Class representing an element of the \( \mathbb{F}_2 \) field. More...

#include <gudhi/Fields/Z2_field.h>

Public Types
using	Element = bool

Public Member Functions
	Z2_field_element ()
	Default constructor.

template<typename Integer_type , class = isInteger<Integer_type>>
	Z2_field_element (Integer_type element)
	Constructor setting the element to the given value. More...

	Z2_field_element (const Z2_field_element &toCopy)
	Copy constructor. More...

	Z2_field_element (Z2_field_element &&toMove) noexcept
	Move constructor. More...

Z2_field_element &	operator= (Z2_field_element other)
	Assign operator.

Z2_field_element &	operator= (const unsigned int value)
	Assign operator.

	operator unsigned int () const
	Casts the element into an unsigned int.

Z2_field_element	get_inverse () const
	Returns the inverse of the element. More...

std::pair< Z2_field_element, unsigned int >	get_partial_inverse (unsigned int productOfCharacteristics) const
	For interface purposes with multi-fields. Returns the inverse together with the second argument. More...

Element	get_value () const
	Returns the value of the element. More...

Static Public Member Functions
static Z2_field_element	get_additive_identity ()
	Returns the additive identity of the field. More...

static Z2_field_element	get_multiplicative_identity ()
	Returns the multiplicative identity of the field. More...

static Z2_field_element	get_partial_multiplicative_identity (unsigned int productOfCharacteristics)
	For interface purposes with multi-fields. Returns the multiplicative identity of the field. More...

static constexpr unsigned int	get_characteristic ()
	Returns the characteristic of the field, that is `2`. More...

Friends
void	operator+= (Z2_field_element &f1, Z2_field_element const &f2)
	operator+=

Z2_field_element	operator+ (Z2_field_element f1, Z2_field_element const &f2)
	operator+

template<typename Integer_type , class = isInteger<Integer_type>>
void	operator+= (Z2_field_element &f, const Integer_type &v)
	operator+= More...

template<typename Integer_type , class = isInteger<Integer_type>>
Z2_field_element	operator+ (Z2_field_element f, const Integer_type &v)
	operator+ More...

template<typename Integer_type , class = isInteger<Integer_type>>
Integer_type	operator+ (const Integer_type &v, const Z2_field_element &f)
	operator+ More...

void	operator-= (Z2_field_element &f1, Z2_field_element const &f2)
	operator-=

Z2_field_element	operator- (Z2_field_element f1, Z2_field_element const &f2)
	operator-

template<typename Integer_type , class = isInteger<Integer_type>>
void	operator-= (Z2_field_element &f, const Integer_type &v)
	operator-= More...

template<typename Integer_type , class = isInteger<Integer_type>>
Z2_field_element	operator- (Z2_field_element f, const Integer_type &v)
	operator- More...

template<typename Integer_type , class = isInteger<Integer_type>>
Integer_type	operator- (const Integer_type v, Z2_field_element const &f)
	operator- More...

void	*operator=** (Z2_field_element &f1, Z2_field_element const &f2)
	operator*=

Z2_field_element	operator* (Z2_field_element f1, Z2_field_element const &f2)
	operator*

template<typename Integer_type , class = isInteger<Integer_type>>
void	operator*= (Z2_field_element &f, const Integer_type &v)
	operator*= More...

template<typename Integer_type , class = isInteger<Integer_type>>
Z2_field_element	operator* (Z2_field_element f, const Integer_type &v)
	operator* More...

template<typename Integer_type , class = isInteger<Integer_type>>
Integer_type	operator* (const Integer_type &v, Z2_field_element const &f)
	operator* More...

bool	operator== (const Z2_field_element &f1, const Z2_field_element &f2)
	operator==

template<typename Integer_type , class = isInteger<Integer_type>>
bool	operator== (const Integer_type &v, const Z2_field_element &f)
	operator== More...

template<typename Integer_type , class = isInteger<Integer_type>>
bool	operator== (const Z2_field_element &f, const Integer_type &v)
	operator== More...

bool	operator!= (const Z2_field_element &f1, const Z2_field_element &f2)
	operator!=

template<typename Integer_type , class = isInteger<Integer_type>>
bool	operator!= (const Integer_type v, const Z2_field_element &f)
	operator!= More...

template<typename Integer_type , class = isInteger<Integer_type>>
bool	operator!= (const Z2_field_element &f, const Integer_type v)
	operator!= More...

void	swap (Z2_field_element &f1, Z2_field_element &f2)
	Swap operator.

Detailed Description

Class representing an element of the \( \mathbb{F}_2 \) field.

Examples: example_field_operations.cpp.

Member Typedef Documentation

◆ Element

using Gudhi::persistence_fields::Z2_field_element::Element = bool

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Z2_field_element() [1/3]

template<typename Integer_type , class >

Gudhi::persistence_fields::Z2_field_element::Z2_field_element ( Integer_type element )

inline

Constructor setting the element to the given value.

Template Parameters

Integer_type A native integer type. Should be able to contain the characteristic.

Parameters

element Value of the element.

◆ Z2_field_element() [2/3]

Gudhi::persistence_fields::Z2_field_element::Z2_field_element ( const Z2_field_element & toCopy )

inline

Copy constructor.

Parameters

toCopy Element to copy.

◆ Z2_field_element() [3/3]

Gudhi::persistence_fields::Z2_field_element::Z2_field_element ( Z2_field_element && toMove )

inlinenoexcept

Move constructor.

Parameters

toMove Element to move.

Member Function Documentation

◆ get_additive_identity()

Z2_field_element Gudhi::persistence_fields::Z2_field_element::get_additive_identity ( )

inlinestatic

Returns the additive identity of the field.

Returns: false.

◆ get_characteristic()

constexpr unsigned int Gudhi::persistence_fields::Z2_field_element::get_characteristic ( )

inlinestaticconstexpr

Returns the characteristic of the field, that is 2.

Returns: 2.

◆ get_inverse()

Z2_field_element Gudhi::persistence_fields::Z2_field_element::get_inverse ( ) const

inline

Returns the inverse of the element.

Returns: The inverse.

◆ get_multiplicative_identity()

Z2_field_element Gudhi::persistence_fields::Z2_field_element::get_multiplicative_identity ( )

inlinestatic

Returns the multiplicative identity of the field.

Returns: true.

◆ get_partial_inverse()

std::pair< Z2_field_element, unsigned int > Gudhi::persistence_fields::Z2_field_element::get_partial_inverse ( unsigned int productOfCharacteristics ) const

inline

For interface purposes with multi-fields. Returns the inverse together with the second argument.

Parameters

productOfCharacteristics Some value.

Returns: Pair whose first element is the inverse of e and the second element is productOfCharacteristics.

◆ get_partial_multiplicative_identity()

Z2_field_element Gudhi::persistence_fields::Z2_field_element::get_partial_multiplicative_identity ( unsigned int productOfCharacteristics )

inlinestatic

For interface purposes with multi-fields. Returns the multiplicative identity of the field.

Parameters

productOfCharacteristics Some value.

Returns: true.

◆ get_value()

Z2_field_element::Element Gudhi::persistence_fields::Z2_field_element::get_value ( ) const

inline

Returns the value of the element.

Returns: Value of the element.

Friends And Related Function Documentation

◆ operator!= [1/2]

template<typename Integer_type , class = isInteger<Integer_type>>

bool operator!=	(	const Integer_type	v,
		const Z2_field_element &	f
	)

friend

operator!=

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator!= [2/2]

template<typename Integer_type , class = isInteger<Integer_type>>

bool operator!=	(	const Z2_field_element &	f,
		const Integer_type	v
	)

friend

operator!=

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator* [1/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Integer_type operator*	(	const Integer_type &	v,
		Z2_field_element const &	f
	)

friend

operator*

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator* [2/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Z2_field_element operator*	(	Z2_field_element	f,
		const Integer_type &	v
	)

friend

operator*

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator*=

template<typename Integer_type , class = isInteger<Integer_type>>

void operator*=	(	Z2_field_element &	f,
		const Integer_type &	v
	)

friend

operator*=

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator+ [1/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Integer_type operator+	(	const Integer_type &	v,
		const Z2_field_element &	f
	)

friend

operator+

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator+ [2/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Z2_field_element operator+	(	Z2_field_element	f,
		const Integer_type &	v
	)

friend

operator+

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator+=

template<typename Integer_type , class = isInteger<Integer_type>>

void operator+=	(	Z2_field_element &	f,
		const Integer_type &	v
	)

friend

operator+=

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator- [1/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Integer_type operator-	(	const Integer_type	v,
		Z2_field_element const &	f
	)

friend

operator-

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator- [2/2]

template<typename Integer_type , class = isInteger<Integer_type>>

Z2_field_element operator-	(	Z2_field_element	f,
		const Integer_type &	v
	)

friend

operator-

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator-=

template<typename Integer_type , class = isInteger<Integer_type>>

void operator-=	(	Z2_field_element &	f,
		const Integer_type &	v
	)

friend

operator-=

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator== [1/2]

template<typename Integer_type , class = isInteger<Integer_type>>

bool operator==	(	const Integer_type &	v,
		const Z2_field_element &	f
	)

friend

operator==

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

◆ operator== [2/2]

template<typename Integer_type , class = isInteger<Integer_type>>

bool operator==	(	const Z2_field_element &	f,
		const Integer_type &	v
	)

friend

operator==

Template Parameters

Integer_type A native integer type: int, unsigned int, long int, bool, etc.

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

include/gudhi/Fields/Z2_field.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Element

Constructor & Destructor Documentation

◆ Z2_field_element() [1/3]

◆ Z2_field_element() [2/3]

◆ Z2_field_element() [3/3]

Member Function Documentation

◆ get_additive_identity()

◆ get_characteristic()

◆ get_inverse()

◆ get_multiplicative_identity()

◆ get_partial_inverse()

◆ get_partial_multiplicative_identity()

◆ get_value()

Friends And Related Function Documentation

◆ operator!= [1/2]

◆ operator!= [2/2]

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator*=

◆ operator+ [1/2]

◆ operator+ [2/2]

◆ operator+=

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator-=

◆ operator== [1/2]

◆ operator== [2/2]