomp.h.

References tMatrixSNF< CoefT >::add().

Referenced by tMatrixSNF< CoefT >::getNewChain(), tMatrixSNF< CoefT >::getNewChainRow(), tMatrixSNF< CoefT >::getOldChain(), tMatrixSNF< CoefT >::getOldChainRow(), and tMatrixSNF< CoefT >::getRowCell().

◆ add()

template<class CoefT >

void tMatrixSNF< CoefT >::add	(	int	q,
		int_t	row,
		int_t	column,
		const CoefT &	element
	)

inline

Adds an element to the matrix whose SNF will be computed.

Definition at line 234 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

Referenced by tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::computeSNF().

◆ computeSNF()

template<class CoefT >

void tMatrixSNF< CoefT >::computeSNF ( int numMatr )

inline

Computes the almost Smith Normal Form of all the matrices whose number is provided (indexing stats from 0 and ends at the given mumber minus 1).

After all the matrices have been defined, this procedure must be called once to compute the SNF and all the auxiliary data, including the change of basis matrices A and G. Then the results of the computations can be read with the other methods available in this class.

Definition at line 254 of file snfchomp.h.

References tMatrixSNF< CoefT >::add(), tMatrixSNF< CoefT >::chgBasisA, tMatrixSNF< CoefT >::chgBasisG, tMatrixSNF< CoefT >::computedSNF, identity(), and tMatrixSNF< CoefT >::matrices.

◆ getColCell()

template<class CoefT >

int_t tMatrixSNF< CoefT >::getColCell	(	int	q,
		int_t	n
	)		const

inline

Returns the cell number in the given column of the given matrix in the SNF, or -1 if the column is zero.

Definition at line 323 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

◆ getColCoef()

template<class CoefT >

CoefT tMatrixSNF< CoefT >::getColCoef	(	int	q,
		int_t	n
	)		const

inline

Returns the coefficient in the given column of the given matrix in the SNF.

Definition at line 312 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

◆ getNewChain()

template<class CoefT >

tMatrixSNF< CoefT >::ChainType tMatrixSNF< CoefT >::getNewChain	(	int	q,
		int_t	n
	)		const

inline

For a cell in the original basis, returns the corresponding combination of elements in the new basis (the column of the change-of-basis matrix in this direction).

Definition at line 371 of file snfchomp.h.

References tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::chgBasisA.

◆ getNewChainRow()

template<class CoefT >

tMatrixSNF< CoefT >::ChainType tMatrixSNF< CoefT >::getNewChainRow	(	int	q,
		int_t	n
	)		const

inline

For a cell in the original basis, returns the given row of the change-of-basis matrix towards the new basis.

Definition at line 378 of file snfchomp.h.

References tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::chgBasisA.

◆ getNumCols()

template<class CoefT >

int_t tMatrixSNF< CoefT >::getNumCols ( int q ) const

inline

Returns the number of columns of the matrix.

Definition at line 248 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

◆ getNumRows()

template<class CoefT >

int_t tMatrixSNF< CoefT >::getNumRows ( int q ) const

inline

Returns the number of rows of the matrix.

Definition at line 242 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

◆ getOldChain()

template<class CoefT >

tMatrixSNF< CoefT >::ChainType tMatrixSNF< CoefT >::getOldChain	(	int	q,
		int_t	n
	)		const

inline

For a cell in the new basis, returns a combination of the original cells that correspond to this cell (the column of the change-of-basis matrix in this direction).

Definition at line 385 of file snfchomp.h.

References tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::chgBasisG.

◆ getOldChainRow()

template<class CoefT >

tMatrixSNF< CoefT >::ChainType tMatrixSNF< CoefT >::getOldChainRow	(	int	q,
		int_t	n
	)		const

inline

For a cell in the new basis, returns the given row of the change-of-basis matrix towards the original basis.

Definition at line 392 of file snfchomp.h.

References tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::chgBasisG.

◆ getRowCell()

template<class CoefT >

int_t tMatrixSNF< CoefT >::getRowCell	(	int	q,
		int_t	n
	)		const

inline

Returns the cell number in the given row of the given matrix in the SNF, or -1 if the row is zero.

Definition at line 345 of file snfchomp.h.

References tMatrixSNF< CoefT >::abstractChain(), and tMatrixSNF< CoefT >::matrices.

◆ getRowCoef()

template<class CoefT >

CoefT tMatrixSNF< CoefT >::getRowCoef	(	int	q,
		int_t	n
	)		const

inline

Returns the coefficient in the given row of the given matrix in the SNF.

Definition at line 334 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

◆ operator=()

template<class CoefT >

tMatrixSNF< CoefT > & tMatrixSNF< CoefT >::operator= ( const tMatrixSNF< CoefT > & other )

inlineprivate

Assignment operator is not allowed.

Definition at line 215 of file snfchomp.h.

◆ setSize()

template<class CoefT >

void tMatrixSNF< CoefT >::setSize	(	int	q,
		int_t	numRows,
		int_t	numColumns
	)

inline

Sets the number of rows and columns in a given sub-matrix.

Definition at line 224 of file snfchomp.h.

References tMatrixSNF< CoefT >::matrices.

Member Data Documentation

◆ chgBasisA

template<class CoefT>

chomp::homology::multitable<chomp::homology::mmatrix<tEuclWrap<CoefT> > > tMatrixSNF< CoefT >::chgBasisA

private

Change of basis matrices from the original one to the SNF one.

Definition at line 177 of file snfchomp.h.

Referenced by tMatrixSNF< CoefT >::computeSNF(), tMatrixSNF< CoefT >::getNewChain(), and tMatrixSNF< CoefT >::getNewChainRow().

◆ chgBasisG

template<class CoefT>

chomp::homology::multitable<chomp::homology::mmatrix<tEuclWrap<CoefT> > > tMatrixSNF< CoefT >::chgBasisG

private

Change of basis matrices from the SNF one to the original one.

Definition at line 181 of file snfchomp.h.

Referenced by tMatrixSNF< CoefT >::computeSNF(), tMatrixSNF< CoefT >::getOldChain(), and tMatrixSNF< CoefT >::getOldChainRow().

◆ computedSNF

template<class CoefT>

bool tMatrixSNF< CoefT >::computedSNF

private

Remembers if the SNF has already been computed.

Definition at line 188 of file snfchomp.h.

Referenced by tMatrixSNF< CoefT >::computeSNF().

◆ matrices

template<class CoefT>

chomp::homology::multitable<chomp::homology::mmatrix<tEuclWrap<CoefT> > > tMatrixSNF< CoefT >::matrices

private

The matrices whose Smith Normal Form will be computed.

Definition at line 173 of file snfchomp.h.

Referenced by tMatrixSNF< CoefT >::add(), tMatrixSNF< CoefT >::computeSNF(), tMatrixSNF< CoefT >::getColCell(), tMatrixSNF< CoefT >::getColCoef(), tMatrixSNF< CoefT >::getNumCols(), tMatrixSNF< CoefT >::getNumRows(), tMatrixSNF< CoefT >::getRowCell(), tMatrixSNF< CoefT >::getRowCoef(), and tMatrixSNF< CoefT >::setSize().

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

chaincon/snfchomp.h

Public Types

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<class CoefT> class tMatrixSNF< CoefT >

Member Typedef Documentation

◆ CellType

◆ ChainType

◆ CoefType

Constructor & Destructor Documentation

◆ tMatrixSNF() [1/2]

◆ ~tMatrixSNF()

◆ tMatrixSNF() [2/2]

Member Function Documentation

◆ abstractChain()

◆ add()

◆ computeSNF()

◆ getColCell()

◆ getColCoef()

◆ getNewChain()

◆ getNewChainRow()

◆ getNumCols()

◆ getNumRows()

◆ getOldChain()

◆ getOldChainRow()

◆ getRowCell()

◆ getRowCoef()

◆ operator=()

◆ setSize()

Member Data Documentation

◆ chgBasisA

◆ chgBasisG

◆ computedSNF

◆ matrices

template<class CoefT>
class tMatrixSNF< CoefT >