Class representing an element of a multi-field, such that the product of all characteristics fits into the given Unsigned_integer_type template argument. The characteristics will corresponds to all prime numbers in the interval given as other template arguments. More...

#include <gudhi/Fields/Multi_field_small.h>

Public Types
using	Element = Unsigned_integer_type
using	Characteristic = Element

Public Member Functions
	Multi_field_element_with_small_characteristics ()
	Default constructor. Sets the element to 0.
template<typename Integer_type, class = isInteger<Integer_type>>
	Multi_field_element_with_small_characteristics (Integer_type element)
	Constructor setting the element to the given value.
	operator unsigned int () const
	Casts the element into an unsigned int.
Multi_field_element_with_small_characteristics	get_inverse () const
	Returns the inverse of the element in the multi-field, see [boissonnat:hal-00922572].
std::pair< Multi_field_element_with_small_characteristics, Characteristic >	get_partial_inverse (Characteristic productOfCharacteristics) const
	Returns the inverse of the element with respect to a sub-product of the characteristics in the multi-field, see [boissonnat:hal-00922572].
Element	get_value () const
	Returns the value of the element.

Static Public Member Functions
static Multi_field_element_with_small_characteristics	get_additive_identity ()
	Returns the additive identity of a field.
static Multi_field_element_with_small_characteristics	get_multiplicative_identity ()
	Returns the multiplicative identity of a field.
static Multi_field_element_with_small_characteristics	get_partial_multiplicative_identity (const Characteristic &productOfCharacteristics)
	Returns the partial multiplicative identity of the multi-field from the given product. See [boissonnat:hal-00922572] for more details.
static constexpr Characteristic	get_characteristic ()
	Returns the product of all characteristics.

Friends
void	operator+= (Multi_field_element_with_small_characteristics &f1, Multi_field_element_with_small_characteristics const &f2)
	operator+=
Multi_field_element_with_small_characteristics	operator+ (Multi_field_element_with_small_characteristics f1, Multi_field_element_with_small_characteristics const &f2)
	operator+
template<typename Integer_type, class = isInteger<Integer_type>>
void	operator+= (Multi_field_element_with_small_characteristics &f, const Integer_type &v)
	operator+=
template<typename Integer_type, class = isInteger<Integer_type>>
Multi_field_element_with_small_characteristics	operator+ (Multi_field_element_with_small_characteristics f, const Integer_type &v)
	operator+
template<typename Integer_type, class = isInteger<Integer_type>>
Integer_type	operator+ (const Integer_type &v, Multi_field_element_with_small_characteristics f)
	operator+
void	operator-= (Multi_field_element_with_small_characteristics &f1, Multi_field_element_with_small_characteristics const &f2)
	operator-=
Multi_field_element_with_small_characteristics	operator- (Multi_field_element_with_small_characteristics f1, Multi_field_element_with_small_characteristics const &f2)
	operator-
template<typename Integer_type, class = isInteger<Integer_type>>
void	operator-= (Multi_field_element_with_small_characteristics &f, const Integer_type &v)
	operator-=
template<typename Integer_type, class = isInteger<Integer_type>>
Multi_field_element_with_small_characteristics	operator- (Multi_field_element_with_small_characteristics f, const Integer_type &v)
	operator-
template<typename Integer_type, class = isInteger<Integer_type>>
Integer_type	operator- (const Integer_type &v, const Multi_field_element_with_small_characteristics &f)
	operator-
void	*operator=** (Multi_field_element_with_small_characteristics &f1, Multi_field_element_with_small_characteristics const &f2)
	operator*=
Multi_field_element_with_small_characteristics	operator* (Multi_field_element_with_small_characteristics f1, Multi_field_element_with_small_characteristics const &f2)
	operator*
template<typename Integer_type, class = isInteger<Integer_type>>
void	operator*= (Multi_field_element_with_small_characteristics &f, const Integer_type &v)
	operator*=
template<typename Integer_type, class = isInteger<Integer_type>>
Multi_field_element_with_small_characteristics	operator* (Multi_field_element_with_small_characteristics f, const Integer_type &v)
	operator*
template<typename Integer_type, class = isInteger<Integer_type>>
Integer_type	operator* (const Integer_type &v, Multi_field_element_with_small_characteristics f)
	operator*
bool	operator== (const Multi_field_element_with_small_characteristics &f1, const Multi_field_element_with_small_characteristics &f2)
	operator==
template<typename Integer_type, class = isInteger<Integer_type>>
bool	operator== (const Integer_type v, const Multi_field_element_with_small_characteristics &f)
	operator==
template<typename Integer_type, class = isInteger<Integer_type>>
bool	operator== (const Multi_field_element_with_small_characteristics &f, const Integer_type v)
	operator==
bool	operator!= (const Multi_field_element_with_small_characteristics &f1, const Multi_field_element_with_small_characteristics &f2)
	operator!=
template<typename Integer_type, class = isInteger<Integer_type>>
bool	operator!= (const Integer_type v, const Multi_field_element_with_small_characteristics &f)
	operator!=
template<typename Integer_type, class = isInteger<Integer_type>>
bool	operator!= (const Multi_field_element_with_small_characteristics &f, const Integer_type v)
	operator!=
void	swap (Multi_field_element_with_small_characteristics &f1, Multi_field_element_with_small_characteristics &f2) noexcept
	Assign operator.

Detailed Description

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

Class representing an element of a multi-field, such that the product of all characteristics fits into the given Unsigned_integer_type template argument. The characteristics will corresponds to all prime numbers in the interval given as other template arguments.

Template Parameters

minimum	Interval closed lower bound.
maximum	Interval closed upper bound.
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 minimum, unsigned int maximum, typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

using Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::Characteristic = Element

Type for the field characteristic.

◆ Element

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

using Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::Element = Unsigned_integer_type

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Multi_field_element_with_small_characteristics()

template<unsigned int minimum, unsigned int maximum, 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::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::Multi_field_element_with_small_characteristics ( Integer_type element )

inline

Constructor setting the element to the given value.

Parameters

element Value of the element.

Member Function Documentation

◆ get_additive_identity()

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

Multi_field_element_with_small_characteristics Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_additive_identity ( )

inlinestatic

Returns the additive identity of a field.

Returns: The additive identity of a field.

◆ get_characteristic()

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

constexpr Characteristic Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_characteristic ( )

inlinestaticconstexpr

Returns the product of all characteristics.

Returns: The product of all characteristics.

◆ get_inverse()

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

Multi_field_element_with_small_characteristics Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_inverse ( ) const

inline

Returns the inverse of the element in the multi-field, see [boissonnat:hal-00922572].

Returns: The inverse.

◆ get_multiplicative_identity()

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

Multi_field_element_with_small_characteristics Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_multiplicative_identity ( )

inlinestatic

Returns the multiplicative identity of a field.

Returns: The multiplicative identity of a field.

◆ get_partial_inverse()

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

std::pair< Multi_field_element_with_small_characteristics, Characteristic > Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_partial_inverse ( Characteristic productOfCharacteristics ) const

inline

Returns the inverse of the element with respect to a sub-product of the characteristics in the multi-field, see [boissonnat:hal-00922572].

Parameters

productOfCharacteristics Sub-product of the characteristics.

Returns: Pair of the inverse and the characteristic the inverse corresponds to.

◆ get_partial_multiplicative_identity()

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

Multi_field_element_with_small_characteristics Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_partial_multiplicative_identity ( const Characteristic & productOfCharacteristics )

inlinestatic

Returns the partial multiplicative identity of the multi-field from the given product. See [boissonnat:hal-00922572] for more details.

Parameters

productOfCharacteristics Product of the different characteristics to take into account in the multi-field.

Returns: The partial multiplicative identity of the multi-field.

◆ get_value()

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

Element Gudhi::persistence_fields::Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class >::get_value ( ) const

inline

Returns the value of the element.

Returns: Value of the element.

◆ operator!= [1/2]

template<unsigned int minimum, unsigned int maximum, 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 Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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 Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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,
		Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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>>

Multi_field_element_with_small_characteristics operator*	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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*=

template<unsigned int minimum, unsigned int maximum, 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>>

void operator*=	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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,
		Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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>>

Multi_field_element_with_small_characteristics operator+	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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+=

template<unsigned int minimum, unsigned int maximum, 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>>

void operator+=	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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 Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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>>

Multi_field_element_with_small_characteristics operator-	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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-=

template<unsigned int minimum, unsigned int maximum, 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>>

void operator-=	(	Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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 Multi_field_element_with_small_characteristics< minimum, maximum, 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 minimum, unsigned int maximum, 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 Multi_field_element_with_small_characteristics< minimum, maximum, 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.

◆ swap

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

void swap	(	Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class > &	f1,
		Multi_field_element_with_small_characteristics< minimum, maximum, Unsigned_integer_type, class > &	f2 )

friend

Assign operator.

Template Parameters

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

Swap operator.

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

include/gudhi/Fields/Multi_field_small.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Characteristic

◆ Element

Constructor & Destructor Documentation

◆ Multi_field_element_with_small_characteristics()

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 Symbol 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]

◆ swap