A finite field whose prime should be a generalized fermat number. More...

#include <GeneralizedFermatPrimeField.hpp>

Simplified semantic inheritance diagram for GeneralizedFermatPrimeField:

Full inheritance diagram for GeneralizedFermatPrimeField:

Public Member Functions
	GeneralizedFermatPrimeField (mpz_class a)

	GeneralizedFermatPrimeField (int a)

	GeneralizedFermatPrimeField (const GeneralizedFermatPrimeField &c)

	GeneralizedFermatPrimeField (const Integer &c)

	GeneralizedFermatPrimeField (const RationalNumber &c)

	GeneralizedFermatPrimeField (const SmallPrimeField &c)

	GeneralizedFermatPrimeField (const BigPrimeField &c)

	GeneralizedFermatPrimeField (const DenseUnivariateIntegerPolynomial &c)

	GeneralizedFermatPrimeField (const DenseUnivariateRationalPolynomial &c)

	GeneralizedFermatPrimeField (const SparseUnivariatePolynomial< Integer > &c)

	GeneralizedFermatPrimeField (const SparseUnivariatePolynomial< RationalNumber > &c)

	GeneralizedFermatPrimeField (const SparseUnivariatePolynomial< ComplexRationalNumber > &c)

template<class Ring >
	GeneralizedFermatPrimeField (const SparseUnivariatePolynomial< Ring > &c)

GeneralizedFermatPrimeField *	GPFpointer (GeneralizedFermatPrimeField *a)

GeneralizedFermatPrimeField *	GPFpointer (RationalNumber *a)

GeneralizedFermatPrimeField *	GPFpointer (SmallPrimeField *a)

GeneralizedFermatPrimeField *	GPFpointer (BigPrimeField *a)

mpz_class	getCharacteristic () const override
	The characteristic of this ring class.

void	setX (mpz_class a)

mpz_class	Prime () const

mpz_class	number () const

GeneralizedFermatPrimeField	unitCanonical (GeneralizedFermatPrimeField u=NULL, GeneralizedFermatPrimeField v=NULL) const
	Obtain the unit normal (a.k.a canonical associate) of an element. More...

GeneralizedFermatPrimeField	findPrimitiveRootOfUnity (long int n) const

GeneralizedFermatPrimeField &	operator= (const GeneralizedFermatPrimeField &c)
	Copy assignment.

GeneralizedFermatPrimeField &	operator= (const mpz_class &c)

GeneralizedFermatPrimeField &	operator= (int c)

bool	isZero () const
	Determine if *this ring element is zero, that is the additive identity. More...

void	zero ()
	Make *this ring element zero.

bool	isOne () const
	Determine if *this ring element is one, that is the multiplication identity. More...

void	one ()
	Make *this ring element one.

bool	isNegativeOne () const

void	negativeOne ()

int	isConstant () const

bool	operator== (const GeneralizedFermatPrimeField &c) const
	Equality test,. More...

bool	operator== (const mpz_class &c) const

bool	operator!= (const GeneralizedFermatPrimeField &c) const
	Inequality test,. More...

bool	operator!= (const mpz_class &c) const

GeneralizedFermatPrimeField	operator+ (const GeneralizedFermatPrimeField &c) const
	Addition.

GeneralizedFermatPrimeField	operator+ (const mpz_class &c) const

GeneralizedFermatPrimeField &	operator+= (const mpz_class &c)

GeneralizedFermatPrimeField	operator+ (int c) const

GeneralizedFermatPrimeField &	operator+= (int c)

GeneralizedFermatPrimeField &	operator+= (const GeneralizedFermatPrimeField &y)
	Addition assignment.

GeneralizedFermatPrimeField	operator- (const GeneralizedFermatPrimeField &c) const
	Subtraction.

GeneralizedFermatPrimeField	operator- (const mpz_class &c) const

GeneralizedFermatPrimeField &	operator-= (const mpz_class &c)

GeneralizedFermatPrimeField	operator- (int c) const

GeneralizedFermatPrimeField &	operator-= (int c)

GeneralizedFermatPrimeField &	operator-= (const GeneralizedFermatPrimeField &y)
	Subtraction assignment.

GeneralizedFermatPrimeField	operator- () const
	Negation.

void	smallAdd2 (usfixn64 xm, usfixn64 ym, short &c)

void	oneShiftRight (usfixn64 *xs)

void	mulLong_2 (usfixn64 x, usfixn64 y, usfixn64 &s0, usfixn64 &s1, usfixn64 &s2)

void	mulLong_3 (usfixn64 const &x, usfixn64 const &y, usfixn64 &s0, usfixn64 &s1, usfixn64 &s2)

void	multiplication (usfixn64 __restrict__ xs, const usfixn64 __restrict__ ys, usfixn64 permutationStride, usfixn64 lVector, usfixn64 hVector, usfixn64 cVector, usfixn64 lVectorSub, usfixn64 hVectorSub, usfixn64 cVectorSub)

void	multiplication_step2 (usfixn64 __restrict__ xs, usfixn64 permutationStride, usfixn64 __restrict__ lVector, usfixn64 __restrict__ hVector, usfixn64 __restrict__ cVector)

GeneralizedFermatPrimeField	operator* (const GeneralizedFermatPrimeField &c) const
	Multiplication.

GeneralizedFermatPrimeField	operator* (const mpz_class &c) const

GeneralizedFermatPrimeField &	*operator=** (const mpz_class &c)

GeneralizedFermatPrimeField	operator* (int c) const

GeneralizedFermatPrimeField &	*operator=** (int c)

GeneralizedFermatPrimeField &	operator*= (const GeneralizedFermatPrimeField &c)
	Multiplication assignment.

GeneralizedFermatPrimeField	MultiP3 (GeneralizedFermatPrimeField ys)

GeneralizedFermatPrimeField	MulPowR (int s)

void	egcd (const mpz_class &x, const mpz_class &y, mpz_class ao, mpz_class bo, mpz_class *vo, mpz_class P)

GeneralizedFermatPrimeField	inverse2 ()

GeneralizedFermatPrimeField	operator^ (long long int c) const
	Exponentiation.

GeneralizedFermatPrimeField	operator^ (const mpz_class &exp) const

GeneralizedFermatPrimeField &	operator^= (long long int c)
	Exponentiation assignment.

GeneralizedFermatPrimeField &	operator^= (const mpz_class &c)

ExpressionTree	convertToExpressionTree () const
	Convert this to an expression tree. More...

GeneralizedFermatPrimeField	operator/ (const GeneralizedFermatPrimeField &c) const
	Exact division. More...

GeneralizedFermatPrimeField	operator/ (long int c) const

GeneralizedFermatPrimeField	operator/ (const mpz_class &c) const

GeneralizedFermatPrimeField &	operator/= (const GeneralizedFermatPrimeField &c)
	Exact division assignment. More...

GeneralizedFermatPrimeField &	operator/= (long int c)

GeneralizedFermatPrimeField &	operator/= (const mpz_class &c)

GeneralizedFermatPrimeField	operator% (const GeneralizedFermatPrimeField &c) const
	Get the remainder of *this and b;. More...

GeneralizedFermatPrimeField &	operator%= (const GeneralizedFermatPrimeField &c)
	Assign this to be the remainder of this and b. More...

GeneralizedFermatPrimeField	gcd (const GeneralizedFermatPrimeField &a) const
	Get GCD of *this and other. More...

Factors< GeneralizedFermatPrimeField >	squareFree () const
	Compute squarefree factorization of *this.

Integer	euclideanSize () const
	Get the euclidean size of *this.

GeneralizedFermatPrimeField	euclideanDivision (const GeneralizedFermatPrimeField &b, GeneralizedFermatPrimeField *q=NULL) const
	Perform the eucldiean division of *this and b. More...

GeneralizedFermatPrimeField	extendedEuclidean (const GeneralizedFermatPrimeField &b, GeneralizedFermatPrimeField s=NULL, GeneralizedFermatPrimeField t=NULL) const
	Perform the extended euclidean division on *this and b. More...

GeneralizedFermatPrimeField	quotient (const GeneralizedFermatPrimeField &b) const
	Get the quotient of *this and b.

GeneralizedFermatPrimeField	remainder (const GeneralizedFermatPrimeField &b) const
	Get the remainder of *this and b.

GeneralizedFermatPrimeField	inverse () const
	Get the inverse of *this. More...

Static Public Member Functions
static void	setPrime (mpz_class p, usfixn64 R, int K)

static mpz_class	power (mpz_class xi, mpz_class yi)

static mpz_class	findPrimitiveRootofUnity_plain (mpz_class n)

static GeneralizedFermatPrimeField	findPrimitiveRootofUnity (mpz_class n)

Public Attributes
usfixn64 *	x

Static Public Attributes
static mpz_class	characteristic

static usfixn64	r

static int	k

Detailed Description

A finite field whose prime should be a generalized fermat number.

That is, for r = (2^w +/- 2^u), the prime is r^k, for some k.

Member Function Documentation

◆ convertToExpressionTree()

ExpressionTree GeneralizedFermatPrimeField::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ euclideanDivision()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::euclideanDivision	(	const GeneralizedFermatPrimeField &	b,
		GeneralizedFermatPrimeField *	q = `NULL`
	)		const

virtual

Perform the eucldiean division of *this and b.

Returns the remainder. If q is not NULL, then returns the quotient in q.

Implements BPASEuclideanDomain< GeneralizedFermatPrimeField >.

◆ extendedEuclidean()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::extendedEuclidean	(	const GeneralizedFermatPrimeField &	b,
		GeneralizedFermatPrimeField *	s = `NULL`,
		GeneralizedFermatPrimeField *	t = `NULL`
	)		const

virtual

Perform the extended euclidean division on *this and b.

Returns the GCD. If s and t are not NULL, returns the bezout coefficients in them.

Implements BPASEuclideanDomain< GeneralizedFermatPrimeField >.

◆ gcd()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::gcd ( const GeneralizedFermatPrimeField & other ) const

inlinevirtual

Get GCD of *this and other.

Parameters

other the other element to get a gcd with.

Returns: the gcd.

Implements BPASGCDDomain< GeneralizedFermatPrimeField >.

◆ inverse()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::inverse ( ) const

virtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< GeneralizedFermatPrimeField >.

◆ isOne()

bool GeneralizedFermatPrimeField::isOne ( ) const

inlinevirtual

Determine if *this ring element is one, that is the multiplication identity.

returns true iff *this is one.

Implements BPASRing< GeneralizedFermatPrimeField >.

◆ isZero()

bool GeneralizedFermatPrimeField::isZero ( ) const

inlinevirtual

Determine if *this ring element is zero, that is the additive identity.

returns true iff *this is zero.

Implements BPASRing< GeneralizedFermatPrimeField >.

◆ operator!=()

bool GeneralizedFermatPrimeField::operator!= ( const GeneralizedFermatPrimeField & ) const

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< GeneralizedFermatPrimeField >.

◆ operator%()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::operator% ( const GeneralizedFermatPrimeField & b ) const

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< GeneralizedFermatPrimeField >.

◆ operator%=()

GeneralizedFermatPrimeField& GeneralizedFermatPrimeField::operator%= ( const GeneralizedFermatPrimeField & b )

inlinevirtual

Assign *this to be the remainder of *this and b.

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< GeneralizedFermatPrimeField >.

◆ operator/()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::operator/ ( const GeneralizedFermatPrimeField & d ) const

inlinevirtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< GeneralizedFermatPrimeField >.

◆ operator/=()

GeneralizedFermatPrimeField& GeneralizedFermatPrimeField::operator/= ( const GeneralizedFermatPrimeField & d )

inlinevirtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< GeneralizedFermatPrimeField >.

◆ operator==()

bool GeneralizedFermatPrimeField::operator== ( const GeneralizedFermatPrimeField & ) const

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< GeneralizedFermatPrimeField >.

◆ unitCanonical()

GeneralizedFermatPrimeField GeneralizedFermatPrimeField::unitCanonical	(	GeneralizedFermatPrimeField *	u = `NULL`,
		GeneralizedFermatPrimeField *	v = `NULL`
	)		const

virtual

Obtain the unit normal (a.k.a canonical associate) of an element.

If either parameters u, v, are non-NULL then the units are returned such that b = ua, v = u^-1. Where b is the unit normal of a, and is the returned value.

Implements BPASRing< GeneralizedFermatPrimeField >.

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

include/FiniteFields/GeneralizedFermatPrimeField.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Function Documentation

◆ convertToExpressionTree()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isOne()

◆ isZero()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ unitCanonical()