Algebraic topological model computation: Algorithm 3, using the SNF; combinatorial version - for coefficients in Z_2. More...

#include <istream>
#include <ostream>
#include "chomp/system/config.h"
#include "chomp/system/textfile.h"
#include "chomp/system/timeused.h"
#include "chomp/struct/hashsets.h"
#include "chomp/struct/multitab.h"
#include "chomp/struct/integer.h"
#include "chomp/homology/chains.h"
#include "chaincon/combchain.h"
#include "chaincon/comblinmap.h"

Macros
#define	_product_is_identity_

Functions
bool	product_is_identity (const chomp::homology::mmatrix< chomp::homology::integer > &A, const chomp::homology::mmatrix< chomp::homology::integer > &G)
	Verifies if the product of the given two matrices is an identity matrix. More...

template<class CellT , class CellArray1 , class CellArray2 , class CellRestrT >
void	algTopModel3 (const CellArray1 &K, CellArray2 &H, tCombLinMap< CellT, CellT > &pi, tCombLinMap< CellT, CellT > &incl, tCombLinMap< CellT, CellT > &phi, const CellRestrT &restr)
	Computes an algebraic topological model for the given filtered finite cell complex "K". More...

Detailed Description

Algebraic topological model computation: Algorithm 3, using the SNF; combinatorial version - for coefficients in Z_2.

Definition in file atmodel3.h.

Macro Definition Documentation

◆ _product_is_identity_

#define _product_is_identity_

Definition at line 56 of file atmodel3.h.

Function Documentation

◆ algTopModel3()

template<class CellT , class CellArray1 , class CellArray2 , class CellRestrT >

void algTopModel3	(	const CellArray1 &	K,
		CellArray2 &	H,
		tCombLinMap< CellT, CellT > &	pi,
		tCombLinMap< CellT, CellT > &	incl,
		tCombLinMap< CellT, CellT > &	phi,
		const CellRestrT &	restr
	)

Computes an algebraic topological model for the given filtered finite cell complex "K".

Cells that represent homology generators are appended to the vector "H". The projection map "pi", the inclusion from "H" to the complex "K", and the homology gradient vector field "phi" are assumed to be initially zero and are constructed.

Definition at line 102 of file atmodel3.h.

References product_is_identity().

Referenced by algTopModel().

◆ product_is_identity()

bool product_is_identity	(	const chomp::homology::mmatrix< chomp::homology::integer > &	A,
		const chomp::homology::mmatrix< chomp::homology::integer > &	G
	)

inline

Verifies if the product of the given two matrices is an identity matrix.

For each column C of A, computes G(C) and checks this chain.

Definition at line 60 of file atmodel3.h.

Referenced by algTopModel3().