Galois Field numbers, i.e. More...

#include <GFNumber.h>

Public Member Functions
	GFNumber ()=default

	GFNumber (IntegerType n, const GaloisField< IntegerType > *gf=nullptr)

	GFNumber (const GFNumber &n, const GaloisField< IntegerType > *gf)

const GaloisField< IntegerType > *	gf () const

GFNumber< IntegerType >	toGF (const GaloisField< IntegerType > *newfield) const

void	normalize ()

bool	is_zero () const

bool	is_one () const

bool	is_unit () const

const IntegerType &	representing_integer () const

GFNumber	inverse () const

const GFNumber	operator- () const

GFNumber &	operator++ ()

GFNumber &	operator+= (const GFNumber &rhs)

GFNumber &	operator+= (const IntegerType &rhs)

GFNumber &	operator-- ()

GFNumber &	operator-= (const GFNumber &rhs)

GFNumber &	operator-= (const IntegerType &rhs)

GFNumber &	operator*= (const GFNumber &rhs)

GFNumber &	operator*= (const IntegerType &rhs)

GFNumber &	operator/= (const GFNumber &rhs)

Private Attributes
IntegerType	mN = carl::constant_zero<IntegerType>::get()

const GaloisField< IntegerType > *	mGf = nullptr

Friends
template<typename IntegerT >
bool	operator== (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
bool	operator== (const GFNumber< IntegerT > &lhs, const IntegerT &rhs)
	lhs == rhs, if rhs \in [lhs]. More...

template<typename IntegerT >
bool	operator== (const IntegerT &lhs, const GFNumber< IntegerT > &rhs)
	lhs == rhs, if lhs \in [rhs]. More...

template<typename IntegerT >
bool	operator== (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
bool	operator== (const GFNumber< IntegerT > &lhs, int rhs)
	lhs == rhs, if rhs \in [lhs]. More...

template<typename IntegerT >
bool	operator== (int lhs, const GFNumber< IntegerT > &rhs)
	lhs == rhs, if lhs \in [rhs]. More...

template<typename IntegerT >
bool	operator!= (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
bool	operator!= (const GFNumber< IntegerT > &lhs, const IntegerT &rhs)

template<typename IntegerT >
bool	operator!= (const IntegerT &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
bool	operator!= (const GFNumber< IntegerT > &lhs, int rhs)

template<typename IntegerT >
bool	operator!= (int lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator+ (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator+ (const GFNumber< IntegerT > &lhs, const IntegerT &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator+ (const IntegerT &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator- (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator- (const GFNumber< IntegerT > &lhs, const IntegerT &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator- (const IntegerT &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator* (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator* (const GFNumber< IntegerT > &lhs, const IntegerT &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator* (const IntegerT &lhs, const GFNumber< IntegerT > &rhs)

template<typename IntegerT >
GFNumber< IntegerT >	operator/ (const GFNumber< IntegerT > &lhs, const GFNumber< IntegerT > &rhs)

std::ostream &	operator<< (std::ostream &os, const GFNumber &rhs)

Detailed Description

template<typename IntegerType>
class carl::GFNumber< IntegerType >

Galois Field numbers, i.e.

numbers from fields with a finite characteristic.

Definition at line 20 of file GFNumber.h.

Constructor & Destructor Documentation

◆ GFNumber() [1/3]

template<typename IntegerType >

carl::GFNumber< IntegerType >::GFNumber ( )

default

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◆ GFNumber() [2/3]

template<typename IntegerType >

carl::GFNumber< IntegerType >::GFNumber	(	IntegerType	n,
		const GaloisField< IntegerType > *	gf = `nullptr`
	)

inlineexplicit

Definition at line 28 of file GFNumber.h.

◆ GFNumber() [3/3]

template<typename IntegerType >

carl::GFNumber< IntegerType >::GFNumber	(	const GFNumber< IntegerType > &	n,
		const GaloisField< IntegerType > *	gf
	)

inline

Definition at line 34 of file GFNumber.h.

Member Function Documentation

◆ gf()

template<typename IntegerType >

const GaloisField<IntegerType>* carl::GFNumber< IntegerType >::gf ( ) const

inline

Definition at line 40 of file GFNumber.h.

◆ inverse()

template<typename IntegerType >

GFNumber carl::GFNumber< IntegerType >::inverse ( ) const

◆ is_one()

template<typename IntegerType >

bool carl::GFNumber< IntegerType >::is_one ( ) const

inline

Definition at line 62 of file GFNumber.h.

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◆ is_unit()

template<typename IntegerType >

bool carl::GFNumber< IntegerType >::is_unit ( ) const

inline

Definition at line 67 of file GFNumber.h.

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◆ is_zero()

template<typename IntegerType >

bool carl::GFNumber< IntegerType >::is_zero ( ) const

inline

Definition at line 57 of file GFNumber.h.

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◆ normalize()

template<typename IntegerType >

void carl::GFNumber< IntegerType >::normalize ( )

inline

Definition at line 50 of file GFNumber.h.

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◆ operator*=() [1/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator*= ( const GFNumber< IntegerType > & rhs )

◆ operator*=() [2/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator*= ( const IntegerType & rhs )

◆ operator++()

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator++ ( )

◆ operator+=() [1/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator+= ( const GFNumber< IntegerType > & rhs )

◆ operator+=() [2/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator+= ( const IntegerType & rhs )

◆ operator-()

template<typename IntegerType >

const GFNumber carl::GFNumber< IntegerType >::operator- ( ) const

◆ operator--()

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator-- ( )

◆ operator-=() [1/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator-= ( const GFNumber< IntegerType > & rhs )

◆ operator-=() [2/2]

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator-= ( const IntegerType & rhs )

◆ operator/=()

template<typename IntegerType >

GFNumber& carl::GFNumber< IntegerType >::operator/= ( const GFNumber< IntegerType > & rhs )

◆ representing_integer()

template<typename IntegerType >

const IntegerType& carl::GFNumber< IntegerType >::representing_integer ( ) const

inline

Definition at line 72 of file GFNumber.h.

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◆ toGF()

template<typename IntegerType >

GFNumber<IntegerType> carl::GFNumber< IntegerType >::toGF ( const GaloisField< IntegerType > * newfield ) const

inline

Definition at line 45 of file GFNumber.h.

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Friends And Related Function Documentation

◆ operator!= [1/5]

template<typename IntegerType >

template<typename IntegerT >

bool operator!=	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator!= [2/5]

template<typename IntegerType >

template<typename IntegerT >

bool operator!=	(	const GFNumber< IntegerT > &	lhs,
		const IntegerT &	rhs
	)

friend

◆ operator!= [3/5]

template<typename IntegerType >

template<typename IntegerT >

bool operator!=	(	const GFNumber< IntegerT > &	lhs,
		int	rhs
	)

friend

◆ operator!= [4/5]

template<typename IntegerType >

template<typename IntegerT >

bool operator!=	(	const IntegerT &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator!= [5/5]

template<typename IntegerType >

template<typename IntegerT >

bool operator!=	(	int	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator* [1/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator*	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator* [2/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator*	(	const GFNumber< IntegerT > &	lhs,
		const IntegerT &	rhs
	)

friend

◆ operator* [3/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator*	(	const IntegerT &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator+ [1/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator+	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator+ [2/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator+	(	const GFNumber< IntegerT > &	lhs,
		const IntegerT &	rhs
	)

friend

◆ operator+ [3/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator+	(	const IntegerT &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator- [1/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator-	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator- [2/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator-	(	const GFNumber< IntegerT > &	lhs,
		const IntegerT &	rhs
	)

friend

◆ operator- [3/3]

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator-	(	const IntegerT &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator/

template<typename IntegerType >

template<typename IntegerT >

GFNumber<IntegerT> operator/	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator<<

template<typename IntegerType >

std::ostream& operator<<	(	std::ostream &	os,
		const GFNumber< IntegerType > &	rhs
	)

friend

Definition at line 158 of file GFNumber.h.

◆ operator== [1/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator== [2/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	const GFNumber< IntegerT > &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

◆ operator== [3/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	const GFNumber< IntegerT > &	lhs,
		const IntegerT &	rhs
	)

friend

lhs == rhs, if rhs \in [lhs].

Returns

◆ operator== [4/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	const GFNumber< IntegerT > &	lhs,
		int	rhs
	)

friend

lhs == rhs, if rhs \in [lhs].

Returns

◆ operator== [5/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	const IntegerT &	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

lhs == rhs, if lhs \in [rhs].

Returns

◆ operator== [6/6]

template<typename IntegerType >

template<typename IntegerT >

bool operator==	(	int	lhs,
		const GFNumber< IntegerT > &	rhs
	)

friend

lhs == rhs, if lhs \in [rhs].

Returns

Field Documentation

◆ mGf

template<typename IntegerType >

const GaloisField<IntegerType>* carl::GFNumber< IntegerType >::mGf = nullptr

private

Definition at line 23 of file GFNumber.h.

◆ mN

template<typename IntegerType >

IntegerType carl::GFNumber< IntegerType >::mN = carl::constant_zero<IntegerType>::get()

private

Definition at line 22 of file GFNumber.h.

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

carl-arith/numbers/GFNumber.h

Public Member Functions

Private Attributes

Friends

Detailed Description

template<typename IntegerType> class carl::GFNumber< IntegerType >

Constructor & Destructor Documentation

◆ GFNumber() [1/3]

◆ GFNumber() [2/3]

◆ GFNumber() [3/3]

Member Function Documentation

◆ gf()

◆ inverse()

◆ is_one()

◆ is_unit()

◆ is_zero()

◆ normalize()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator++()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator--()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ representing_integer()

◆ toGF()

Friends And Related Function Documentation

◆ operator!= [1/5]

◆ operator!= [2/5]

◆ operator!= [3/5]

◆ operator!= [4/5]

◆ operator!= [5/5]

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/

◆ operator<<

◆ operator== [1/6]

◆ operator== [2/6]

◆ operator== [3/6]

◆ operator== [4/6]

◆ operator== [5/6]

◆ operator== [6/6]

Field Documentation

◆ mGf

◆ mN

template<typename IntegerType>
class carl::GFNumber< IntegerType >