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

Public Types
using	element_type = Unsigned_integer_type

using	characteristic_type = element_type

Public Member Functions
	Zp_field_operators (characteristic_type 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_type characteristic)
	Sets the characteristic of the field. More...

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

element_type	get_value (element_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...

template<typename Signed_integer_type , class = isSignedInteger<Signed_integer_type>>
element_type	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_type	add (element_type e1, element_type e2) const
	Returns the sum of two elements in the field. More...

void	add_inplace (element_type &e1, element_type 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_type	substract (element_type e1, element_type e2) const
	Returns the substraction in the field of the first element by the second element. More...

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

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

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

void	multiply_inplace (element_type &e1, element_type 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_type	multiply_and_add (element_type e, element_type m, element_type 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_type &e, element_type m, element_type 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_type e, element_type m, element_type &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_type	add_and_multiply (element_type e, element_type a, element_type 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_type &e, element_type a, element_type 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_type e, element_type a, element_type &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_type e1, element_type e2) const
	Returns true if the two given elements are equal in the field, false otherwise. More...

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

std::pair< element_type, characteristic_type >	get_partial_inverse (element_type e, characteristic_type 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_type	get_additive_identity ()
	Returns the additive identity of the field. More...

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

static constexpr element_type	get_partial_multiplicative_identity ([[maybe_unused]] characteristic_type 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_type

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_type = element_type

Type for the field characteristic.

◆ element_type

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_type = 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_type 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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add	(	element_type	e1,
		element_type	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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::add_and_multiply	(	element_type	e,
		element_type	a,
		element_type	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_type	e,
		element_type	a,
		element_type &	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_type &	e,
		element_type	a,
		element_type	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_type &	e1,
		element_type	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_type	e1,
		element_type	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_type 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_type& 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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_inverse ( element_type 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_type 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_type, characteristic_type> Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_partial_inverse	(	element_type	e,
		characteristic_type	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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_partial_multiplicative_identity ( [[maybe_unused] ] characteristic_type 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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::get_value ( element_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.

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_type 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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply	(	element_type	e1,
		element_type	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_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::multiply_and_add	(	element_type	e,
		element_type	m,
		element_type	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_type	e,
		element_type	m,
		element_type &	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_type &	e,
		element_type	m,
		element_type	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_type &	e1,
		element_type	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_type characteristic )

inline

Sets the characteristic of the field.

Parameters

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

◆ substract()

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

element_type Gudhi::persistence_fields::Zp_field_operators< Unsigned_integer_type, class >::substract	(	element_type	e1,
		element_type	e2
	)		const

inline

Returns the substraction 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.

◆ substract_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 >::substract_inplace_back	(	element_type	e1,
		element_type &	e2
	)		const

inline

Stores in the second element the substraction 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.

◆ substract_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 >::substract_inplace_front	(	element_type &	e1,
		element_type	e2
	)		const

inline

Stores in the first element the substraction 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

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 >

Member Typedef Documentation

◆ characteristic_type

◆ element_type

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()

◆ substract()

◆ substract_inplace_back()

◆ substract_inplace_front()

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 >