Class representing an element of the \( \mathbb{F}_p \) field for any prime number \( p \). More...

#include <gudhi/Fields/Zp_field.h>

Public Types
using	Element = Unsigned_integer_type

using	Characteristic = Element

Public Member Functions
	Zp_field_element ()
	Default constructor. Sets the element to 0.

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

	Zp_field_element (const Zp_field_element &toCopy)=default
	Copy constructor.

	Zp_field_element (Zp_field_element &&toMove) noexcept
	Move constructor.

Zp_field_element &	operator= (Zp_field_element other)
	Assign operator.

Zp_field_element &	operator= (Zp_field_element &&other) noexcept
	Move assign operator.

template<typename Integer_type, class = isInteger<Integer_type>>
Zp_field_element &	operator= (const Integer_type &value)
	Assign operator.

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

Zp_field_element	get_inverse () const
	Returns the inverse of the element in the field.

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

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

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

static Zp_field_element	get_multiplicative_identity ()
	Returns the multiplicative identity of the field.

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

static constexpr unsigned int	get_characteristic ()
	Returns the current characteristic.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	swap (Zp_field_element &f1, Zp_field_element &f2) noexcept
	Swap operator.

Detailed Description

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>
class Zp_field_element< characteristic, Unsigned_integer_type, class >

Class representing an element of the \( \mathbb{F}_p \) field for any prime number \( p \).

Template Parameters

characteristic	Value of the characteristic of the field. Has to be a positive prime number.
Unsigned_integer_type	A native unsigned integer type: unsigned int, long unsigned int, etc. Will be used as the field element type.

Member Typedef Documentation

◆ Characteristic

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

using Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::Characteristic = Element

Type for the field characteristic.

◆ Element

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

using Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::Element = Unsigned_integer_type

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Zp_field_element() [1/3]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::Zp_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 if signed.

Parameters

element Value of the element.

◆ Zp_field_element() [2/3]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::Zp_field_element ( const Zp_field_element< characteristic, Unsigned_integer_type, class > & toCopy )

default

Copy constructor.

Parameters

toCopy Element to copy.

◆ Zp_field_element() [3/3]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::Zp_field_element ( Zp_field_element< characteristic, Unsigned_integer_type, class > && toMove )

inlinenoexcept

Move constructor.

Parameters

toMove Element to move.

Member Function Documentation

◆ get_additive_identity()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

static Zp_field_element Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_additive_identity ( )

inlinestatic

Returns the additive identity of the field.

Returns: 0.

◆ get_characteristic()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

static constexpr unsigned int Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_characteristic ( )

inlinestaticconstexpr

Returns the current characteristic.

Returns: The value of the current characteristic.

◆ get_inverse()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

Zp_field_element Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_inverse ( ) const

inline

Returns the inverse of the element in the field.

Returns: The inverse.

◆ get_multiplicative_identity()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

static Zp_field_element Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_multiplicative_identity ( )

inlinestatic

Returns the multiplicative identity of the field.

Returns: 1.

◆ get_partial_inverse()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

std::pair< Zp_field_element, unsigned int > Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_partial_inverse ( unsigned int productOfCharacteristics ) const

inline

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

Parameters

productOfCharacteristics Some value.

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

◆ get_partial_multiplicative_identity()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

static Zp_field_element Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::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: 1.

◆ get_value()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

Element Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::get_value ( ) const

inline

Returns the value of the element.

Returns: Value of the element.

◆ operator=()

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Zp_field_element & Gudhi::persistence_fields::Zp_field_element< characteristic, Unsigned_integer_type, class >::operator= ( const Integer_type & value )

inline

Assign operator.

Template Parameters

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

Friends And Related Symbol Documentation

◆ operator!= [1/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

bool operator!=	(	const Integer_type &	v,
		const Zp_field_element< characteristic, Unsigned_integer_type, class > &	f )

friend

operator!=

Template Parameters

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

◆ operator!= [2/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

bool operator!=	(	const Zp_field_element< characteristic, Unsigned_integer_type, class > &	f,
		const Integer_type &	v )

friend

operator!=

Template Parameters

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

◆ operator* [1/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Integer_type operator*	(	const Integer_type &	v,
		Zp_field_element< characteristic, Unsigned_integer_type, class >	f )

friend

operator*

Template Parameters

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

◆ operator* [2/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Zp_field_element operator*	(	Zp_field_element< characteristic, Unsigned_integer_type, class >	f,
		const Integer_type &	v )

friend

operator*

Template Parameters

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

◆ operator+ [1/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Integer_type operator+	(	const Integer_type &	v,
		Zp_field_element< characteristic, Unsigned_integer_type, class >	f )

friend

operator+

Template Parameters

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

◆ operator+ [2/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Zp_field_element operator+	(	Zp_field_element< characteristic, Unsigned_integer_type, class >	f,
		const Integer_type &	v )

friend

operator+

Template Parameters

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

◆ operator- [1/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Integer_type operator-	(	const Integer_type &	v,
		const Zp_field_element< characteristic, Unsigned_integer_type, class > &	f )

friend

operator-

Template Parameters

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

◆ operator- [2/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

Zp_field_element operator-	(	Zp_field_element< characteristic, Unsigned_integer_type, class >	f,
		const Integer_type &	v )

friend

operator-

Template Parameters

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

◆ operator== [1/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

bool operator==	(	const Integer_type &	v,
		const Zp_field_element< characteristic, Unsigned_integer_type, class > &	f )

friend

operator==

Template Parameters

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

◆ operator== [2/2]

template<unsigned int characteristic, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

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

bool operator==	(	const Zp_field_element< characteristic, Unsigned_integer_type, class > &	f,
		const Integer_type &	v )

friend

operator==

Template Parameters

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

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

include/gudhi/Fields/Zp_field.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Characteristic

◆ Element

Constructor & Destructor Documentation

◆ Zp_field_element() [1/3]

◆ Zp_field_element() [2/3]

◆ Zp_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()

◆ operator=()

Friends And Related Symbol Documentation

◆ operator!= [1/2]

◆ operator!= [2/2]

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator+ [1/2]

◆ operator+ [2/2]

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator== [1/2]

◆ operator== [2/2]