Class defining operators for the \( \mathbb{F}_2 \) field. More...

Public Types
using	element_type = bool

using	characteristic_type = unsigned int

Public Member Functions
	Z2_field_operators ()
	Default constructor.

Static Public Member Functions
static constexpr characteristic_type	get_characteristic ()
	Returns the characteristic of the field, that is `2`. More...

template<typename Integer_type , class = isInteger<Integer_type>>
static element_type	get_value (Integer_type e)
	Returns the value of an integer in the field. That is the positive value of the integer modulo the current characteristic. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	add (Unsigned_integer_type e1, Unsigned_integer_type e2)
	Returns the sum of two elements in the field. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	add_inplace (Unsigned_integer_type &e1, Unsigned_integer_type e2)
	Stores in the first element the sum of two given elements in the field, that is `(e1 + e2) % 2`, such that the result is positive. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	substract (Unsigned_integer_type e1, Unsigned_integer_type e2)
	Returns the substraction in the field of the first element by the second element. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	substract_inplace_front (Unsigned_integer_type &e1, Unsigned_integer_type e2)
	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...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	substract_inplace_back (Unsigned_integer_type e1, Unsigned_integer_type &e2)
	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...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	multiply (Unsigned_integer_type e1, Unsigned_integer_type e2)
	Returns the multiplication of two elements in the field. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	multiply_inplace (Unsigned_integer_type &e1, Unsigned_integer_type e2)
	Stores in the first element the multiplication of two given elements in the field, that is `(e1 * e2) % 2`, such that the result is positive. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	multiply_and_add (Unsigned_integer_type e, Unsigned_integer_type m, Unsigned_integer_type a)
	Multiplies the first element with the second one and adds the third one. Returns the result in the field. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	multiply_and_add_inplace_front (Unsigned_integer_type &e, Unsigned_integer_type m, Unsigned_integer_type a)
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % 2`, such that the result is positive. Stores the result in the first element. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	multiply_and_add_inplace_back (Unsigned_integer_type e, Unsigned_integer_type m, Unsigned_integer_type &a)
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % 2`, such that the result is positive. Stores the result in the third element. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	add_and_multiply (Unsigned_integer_type e, Unsigned_integer_type a, Unsigned_integer_type m)
	Adds the first element to the second one and multiplies the third one with it. Returns the result in the field. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	add_and_multiply_inplace_front (Unsigned_integer_type &e, Unsigned_integer_type a, Unsigned_integer_type m)
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % 2`, such that the result is positive. Stores the result in the first element. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static void	add_and_multiply_inplace_back (Unsigned_integer_type &e, Unsigned_integer_type a, Unsigned_integer_type m)
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % 2`, such that the result is positive. Stores the result in the third element. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static bool	are_equal (Unsigned_integer_type e1, Unsigned_integer_type e2)
	Returns true if the two given elements are equal in the field, false otherwise. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static element_type	get_inverse (Unsigned_integer_type e)
	Returns the inverse of the given element in the field. More...

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>
static std::pair< element_type, characteristic_type >	get_partial_inverse (Unsigned_integer_type e, characteristic_type productOfCharacteristics)
	For interface purposes with multi-fields. Returns the inverse together with the second argument. More...

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...

Detailed Description

Class defining operators for the \( \mathbb{F}_2 \) field.

Examples: example_field_operations.cpp.

Member Typedef Documentation

◆ characteristic_type

using Gudhi::persistence_fields::Z2_field_operators::characteristic_type = unsigned int

Type for the field characteristic.

◆ element_type

using Gudhi::persistence_fields::Z2_field_operators::element_type = bool

Type for the elements in the field.

Member Function Documentation

◆ add()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::add	(	Unsigned_integer_type	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

Returns the sum of two elements in the field.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 + e2) % 2 as a boolean.

◆ add_and_multiply()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::add_and_multiply	(	Unsigned_integer_type	e,
		Unsigned_integer_type	a,
		Unsigned_integer_type	m
	)

inlinestatic

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

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

Returns: ((e + a) * m) % 2 as a boolean.

◆ add_and_multiply_inplace_back()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::add_and_multiply_inplace_back	(	Unsigned_integer_type &	e,
		Unsigned_integer_type	a,
		Unsigned_integer_type	m
	)

inlinestatic

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % 2, such that the result is positive. Stores the result in the third element.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

◆ add_and_multiply_inplace_front()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::add_and_multiply_inplace_front	(	Unsigned_integer_type &	e,
		Unsigned_integer_type	a,
		Unsigned_integer_type	m
	)

inlinestatic

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % 2, such that the result is positive. Stores the result in the first element.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

◆ add_inplace()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::add_inplace	(	Unsigned_integer_type &	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

Stores in the first element the sum of two given elements in the field, that is (e1 + e2) % 2, such that the result is positive.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

◆ are_equal()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static bool Gudhi::persistence_fields::Z2_field_operators::are_equal	(	Unsigned_integer_type	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

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

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

Returns: true If e1 % 2 == e2 % 2.; false Otherwise.

◆ get_additive_identity()

static constexpr element_type Gudhi::persistence_fields::Z2_field_operators::get_additive_identity ( )

inlinestaticconstexpr

Returns the additive identity of the field.

Returns: false.

◆ get_characteristic()

static constexpr characteristic_type Gudhi::persistence_fields::Z2_field_operators::get_characteristic ( )

inlinestaticconstexpr

Returns the characteristic of the field, that is 2.

Returns: 2.

◆ get_inverse()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::get_inverse ( Unsigned_integer_type e )

inlinestatic

Returns the inverse of the given element in the field.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e	Element to get the inverse from.

Returns: Inverse in the current field of e % 2.

◆ get_multiplicative_identity()

static constexpr element_type Gudhi::persistence_fields::Z2_field_operators::get_multiplicative_identity ( )

inlinestaticconstexpr

Returns the multiplicative identity of the field.

Returns: true.

◆ get_partial_inverse()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static std::pair<element_type, characteristic_type> Gudhi::persistence_fields::Z2_field_operators::get_partial_inverse	(	Unsigned_integer_type	e,
		characteristic_type	productOfCharacteristics
	)

inlinestatic

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

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

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()

static constexpr element_type Gudhi::persistence_fields::Z2_field_operators::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: true.

◆ get_value()

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

static element_type Gudhi::persistence_fields::Z2_field_operators::get_value ( Integer_type e )

inlinestatic

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

Template Parameters

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

Parameters

e	Integer to return the value from.

Returns: A boolean representing e % 2.

◆ multiply()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::multiply	(	Unsigned_integer_type	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

Returns the multiplication of two elements in the field.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 * e2) % 2 as a boolean.

◆ multiply_and_add()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::multiply_and_add	(	Unsigned_integer_type	e,
		Unsigned_integer_type	m,
		Unsigned_integer_type	a
	)

inlinestatic

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

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

Returns: (e * m + a) % 2 as a boolean.

◆ multiply_and_add_inplace_back()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::multiply_and_add_inplace_back	(	Unsigned_integer_type	e,
		Unsigned_integer_type	m,
		Unsigned_integer_type &	a
	)

inlinestatic

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % 2, such that the result is positive. Stores the result in the third element.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

◆ multiply_and_add_inplace_front()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::multiply_and_add_inplace_front	(	Unsigned_integer_type &	e,
		Unsigned_integer_type	m,
		Unsigned_integer_type	a
	)

inlinestatic

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % 2, such that the result is positive. Stores the result in the first element.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

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

◆ multiply_inplace()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::multiply_inplace	(	Unsigned_integer_type &	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

Stores in the first element the multiplication of two given elements in the field, that is (e1 * e2) % 2, such that the result is positive.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

◆ substract()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static element_type Gudhi::persistence_fields::Z2_field_operators::substract	(	Unsigned_integer_type	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

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

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 - e2) % 2 as a boolean.

◆ substract_inplace_back()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::substract_inplace_back	(	Unsigned_integer_type	e1,
		Unsigned_integer_type &	e2
	)

inlinestatic

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.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

◆ substract_inplace_front()

template<typename Unsigned_integer_type , class = isUnsignedInteger<Unsigned_integer_type>>

static void Gudhi::persistence_fields::Z2_field_operators::substract_inplace_front	(	Unsigned_integer_type &	e1,
		Unsigned_integer_type	e2
	)

inlinestatic

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.

Template Parameters

Unsigned_integer_type A native unsigned integer type: unsigned int, bool, etc.

Parameters

e1	First element.
e2	Second element.

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

include/gudhi/Fields/Z2_field_operators.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ characteristic_type

◆ element_type

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()

◆ multiply()

◆ multiply_and_add()

◆ multiply_and_add_inplace_back()

◆ multiply_and_add_inplace_front()

◆ multiply_inplace()

◆ substract()

◆ substract_inplace_back()

◆ substract_inplace_front()