A prime field whose prime is 32 bits or less. More...

#include <SmallPrimeField.hpp>

Simplified semantic inheritance diagram for SmallPrimeField:

Full inheritance diagram for SmallPrimeField:

Public Member Functions
	SmallPrimeField (long long int _a)

	SmallPrimeField (const SmallPrimeField &c)

	SmallPrimeField (const Integer &c)

	SmallPrimeField (const RationalNumber &c)

	SmallPrimeField (const ComplexRationalNumber &c)

	SmallPrimeField (const BigPrimeField &c)

	SmallPrimeField (const GeneralizedFermatPrimeField &c)

	SmallPrimeField (const DenseUnivariateIntegerPolynomial &c)

	SmallPrimeField (const DenseUnivariateRationalPolynomial &c)

	SmallPrimeField (const SparseUnivariatePolynomial< Integer > &c)

	SmallPrimeField (const SparseUnivariatePolynomial< RationalNumber > &c)

	SmallPrimeField (const SparseUnivariatePolynomial< ComplexRationalNumber > &c)

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

SmallPrimeField *	SPFpointer (SmallPrimeField *b)

SmallPrimeField *	SPFpointer (RationalNumber *a)

SmallPrimeField *	SPFpointer (BigPrimeField *a)

SmallPrimeField *	SPFpointer (GeneralizedFermatPrimeField *a)

long long int	number () const

void	whichprimefield ()

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

long long int	Prime ()

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

SmallPrimeField &	operator= (long long int k)

SmallPrimeField	findPrimitiveRootOfUnity (long int n) const

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 ()

void	negativeOne ()

int	isConstant ()

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

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

SmallPrimeField	operator+ (const long long int &c) const

SmallPrimeField	operator+ (const int &c) const

SmallPrimeField	operator+= (const long long int &c)

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

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

SmallPrimeField	operator- (const long long int &c) const

SmallPrimeField	operator-= (const long long int &c)

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

SmallPrimeField	operator- () const
	Negation.

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

SmallPrimeField	operator* (long long int c) const

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

long long int *	pinverse ()

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

SmallPrimeField	inverse2 ()

SmallPrimeField	operator^ (long long int e) const
	Exponentiation.

SmallPrimeField &	operator^= (long long int e)
	Exponentiation assignment.

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

bool	operator== (long long int k) const

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

bool	operator!= (long long int k) const

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

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

SmallPrimeField	operator/ (long long int c) const

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

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

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

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

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

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

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

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

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

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

Static Public Member Functions
static void	setPrime (long long int p)

static SmallPrimeField	findPrimitiveRootofUnity (long long int n)

static long long int	Mont (long long int b, long long int c)

static long long int	getRsquare ()

Static Public Attributes
static mpz_class	characteristic

Detailed Description

A prime field whose prime is 32 bits or less.

Elements of this field are encoded using montgomery trick.

Member Function Documentation

◆ convertToExpressionTree()

ExpressionTree SmallPrimeField::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ euclideanDivision()

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

◆ extendedEuclidean()

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

◆ gcd()

SmallPrimeField SmallPrimeField::gcd ( const SmallPrimeField & other ) const

inlinevirtual

Get GCD of *this and other.

Parameters

other the other element to get a gcd with.

Returns: the gcd.

Implements BPASGCDDomain< SmallPrimeField >.

◆ inverse()

SmallPrimeField SmallPrimeField::inverse ( ) const

inlinevirtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< SmallPrimeField >.

◆ isOne()

bool SmallPrimeField::isOne ( ) const

inlinevirtual

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

returns true iff *this is one.

Implements BPASRing< SmallPrimeField >.

◆ isZero()

bool SmallPrimeField::isZero ( ) const

inlinevirtual

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

returns true iff *this is zero.

Implements BPASRing< SmallPrimeField >.

◆ operator!=()

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

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< SmallPrimeField >.

◆ operator%()

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

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< SmallPrimeField >.

◆ operator%=()

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

inlinevirtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< SmallPrimeField >.

◆ operator/()

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

inlinevirtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< SmallPrimeField >.

◆ operator/=()

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

inlinevirtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< SmallPrimeField >.

◆ operator==()

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

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< SmallPrimeField >.

◆ unitCanonical()

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

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

include/FiniteFields/SmallPrimeField.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()