A linear map. More...

#include <linmap.h>

Public Types
typedef CellDomT	CellDomType
	The type of cells in the domain of the linear map. More...

typedef CellImgT	CellImgType
	The type of cells in the images of the linear map. More...

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

typedef tChain< CellDomT, CoefT >	ChainDomType
	The type of the corresponding domain chain. More...

typedef tChain< CellImgT, CoefT >	ChainImgType
	The type of the corresponding image chain. More...

typedef tTensor< CellDomT, CellDomT, CoefT >	TensorDomType
	The type of the corresponding domain chain. More...

typedef tTensor< CellImgT, CellImgT, CoefT >	TensorImgType
	The type of the corresponding image chain. More...

Public Member Functions
	tLinMap ()
	The default constructor. More...

int_t	add (const CellDomT &c)
	Adds a cell to the domain of the map, with zero image, and returns its number. More...

void	add (const CellDomT &c, const CellImgT &d, const CoefT &coef)
	Adds a cell to the image of the given cell. More...

void	add (const CellDomT &c, const tChain< CellImgT, CoefT > &ch)
	Adds a chain to the image of the given cell. More...

tLinMap< CellDomT, CellImgT, CoefT > &	operator+= (const tLinMap< CellDomT, CellImgT, CoefT > &f)
	Adds another map to the given map. More...

tLinMap< CellDomT, CellImgT, CoefT > &	negate ()
	Replaces all the coefficients in the map with their negation. More...

tLinMap< CellDomT, CellImgT, CoefT > &	operator*= (const CoefT &c)
	Multiplies all the coefficients in the map by the given number. More...

void	removenum (int_t n)
	Removes the given cell from the domain of the map. More...

void	remove (const CellDomT &c)
	Removes the given cell from the domain of the map. More...

const tChain< CellImgT, CoefT > &	operator() (int_t n) const
	Returns the image of the given cell. More...

tChain< CellImgT, CoefT >	operator() (const CellDomT &c) const
	Returns the image of the given cell. More...

tChain< CellImgT, CoefT >	operator() (const tChain< CellDomT, CoefT > &ch) const
	Computes the image of the given chain. More...

tTensor< CellImgT, CellImgT, CoefT >	operator() (const tTensor< CellDomT, CellDomT, CoefT > &ch) const
	Computes the image of the given tensor. More...

int_t	size () const
	Returns the number of elements in the domain of the map. More...

const CellDomT &	operator[] (int_t n) const
	Returns the n-th element of the domain of the map. More...

const chomp::homology::hashedset< CellDomT > &	getDomain () const
	Returns the domain of the map. More...

tChain< CellImgT, CoefT > &	getImage (int_t n)
	Returns the image of the given cell for editing. More...

tChain< CellImgT, CoefT > &	getImage (const CellDomT &c)
	Returns the image of the given cell for editing. More...

bool	operator== (const tLinMap< CellDomT, CellImgT, CoefT > &f) const
	Verifies if the two linear maps are the same. More...

void	swap (tLinMap< CellDomT, CellImgT, CoefT > &f)
	Swaps the data with another linear map. More...

Private Attributes
chomp::homology::hashedset< CellDomT >	domain
	The domain of the map. More...

chomp::homology::multitable< tChain< CellImgT, CoefT > >	images
	The chains in the images of each domain element. More...

Detailed Description

template<class CellDomT, class CellImgT, class CoefT>
class tLinMap< CellDomT, CellImgT, CoefT >

A linear map.

This is in fact a finite set of cells mapped to a chain each. It corresponds to a linear map on the vector space generated by the cells over the coefficients field F_2 (a.k.a. Z_2).

Definition at line 55 of file linmap.h.

Member Typedef Documentation

◆ CellDomType

template<class CellDomT, class CellImgT, class CoefT>

typedef CellDomT tLinMap< CellDomT, CellImgT, CoefT >::CellDomType

The type of cells in the domain of the linear map.

Definition at line 59 of file linmap.h.

◆ CellImgType

template<class CellDomT, class CellImgT, class CoefT>

typedef CellImgT tLinMap< CellDomT, CellImgT, CoefT >::CellImgType

The type of cells in the images of the linear map.

Definition at line 62 of file linmap.h.

◆ ChainDomType

template<class CellDomT, class CellImgT, class CoefT>

typedef tChain<CellDomT,CoefT> tLinMap< CellDomT, CellImgT, CoefT >::ChainDomType

The type of the corresponding domain chain.

Definition at line 68 of file linmap.h.

◆ ChainImgType

template<class CellDomT, class CellImgT, class CoefT>

typedef tChain<CellImgT,CoefT> tLinMap< CellDomT, CellImgT, CoefT >::ChainImgType

The type of the corresponding image chain.

Definition at line 71 of file linmap.h.

◆ CoefType

template<class CellDomT, class CellImgT, class CoefT>

typedef CoefT tLinMap< CellDomT, CellImgT, CoefT >::CoefType

The type of coefficients in the chain.

Definition at line 65 of file linmap.h.

◆ TensorDomType

template<class CellDomT, class CellImgT, class CoefT>

typedef tTensor<CellDomT,CellDomT,CoefT> tLinMap< CellDomT, CellImgT, CoefT >::TensorDomType

The type of the corresponding domain chain.

Definition at line 74 of file linmap.h.

◆ TensorImgType

template<class CellDomT, class CellImgT, class CoefT>

typedef tTensor<CellImgT,CellImgT,CoefT> tLinMap< CellDomT, CellImgT, CoefT >::TensorImgType

The type of the corresponding image chain.

Definition at line 77 of file linmap.h.

Constructor & Destructor Documentation

◆ tLinMap()

template<class CellDomT , class CellImgT , class CoefT >

tLinMap< CellDomT, CellImgT, CoefT >::tLinMap ( )

inline

The default constructor.

Definition at line 163 of file linmap.h.

Member Function Documentation

◆ add() [1/3]

template<class CellDomT , class CellImgT , class CoefT >

int_t tLinMap< CellDomT, CellImgT, CoefT >::add ( const CellDomT & c )

inline

Adds a cell to the domain of the map, with zero image, and returns its number.

Definition at line 170 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain.

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::add(), addIdentity(), tLinMap< CellDomT, CellImgT, CoefT >::getImage(), tLinMap< CellDomT, CellImgT, CoefT >::operator()(), operator*(), and tLinMap< CellDomT, CellImgT, CoefT >::operator+=().

◆ add() [2/3]

template<class CellDomT , class CellImgT , class CoefT >

void tLinMap< CellDomT, CellImgT, CoefT >::add	(	const CellDomT &	c,
		const CellImgT &	d,
		const CoefT &	coef
	)

inline

Adds a cell to the image of the given cell.

Definition at line 177 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ add() [3/3]

template<class CellDomT , class CellImgT , class CoefT >

void tLinMap< CellDomT, CellImgT, CoefT >::add	(	const CellDomT &	c,
		const tChain< CellImgT, CoefT > &	ch
	)

inline

Adds a chain to the image of the given cell.

Definition at line 191 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ getDomain()

template<class CellDomT , class CellImgT , class CoefT >

const chomp::homology::hashedset< CellDomT > & tLinMap< CellDomT, CellImgT, CoefT >::getDomain ( ) const

inline

Returns the domain of the map.

Definition at line 357 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, and tLinMap< CellDomT, CellImgT, CoefT >::getImage().

◆ getImage() [1/2]

template<class CellDomT , class CellImgT , class CoefT >

tChain< CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::getImage ( int_t n )

inline

Returns the image of the given cell for editing.

Definition at line 364 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::images.

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::getDomain().

◆ getImage() [2/2]

template<class CellDomT , class CellImgT , class CoefT >

tChain< CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::getImage ( const CellDomT & c )

inline

Returns the image of the given cell for editing.

Definition at line 371 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ negate()

template<class CellDomT , class CellImgT , class CoefT >

tLinMap< CellDomT, CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::negate ( )

inline

Replaces all the coefficients in the map with their negation.

Definition at line 235 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ operator()() [1/4]

template<class CellDomT , class CellImgT , class CoefT >

const tChain< CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::operator() ( int_t n ) const

inline

Returns the image of the given cell.

Definition at line 275 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::images.

◆ operator()() [2/4]

template<class CellDomT , class CellImgT , class CoefT >

tChain< CellImgT, CoefT > tLinMap< CellDomT, CellImgT, CoefT >::operator() ( const CellDomT & c ) const

inline

Returns the image of the given cell.

Definition at line 282 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, and tLinMap< CellDomT, CellImgT, CoefT >::images.

◆ operator()() [3/4]

template<class CellDomT , class CellImgT , class CoefT >

tChain< CellImgT, CoefT > tLinMap< CellDomT, CellImgT, CoefT >::operator() ( const tChain< CellDomT, CoefT > & ch ) const

inline

Computes the image of the given chain.

Definition at line 293 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ operator()() [4/4]

template<class CellDomT , class CellImgT , class CoefT >

tTensor< CellImgT, CellImgT, CoefT > tLinMap< CellDomT, CellImgT, CoefT >::operator() ( const tTensor< CellDomT, CellDomT, CoefT > & ch ) const

inline

Computes the image of the given tensor.

Definition at line 318 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ operator*=()

template<class CellDomT , class CellImgT , class CoefT >

tLinMap< CellDomT, CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::operator*= ( const CoefT & c )

inline

Multiplies all the coefficients in the map by the given number.

Definition at line 245 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ operator+=()

template<class CellDomT , class CellImgT , class CoefT >

tLinMap< CellDomT, CellImgT, CoefT > & tLinMap< CellDomT, CellImgT, CoefT >::operator+= ( const tLinMap< CellDomT, CellImgT, CoefT > & f )

inline

Adds another map to the given map.

Definition at line 221 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, and tLinMap< CellDomT, CellImgT, CoefT >::size().

◆ operator==()

template<class CellDomT , class CellImgT , class CoefT >

bool tLinMap< CellDomT, CellImgT, CoefT >::operator== ( const tLinMap< CellDomT, CellImgT, CoefT > & f ) const

inline

Verifies if the two linear maps are the same.

Definition at line 384 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, tLinMap< CellDomT, CellImgT, CoefT >::size(), and tLinMap< CellDomT, CellImgT, CoefT >::swap().

◆ operator[]()

template<class CellDomT , class CellImgT , class CoefT >

const CellDomT & tLinMap< CellDomT, CellImgT, CoefT >::operator[] ( int_t n ) const

inline

Returns the n-th element of the domain of the map.

Definition at line 350 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain.

◆ remove()

template<class CellDomT , class CellImgT , class CoefT >

void tLinMap< CellDomT, CellImgT, CoefT >::remove ( const CellDomT & c )

inline

Removes the given cell from the domain of the map.

Note that this may change the order of cells in the domain.

Definition at line 265 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, and tLinMap< CellDomT, CellImgT, CoefT >::removenum().

◆ removenum()

template<class CellDomT , class CellImgT , class CoefT >

void tLinMap< CellDomT, CellImgT, CoefT >::removenum ( int_t n )

inline

Removes the given cell from the domain of the map.

Note that this may change the order of cells in the domain.

Definition at line 254 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, tLinMap< CellDomT, CellImgT, CoefT >::images, tLinMap< CellDomT, CellImgT, CoefT >::size(), and tLinMap< CellDomT, CellImgT, CoefT >::swap().

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::remove().

◆ size()

template<class CellDomT , class CellImgT , class CoefT >

int_t tLinMap< CellDomT, CellImgT, CoefT >::size ( ) const

inline

Returns the number of elements in the domain of the map.

Note that the images of some of the elements might be zero.

Definition at line 343 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain.

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::add(), addIdentity(), tLinMap< CellDomT, CellImgT, CoefT >::getImage(), tLinMap< CellDomT, CellImgT, CoefT >::negate(), tLinMap< CellDomT, CellImgT, CoefT >::operator()(), operator*(), tLinMap< CellDomT, CellImgT, CoefT >::operator*=(), tLinMap< CellDomT, CellImgT, CoefT >::operator+=(), operator<<(), tLinMap< CellDomT, CellImgT, CoefT >::operator==(), and tLinMap< CellDomT, CellImgT, CoefT >::removenum().

◆ swap()

template<class CellDomT , class CellImgT , class CoefT >

void tLinMap< CellDomT, CellImgT, CoefT >::swap ( tLinMap< CellDomT, CellImgT, CoefT > & f )

inline

Swaps the data with another linear map.

Definition at line 417 of file linmap.h.

References tLinMap< CellDomT, CellImgT, CoefT >::domain, and tLinMap< CellDomT, CellImgT, CoefT >::images.

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::operator==(), and tLinMap< CellDomT, CellImgT, CoefT >::removenum().

Member Data Documentation

◆ domain

template<class CellDomT, class CellImgT, class CoefT>

chomp::homology::hashedset<CellDomT> tLinMap< CellDomT, CellImgT, CoefT >::domain

private

The domain of the map.

Definition at line 153 of file linmap.h.

◆ images

template<class CellDomT, class CellImgT, class CoefT>

chomp::homology::multitable<tChain<CellImgT,CoefT> > tLinMap< CellDomT, CellImgT, CoefT >::images

private

The chains in the images of each domain element.

Definition at line 156 of file linmap.h.

Referenced by tLinMap< CellDomT, CellImgT, CoefT >::add(), tLinMap< CellDomT, CellImgT, CoefT >::getImage(), tLinMap< CellDomT, CellImgT, CoefT >::negate(), tLinMap< CellDomT, CellImgT, CoefT >::operator()(), tLinMap< CellDomT, CellImgT, CoefT >::operator*=(), tLinMap< CellDomT, CellImgT, CoefT >::operator+=(), tLinMap< CellDomT, CellImgT, CoefT >::operator==(), tLinMap< CellDomT, CellImgT, CoefT >::removenum(), and tLinMap< CellDomT, CellImgT, CoefT >::swap().

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

chaincon/linmap.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

template<class CellDomT, class CellImgT, class CoefT> class tLinMap< CellDomT, CellImgT, CoefT >

Member Typedef Documentation

◆ CellDomType

◆ CellImgType

◆ ChainDomType

◆ ChainImgType

◆ CoefType

◆ TensorDomType

◆ TensorImgType

Constructor & Destructor Documentation

◆ tLinMap()

Member Function Documentation

◆ add() [1/3]

◆ add() [2/3]

◆ add() [3/3]

◆ getDomain()

◆ getImage() [1/2]

◆ getImage() [2/2]

◆ negate()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ operator*=()

◆ operator+=()

◆ operator==()

◆ operator[]()

◆ remove()

◆ removenum()

◆ size()

◆ swap()

Member Data Documentation

◆ domain

◆ images

template<class CellDomT, class CellImgT, class CoefT>
class tLinMap< CellDomT, CellImgT, CoefT >