awdiagcubs.h File Reference

A cubical version of the Alexander-Whitney diagonal, based on simplicial subdivision of cubical cells. More...

#include <istream>
#include <ostream>
#include "chomp/system/config.h"
#include "chomp/cubes/pointbas.h"
#include "chaincon/cubcell.h"
#include "chaincon/combtensor.h"
#include "chaincon/tensor.h"
#include "chaincon/combchain.h"
#include "chaincon/chain.h"
#include "chaincon/simplex.h"
#include "chaincon/awdiagsim.h"
#include "chaincon/awdiag.h"

Go to the source code of this file.

Functions
template<class CoordT , class WrapT , class EmptyT >
void	AWdiagonal (const tCubCell< CoordT, WrapT, EmptyT > &c, tCombTensor< tCubCell< CoordT, WrapT, EmptyT >, tCubCell< CoordT, WrapT, EmptyT > > &t)
	Computes the Alexander-Whitney diagonal of a cubical cell using a simplicial subdivision of the cell. More...
template<class CoordT , class WrapT , class EmptyT , class CoefT >
void	AWdiagonal (const tCubCell< CoordT, WrapT, EmptyT > &, tTensor< tCubCell< CoordT, WrapT, EmptyT >, tCubCell< CoordT, WrapT, EmptyT >, CoefT > &)
	Computes the Alexander-Whitney diagonal of a cubical cell using a simplicial subdivision of the cell. More...

Detailed Description

A cubical version of the Alexander-Whitney diagonal, based on simplicial subdivision of cubical cells.

Definition in file awdiagcubs.h.

Function Documentation

AWdiagonal() [1/2]

template<class CoordT , class WrapT , class EmptyT >

void AWdiagonal ( const tCubCell< CoordT, WrapT, EmptyT > &  c, tCombTensor< tCubCell< CoordT, WrapT, EmptyT >, tCubCell< CoordT, WrapT, EmptyT > > &  t  )

inline

Computes the Alexander-Whitney diagonal of a cubical cell using a simplicial subdivision of the cell.

Please, note that this formula has only been implemented for 2-dimensional cells. Please, use the other function based on Serre's paper for the general formula. This is a combinatorial version of the function (coefficients in Z_p).

Definition at line 63 of file awdiagcubs.h.

AWdiagonal() [2/2]

template<class CoordT , class WrapT , class EmptyT , class CoefT >

void AWdiagonal ( const tCubCell< CoordT, WrapT, EmptyT > &  , tTensor< tCubCell< CoordT, WrapT, EmptyT >, tCubCell< CoordT, WrapT, EmptyT >, CoefT > &    )

inline

Computes the Alexander-Whitney diagonal of a cubical cell using a simplicial subdivision of the cell.

A general version (for any coefficients).

Definition at line 196 of file awdiagcubs.h.