ez_aw.h File Reference

The Alexander-Whitney operator as a component of the Eilenberg-Zilber chain contraction. More...

#include <istream>
#include <ostream>
#include "chomp/system/config.h"
#include "chaincon/combtensor.h"
#include "chaincon/tensor.h"

Go to the source code of this file.

Functions
template<class ArrayT , class SimCellT >
void	AW_cells (ArrayT &sb, const SimCellT &s, bool left)
	Computes the compositions of face operators on the given simplicial cell to get the appropriate cells for the AW operator. More...
template<class SimCellT >
void	EZ_AW (const SimCellT &s1, const SimCellT &s2, tCombTensor< SimCellT, SimCellT > &t)
	Computes the Alexander-Whitney operator on a product of simplicial cells. More...
template<class SimCellT , class CoefT >
void	EZ_AW (const SimCellT &s1, const SimCellT &s2, tTensor< SimCellT, SimCellT, CoefT > &t)
	Computes the Alexander-Whitney operator on a product of simplicial cells. More...
template<class ProdCellT >
void	EZ_AW (const ProdCellT &s, tCombTensor< ProdCellT, ProdCellT > &t)
	Computes the Alexander-Whitney operator on a product of simplicial cells. More...
template<class SimCellT , class ProdCellT , class CoefT >
void	EZ_AW (const ProdCellT &s, tTensor< SimCellT, SimCellT, CoefT > &t)
	Computes the Alexander-Whitney operator on a product of simplicial cells. More...
template<class SimCellT , class ProdCellT >
void	EZ_AW (const tCombChain< ProdCellT > &s, tCombTensor< SimCellT, SimCellT > &t)
	Computes the Alexander-Whitney operator on a chain of products of simplicial cells. More...
template<class SimCellT , class ProdCellT , class CoefT >
void	EZ_AW (const tChain< ProdCellT, CoefT > &s, tTensor< SimCellT, SimCellT, CoefT > &t)
	Computes the Alexander-Whitney operator on a chain of products of simplicial cells. More...

Detailed Description

The Alexander-Whitney operator as a component of the Eilenberg-Zilber chain contraction.

Definition in file ez_aw.h.

Function Documentation

AW_cells()

template<class ArrayT , class SimCellT >

void AW_cells ( ArrayT &  sb, const SimCellT &  s, bool  left  )

inline

Computes the compositions of face operators on the given simplicial cell to get the appropriate cells for the AW operator.

Definition at line 52 of file ez_aw.h.

Referenced by EZ_AW().

EZ_AW() [1/6]

template<class SimCellT >

void EZ_AW ( const SimCellT &  s1, const SimCellT &  s2, tCombTensor< SimCellT, SimCellT > &  t  )

inline

Computes the Alexander-Whitney operator on a product of simplicial cells.

Combinatorial version (coefficients in Z_2).

Definition at line 76 of file ez_aw.h.

References AW_cells().

Referenced by AWdiagonal(), experiment(), EZ_AW(), and ssquares1().

EZ_AW() [2/6]

template<class SimCellT , class CoefT >

void EZ_AW ( const SimCellT &  s1, const SimCellT &  s2, tTensor< SimCellT, SimCellT, CoefT > &  t  )

inline

Computes the Alexander-Whitney operator on a product of simplicial cells.

Definition at line 99 of file ez_aw.h.

References AW_cells().

EZ_AW() [3/6]

template<class ProdCellT >

void EZ_AW ( const ProdCellT &  s, tCombTensor< ProdCellT, ProdCellT > &  t  )

inline

Computes the Alexander-Whitney operator on a product of simplicial cells.

Combinatorial version (coefficients in Z_2).

Definition at line 126 of file ez_aw.h.

References EZ_AW().

EZ_AW() [4/6]

template<class SimCellT , class ProdCellT , class CoefT >

void EZ_AW ( const ProdCellT &  s, tTensor< SimCellT, SimCellT, CoefT > &  t  )

inline

Computes the Alexander-Whitney operator on a product of simplicial cells.

Definition at line 136 of file ez_aw.h.

References EZ_AW().

EZ_AW() [5/6]

template<class SimCellT , class ProdCellT >

void EZ_AW ( const tCombChain< ProdCellT > &  s, tCombTensor< SimCellT, SimCellT > &  t  )

inline

Computes the Alexander-Whitney operator on a chain of products of simplicial cells.

Combinatorial version (coefficients in Z_2).

Definition at line 150 of file ez_aw.h.

References EZ_AW().

EZ_AW() [6/6]

template<class SimCellT , class ProdCellT , class CoefT >

void EZ_AW ( const tChain< ProdCellT, CoefT > &  s, tTensor< SimCellT, SimCellT, CoefT > &  t  )

inline

Computes the Alexander-Whitney operator on a chain of products of simplicial cells.

Definition at line 166 of file ez_aw.h.

References EZ_AW().