Class defining operators for the \( \mathbb{F}_p \) field for any prime number \( p \). More...

#include <gudhi/Fields/Zp_field_operators.h>

Public Types
using	Element = Unsigned_integer_type

using	Characteristic = Element

Public Member Functions
	Zp_field_operators (Characteristic characteristic=0)
	Default constructor. If a non-zero characteristic is given, initializes the field with it. The characteristic can later be changed again or initialized with set_characteristic. More...

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

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

void	set_characteristic (Characteristic characteristic)
	Sets the characteristic of the field. More...

const Characteristic &	get_characteristic () const
	Returns the current characteristic. More...

Element	get_value (Element e) const
	Returns the value of an integer in the field. That is the positive value of the integer modulo the current characteristic. More...

template<typename Signed_integer_type , class = isSignedInteger<Signed_integer_type>>
Element	get_value (Signed_integer_type e) const
	Returns the value of an integer in the field. That is the positive value of the integer modulo the current characteristic. More...

Element	add (Element e1, Element e2) const
	Returns the sum of two elements in the field. More...

void	add_inplace (Element &e1, Element e2) const
	Stores in the first element the sum of two given elements in the field, that is `(e1 + e2) % characteristic`, such that the result is positive. More...

Element	subtract (Element e1, Element e2) const
	Returns the subtraction in the field of the first element by the second element. More...

void	subtract_inplace_front (Element &e1, Element e2) const
	Stores in the first element the subtraction in the field of the first element by the second element, that is `(e1 - e2) % 2`, such that the result is positive. More...

void	subtract_inplace_back (Element e1, Element &e2) const
	Stores in the second element the subtraction in the field of the first element by the second element, that is `(e1 - e2) % 2`, such that the result is positive. More...

Element	multiply (Element e1, Element e2) const
	Returns the multiplication of two elements in the field. More...

void	multiply_inplace (Element &e1, Element e2) const
	Stores in the first element the multiplication of two given elements in the field, that is `(e1 * e2) % characteristic`, such that the result is positive. More...

Element	multiply_and_add (Element e, Element m, Element a) const
	Multiplies the first element with the second one and adds the third one. Returns the result in the field. More...

void	multiply_and_add_inplace_front (Element &e, Element m, Element a) const
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % characteristic`, such that the result is positive. Stores the result in the first element. More...

void	multiply_and_add_inplace_back (Element e, Element m, Element &a) const
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % characteristic`, such that the result is positive. Stores the result in the third element. More...

Element	add_and_multiply (Element e, Element a, Element m) const
	Adds the first element to the second one and multiplies the third one with it. Returns the result in the field. More...

void	add_and_multiply_inplace_front (Element &e, Element a, Element m) const
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % characteristic`, such that the result is positive. Stores the result in the first element. More...

void	add_and_multiply_inplace_back (Element e, Element a, Element &m) const
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % characteristic`, such that the result is positive. Stores the result in the third element. More...

bool	are_equal (Element e1, Element e2) const
	Returns true if the two given elements are equal in the field, false otherwise. More...

Element	get_inverse (Element e) const
	Returns the inverse of the given element in the field. More...

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

Zp_field_operators &	operator= (Zp_field_operators other)
	Assign operator.

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

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

static constexpr Element	get_partial_multiplicative_identity (Characteristic productOfCharacteristics)
	For interface purposes with multi-fields. Returns the multiplicative identity of the field. More...

Friends
void	swap (Zp_field_operators &f1, Zp_field_operators &f2)
	Swap operator.

Detailed Description

template<typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>
class Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >

Class defining operators for the \( \mathbb{F}_p \) field for any prime number \( p \).

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, long unsigned int, etc. Will be used as the field element type.

Examples: example_field_operations.cpp.

Member Typedef Documentation

◆ Characteristic

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

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

Type for the field characteristic.

◆ Element

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

using Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::Element = Unsigned_integer_type

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Zp_field_operators() [1/3]

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

Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::Zp_field_operators ( Characteristic characteristic = 0 )

inline

Default constructor. If a non-zero characteristic is given, initializes the field with it. The characteristic can later be changed again or initialized with set_characteristic.

Parameters

characteristic Prime number corresponding to the desired characteristic of the field.

◆ Zp_field_operators() [2/3]

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

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

inline

Copy constructor.

Parameters

toCopy Operators to copy.

◆ Zp_field_operators() [3/3]

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

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

inlinenoexcept

Move constructor.

Parameters

toMove Operators to move.

Member Function Documentation

◆ add()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add	(	Element	e1,
		Element	e2
	)		const

inline

Returns the sum of two elements in the field.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 + e2) % characteristic, such that the result is positive.

◆ add_and_multiply()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add_and_multiply	(	Element	e,
		Element	a,
		Element	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it. Returns the result in the field.

Warning: Not overflow safe.

Parameters

e	First element.
a	Second element.
m	Third element.

Returns: ((e + a) * m) % characteristic, such that the result is positive.

◆ add_and_multiply_inplace_back()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add_and_multiply_inplace_back	(	Element	e,
		Element	a,
		Element &	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % characteristic, such that the result is positive. Stores the result in the third element.

Warning: Not overflow safe.

Parameters

e	First element.
a	Second element.
m	Third element.

◆ add_and_multiply_inplace_front()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add_and_multiply_inplace_front	(	Element &	e,
		Element	a,
		Element	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % characteristic, such that the result is positive. Stores the result in the first element.

Warning: Not overflow safe.

Parameters

e	First element.
a	Second element.
m	Third element.

◆ add_inplace()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add_inplace	(	Element &	e1,
		Element	e2
	)		const

inline

Stores in the first element the sum of two given elements in the field, that is (e1 + e2) % characteristic, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ are_equal()

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

bool Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::are_equal	(	Element	e1,
		Element	e2
	)		const

inline

Returns true if the two given elements are equal in the field, false otherwise.

Parameters

e1	First element to compare.
e2	Second element to compare.

Returns: true If e1 % characteristic == e2 % characteristic.; false Otherwise.

◆ get_additive_identity()

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

static constexpr Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_additive_identity ( )

inlinestaticconstexpr

Returns the additive identity of the field.

Returns: 0.

◆ get_characteristic()

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

const Characteristic & Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_characteristic ( ) const

inline

Returns the current characteristic.

Returns: The value of the current characteristic.

◆ get_inverse()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_inverse ( Element e ) const

inline

Returns the inverse of the given element in the field.

Parameters

e	Element to get the inverse from.

Returns: Inverse in the current field of e % characteristic.

◆ get_multiplicative_identity()

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

static constexpr Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_multiplicative_identity ( )

inlinestaticconstexpr

Returns the multiplicative identity of the field.

Returns: 1.

◆ get_partial_inverse()

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

std::pair< Element, Characteristic > Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_partial_inverse	(	Element	e,
		Characteristic	productOfCharacteristics
	)		const

inline

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

Parameters

e	Element to get the inverse from.
productOfCharacteristics	Some value.

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

◆ get_partial_multiplicative_identity()

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

static constexpr Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_partial_multiplicative_identity ( Characteristic productOfCharacteristics )

inlinestaticconstexpr

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

Parameters

productOfCharacteristics Some value.

Returns: 1.

◆ get_value() [1/2]

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_value ( Element e ) const

inline

Returns the value of an integer in the field. That is the positive value of the integer modulo the current characteristic.

Parameters

e	Unsigned integer to return the value from.

Returns: e modulo the current characteristic, such that the result is positive.

◆ get_value() [2/2]

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

template<typename Signed_integer_type , class = isSignedInteger<Signed_integer_type>>

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_value ( Signed_integer_type e ) const

inline

Returns the value of an integer in the field. That is the positive value of the integer modulo the current characteristic.

Template Parameters

Signed_integer_type A native signed integer type: int, long int, etc.

Parameters

e	Integer to return the value from.

Returns: e modulo the current characteristic, such that the result is positive.

◆ multiply()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply	(	Element	e1,
		Element	e2
	)		const

inline

Returns the multiplication of two elements in the field.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 * e2) % characteristic, such that the result is positive.

◆ multiply_and_add()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply_and_add	(	Element	e,
		Element	m,
		Element	a
	)		const

inline

Multiplies the first element with the second one and adds the third one. Returns the result in the field.

Warning: Not overflow safe.

Parameters

e	First element.
m	Second element.
a	Third element.

Returns: (e * m + a) % characteristic, such that the result is positive.

◆ multiply_and_add_inplace_back()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply_and_add_inplace_back	(	Element	e,
		Element	m,
		Element &	a
	)		const

inline

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % characteristic, such that the result is positive. Stores the result in the third element.

Warning: Not overflow safe.

Parameters

e	First element.
m	Second element.
a	Third element.

◆ multiply_and_add_inplace_front()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply_and_add_inplace_front	(	Element &	e,
		Element	m,
		Element	a
	)		const

inline

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % characteristic, such that the result is positive. Stores the result in the first element.

Warning: Not overflow safe.

Parameters

e	First element.
m	Second element.
a	Third element.

◆ multiply_inplace()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply_inplace	(	Element &	e1,
		Element	e2
	)		const

inline

Stores in the first element the multiplication of two given elements in the field, that is (e1 * e2) % characteristic, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ set_characteristic()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::set_characteristic ( Characteristic characteristic )

inline

Sets the characteristic of the field.

Parameters

characteristic Prime number corresponding to the desired characteristic of the field.

◆ subtract()

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

Element Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::subtract	(	Element	e1,
		Element	e2
	)		const

inline

Returns the subtraction in the field of the first element by the second element.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 - e2) % characteristic, such that the result is positive.

◆ subtract_inplace_back()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::subtract_inplace_back	(	Element	e1,
		Element &	e2
	)		const

inline

Stores in the second element the subtraction in the field of the first element by the second element, that is (e1 - e2) % 2, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ subtract_inplace_front()

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

void Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::subtract_inplace_front	(	Element &	e1,
		Element	e2
	)		const

inline

Stores in the first element the subtraction in the field of the first element by the second element, that is (e1 - e2) % 2, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

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

include/gudhi/Fields/Zp_field_operators.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Characteristic

◆ Element

Constructor & Destructor Documentation

◆ Zp_field_operators() [1/3]

◆ Zp_field_operators() [2/3]

◆ Zp_field_operators() [3/3]

Member Function Documentation

◆ add()

◆ add_and_multiply()

◆ add_and_multiply_inplace_back()

◆ add_and_multiply_inplace_front()

◆ add_inplace()

◆ are_equal()

◆ get_additive_identity()

◆ get_characteristic()

◆ get_inverse()

◆ get_multiplicative_identity()

◆ get_partial_inverse()

◆ get_partial_multiplicative_identity()

◆ get_value() [1/2]

◆ get_value() [2/2]

◆ multiply()

◆ multiply_and_add()

◆ multiply_and_add_inplace_back()

◆ multiply_and_add_inplace_front()

◆ multiply_inplace()

◆ set_characteristic()

◆ subtract()

◆ subtract_inplace_back()

◆ subtract_inplace_front()