Class representing an element of the \( \mathbb{F}_p \) field for any prime number \( p \). If each instanciation of the class can represent another element, they all share the same characteritics. That is if the characteristics are set for one, they will be set for all the others. The characteristics can be set before instianciating the elements with the static Shared_Zp_field_element::initialize method. More...

Public Types
using	element_type = Unsigned_integer_type

using	characteristic_type = element_type

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

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

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

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

element_type	get_value () const
	Returns the value of the element. More...

Shared_Zp_field_element &	operator= (Shared_Zp_field_element other)
	Assign operator.

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

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

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

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

Static Public Member Functions
static void	initialize (characteristic_type characteristic)
	Initialize the field to the given characteristic. Should be called first before constructing the field elements. More...

static Shared_Zp_field_element	get_additive_identity ()
	Returns the additive identity of the field. More...

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

static Shared_Zp_field_element	get_partial_multiplicative_identity ([[maybe_unused]] characteristic_type productOfCharacteristics)
	For interface purposes with multi-fields. Returns the multiplicative identity of the field. More...

static characteristic_type	get_characteristic ()
	Returns the current characteristic. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	swap (Shared_Zp_field_element &f1, Shared_Zp_field_element &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::Shared_Zp_field_element< Unsigned_integer_type, class >

Class representing an element of the \( \mathbb{F}_p \) field for any prime number \( p \). If each instanciation of the class can represent another element, they all share the same characteritics. That is if the characteristics are set for one, they will be set for all the others. The characteristics can be set before instianciating the elements with the static Shared_Zp_field_element::initialize method.

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::Shared_Zp_field_element< 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::Shared_Zp_field_element< Unsigned_integer_type, class >::element_type = Unsigned_integer_type

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Shared_Zp_field_element() [1/3]

template<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::Shared_Zp_field_element< Unsigned_integer_type, class >::Shared_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.

◆ Shared_Zp_field_element() [2/3]

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

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

inline

Copy constructor.

Parameters

toCopy Element to copy.

◆ Shared_Zp_field_element() [3/3]

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

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

inlinenoexcept

Move constructor.

Parameters

toMove Element to move.

Member Function Documentation

◆ get_additive_identity()

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

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

inlinestatic

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> >>

static characteristic_type Gudhi::persistence_fields::Shared_Zp_field_element< Unsigned_integer_type, class >::get_characteristic ( )

inlinestatic

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> >>

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

inline

Returns the inverse of the element in the field.

Returns: The inverse.

◆ get_multiplicative_identity()

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

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

inlinestatic

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<Shared_Zp_field_element, characteristic_type> Gudhi::persistence_fields::Shared_Zp_field_element< Unsigned_integer_type, class >::get_partial_inverse ( characteristic_type 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<typename Unsigned_integer_type = unsigned int, class = std::enable_if_t<std::is_unsigned_v<Unsigned_integer_type> >>

static Shared_Zp_field_element Gudhi::persistence_fields::Shared_Zp_field_element< Unsigned_integer_type, class >::get_partial_multiplicative_identity ( [[maybe_unused] ] characteristic_type productOfCharacteristics )

inlinestatic

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

Parameters

productOfCharacteristics Some value.

Returns: 1.

◆ get_value()

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

element_type Gudhi::persistence_fields::Shared_Zp_field_element< Unsigned_integer_type, class >::get_value ( ) const

inline

Returns the value of the element.

Returns: Value of the element.

◆ initialize()

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

static void Gudhi::persistence_fields::Shared_Zp_field_element< Unsigned_integer_type, class >::initialize ( characteristic_type characteristic )

inlinestatic

Initialize the field to the given characteristic. Should be called first before constructing the field elements.

Parameters

characteristic Characteristic of the field. A positive prime number.

◆ operator=()

template<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>>

Shared_Zp_field_element& Gudhi::persistence_fields::Shared_Zp_field_element< 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 Function Documentation

◆ operator!= [1/2]

template<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 Shared_Zp_field_element< 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<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 Shared_Zp_field_element< 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<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,
		Shared_Zp_field_element< 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<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>>

Shared_Zp_field_element operator*	(	Shared_Zp_field_element< 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<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*=	(	Shared_Zp_field_element< 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<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,
		Shared_Zp_field_element< 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<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>>

Shared_Zp_field_element operator+	(	Shared_Zp_field_element< 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<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+=	(	Shared_Zp_field_element< 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<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 Shared_Zp_field_element< 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<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>>

Shared_Zp_field_element operator-	(	Shared_Zp_field_element< 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<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-=	(	Shared_Zp_field_element< 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<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 Shared_Zp_field_element< 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<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 Shared_Zp_field_element< 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_shared.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::Shared_Zp_field_element< Unsigned_integer_type, class >

Member Typedef Documentation

◆ characteristic_type

◆ element_type

Constructor & Destructor Documentation

◆ Shared_Zp_field_element() [1/3]

◆ Shared_Zp_field_element() [2/3]

◆ Shared_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()

◆ initialize()

◆ operator=()

Friends And Related Function 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]

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