A prime field whose prime can be arbitrarily large. More...

#include <BigPrimeField.hpp>

Simplified semantic inheritance diagram for BigPrimeField:

Full inheritance diagram for BigPrimeField:

Public Member Functions
	BigPrimeField (mpz_class _a)

	BigPrimeField (long int _a)

	BigPrimeField (const BigPrimeField &c)

	BigPrimeField (const Integer &c)

	BigPrimeField (const RationalNumber &c)

	BigPrimeField (const ComplexRationalNumber &c)

	BigPrimeField (const SmallPrimeField &c)

	BigPrimeField (const GeneralizedFermatPrimeField &c)

	BigPrimeField (const DenseUnivariateIntegerPolynomial &c)

	BigPrimeField (const DenseUnivariateRationalPolynomial &c)

	BigPrimeField (const SparseUnivariatePolynomial< Integer > &c)

	BigPrimeField (const SparseUnivariatePolynomial< RationalNumber > &c)

	BigPrimeField (const SparseUnivariatePolynomial< ComplexRationalNumber > &c)

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

BigPrimeField *	BPFpointer (BigPrimeField *b)

BigPrimeField *	BPFpointer (RationalNumber *a)

BigPrimeField *	BPFpointer (SmallPrimeField *a)

BigPrimeField *	BPFpointer (GeneralizedFermatPrimeField *a)

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

mpz_class	Prime () const

mpz_class	number () const

void	whichprimefield ()

BigPrimeField	findPrimitiveRootOfUnity (long int n) const

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

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

BigPrimeField &	operator= (long int k)

BigPrimeField &	operator= (const mpz_class &k)

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 BigPrimeField &c) const
	Equality test,. More...

bool	operator== (const mpz_class &k) const

bool	operator== (long int k) const

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

bool	operator!= (const mpz_class &k) const

bool	operator!= (long int k) const

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

BigPrimeField	operator+ (long int c) const

BigPrimeField	operator+ (const mpz_class &c) const

BigPrimeField &	operator+= (const BigPrimeField &c)
	Addition assignment.

BigPrimeField	operator+= (long int c)

BigPrimeField	operator+= (const mpz_class &c)

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

BigPrimeField	operator- (long int c) const

BigPrimeField	operator- (const mpz_class &c) const

BigPrimeField &	operator-= (const BigPrimeField &c)
	Subtraction assignment.

BigPrimeField	operator-= (long int c)

BigPrimeField	operator-= (const mpz_class &c)

BigPrimeField	operator- () const
	Negation.

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

BigPrimeField	operator* (const mpz_class &c) const

BigPrimeField	operator* (long int c) const

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

BigPrimeField &	*operator=** (const mpz_class &m)

BigPrimeField &	*operator=** (long int c)

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

BigPrimeField	operator^ (const mpz_class &exp) const

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

BigPrimeField &	operator^= (const mpz_class &e)

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

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

BigPrimeField	operator/ (long int c) const

BigPrimeField	operator/ (const mpz_class &c) const

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

BigPrimeField &	operator/= (long int c)

BigPrimeField &	operator/= (const mpz_class &c)

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

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

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

BigPrimeField	gcd (long int c)

BigPrimeField	gcd (const mpz_class &c) const

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

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

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

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

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

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

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

Static Public Member Functions
static void	setPrime (mpz_class p)

static BigPrimeField	findPrimitiveRootofUnity (mpz_class n)

Static Public Attributes
static mpz_class	characteristic

Detailed Description

A prime field whose prime can be arbitrarily large.

Member Function Documentation

◆ convertToExpressionTree()

ExpressionTree BigPrimeField::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ euclideanDivision()

BigPrimeField BigPrimeField::euclideanDivision	(	const BigPrimeField &	b,
		BigPrimeField *	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< BigPrimeField >.

◆ extendedEuclidean()

BigPrimeField BigPrimeField::extendedEuclidean	(	const BigPrimeField &	b,
		BigPrimeField *	s = `NULL`,
		BigPrimeField *	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< BigPrimeField >.

◆ gcd()

BigPrimeField BigPrimeField::gcd ( const BigPrimeField & other ) const

inlinevirtual

Get GCD of *this and other.

Parameters

other the other element to get a gcd with.

Returns: the gcd.

Implements BPASGCDDomain< BigPrimeField >.

◆ inverse()

BigPrimeField BigPrimeField::inverse ( ) const

inlinevirtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< BigPrimeField >.

◆ isOne()

bool BigPrimeField::isOne ( ) const

inlinevirtual

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

returns true iff *this is one.

Implements BPASRing< BigPrimeField >.

◆ isZero()

bool BigPrimeField::isZero ( ) const

inlinevirtual

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

returns true iff *this is zero.

Implements BPASRing< BigPrimeField >.

◆ operator!=()

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

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< BigPrimeField >.

◆ operator%()

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

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< BigPrimeField >.

◆ operator%=()

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

inlinevirtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< BigPrimeField >.

◆ operator/()

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

inlinevirtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< BigPrimeField >.

◆ operator/=()

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

inlinevirtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< BigPrimeField >.

◆ operator==()

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

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< BigPrimeField >.

◆ unitCanonical()

BigPrimeField BigPrimeField::unitCanonical	(	BigPrimeField *	u = `NULL`,
		BigPrimeField *	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< BigPrimeField >.

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

include/FiniteFields/BigPrimeField.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ convertToExpressionTree()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isOne()

◆ isZero()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ unitCanonical()