ammodel.h File Reference

Computation of the algebraic minimal model using the SNF. More...

#include "chaincon/chain.h"
#include "chaincon/linmap.h"
#include "chaincon/comblinmap.h"
#include "chaincon/filtcomplex.h"
#include "chaincon/algcell.h"
#include "chaincon/snf.h"
#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 <istream>
#include <ostream>
#include <vector>

Go to the source code of this file.

Functions
template<class CellT , class CoefT , class CellArray1 , class CellArray2 , class CellArray3 , class CoefArray >
void	algMinModel (const tFilteredComplex< CellT > &K, CellArray1 &H, CellArray2 &A, CellArray3 &B, CoefArray &Q, tLinMap< CellT, CellT, CoefT > &pi, tLinMap< CellT, CellT, CoefT > &incl, tLinMap< CellT, CellT, CoefT > &phi)
	Computes a minimal model for a given filtered finite cell complex "K". More...

Detailed Description

Computation of the algebraic minimal model using the SNF.

This algorithm works for an arbitrary commutative ring of coefficients that is an Euclidean domain.

Definition in file ammodel.h.

Function Documentation

algMinModel()

template<class CellT , class CoefT , class CellArray1 , class CellArray2 , class CellArray3 , class CoefArray >

void algMinModel	(	const tFilteredComplex< CellT > &	K,
		CellArray1 &	H,
		CellArray2 &	A,
		CellArray3 &	B,
		CoefArray &	Q,
		tLinMap< CellT, CellT, CoefT > &	pi,
		tLinMap< CellT, CellT, CoefT > &	incl,
		tLinMap< CellT, CellT, CoefT > &	phi
	)

Computes a minimal model for a given filtered finite cell complex "K".

Cells that represent those generators of M whose boundary and coboundary are both zero are appended to the vector "H"; note that they represent (co)homology generators corresponding to the free part of the (co)homology module. The other generators of "M" are appended to the vectors "A" and "B" with the corresponding coefficients stored in the vector "Q" in such a way that the boundary of "A[i]" equals the coefficient "Q[i]" times "B[i]". The projection map "pi" onto M, the inclusion from "H+A+B" to "K", and the chain contraction "phi" on "K" are assumed to be initially zero and are constructed.

Definition at line 75 of file ammodel.h.

References verifyChangeOfBasisSNF().

Referenced by computeAlgMinModel().