Basic Polynomial Algebra Subprograms (BPAS)  v. 1.548
Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | List of all members
GeneralizedFermatPrimeField Class Reference

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:
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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)
 
GeneralizedFermatPrimeFieldGPFpointer (GeneralizedFermatPrimeField *a)
 
GeneralizedFermatPrimeFieldGPFpointer (RationalNumber *a)
 
GeneralizedFermatPrimeFieldGPFpointer (SmallPrimeField *a)
 
GeneralizedFermatPrimeFieldGPFpointer (BigPrimeField *a)
 
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
 
GeneralizedFermatPrimeFieldoperator= (const GeneralizedFermatPrimeField &c)
 Copy assignment.
 
GeneralizedFermatPrimeFieldoperator= (const mpz_class &c)
 
GeneralizedFermatPrimeFieldoperator= (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
 
GeneralizedFermatPrimeFieldoperator+= (const mpz_class &c)
 
GeneralizedFermatPrimeField operator+ (int c) const
 
GeneralizedFermatPrimeFieldoperator+= (int c)
 
GeneralizedFermatPrimeFieldoperator+= (const GeneralizedFermatPrimeField &y)
 Addition assignment.
 
GeneralizedFermatPrimeField operator- (const GeneralizedFermatPrimeField &c) const
 Subtraction.
 
GeneralizedFermatPrimeField operator- (const mpz_class &c) const
 
GeneralizedFermatPrimeFieldoperator-= (const mpz_class &c)
 
GeneralizedFermatPrimeField operator- (int c) const
 
GeneralizedFermatPrimeFieldoperator-= (int c)
 
GeneralizedFermatPrimeFieldoperator-= (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
 
GeneralizedFermatPrimeFieldoperator*= (const mpz_class &c)
 
GeneralizedFermatPrimeField operator* (int c) const
 
GeneralizedFermatPrimeFieldoperator*= (int c)
 
GeneralizedFermatPrimeFieldoperator*= (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
 
GeneralizedFermatPrimeFieldoperator^= (long long int c)
 Exponentiation assignment.
 
GeneralizedFermatPrimeFieldoperator^= (const mpz_class &c)
 
ExpressionTree convertToExpressionTree () const
 Convert this to an expression tree. More...
 
GeneralizedFermatPrimeField operator/ (const GeneralizedFermatPrimeField &c) const
 Exact division.
 
GeneralizedFermatPrimeField operator/ (long int c) const
 
GeneralizedFermatPrimeField operator/ (const mpz_class &c) const
 
GeneralizedFermatPrimeFieldoperator/= (const GeneralizedFermatPrimeField &c)
 Exact division assignment.
 
GeneralizedFermatPrimeFieldoperator/= (long int c)
 
GeneralizedFermatPrimeFieldoperator/= (const mpz_class &c)
 
GeneralizedFermatPrimeField operator% (const GeneralizedFermatPrimeField &c) const
 Get the remainder of *this and b;.
 
GeneralizedFermatPrimeFieldoperator%= (const GeneralizedFermatPrimeField &c)
 Assign *this to be the remainder of *this and b.
 
GeneralizedFermatPrimeField gcd (const GeneralizedFermatPrimeField &a) const
 Get GCD of *this and other.
 
Factors< GeneralizedFermatPrimeFieldsquareFree () const
 Compute squarefree factorization of *this.
 
GeneralizedFermatPrimeField 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.
 

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 RingProperties properties
 
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 >.

◆ 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==()

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: