An abstract class defining the interface of a Euclidean domain. More...

#include <BPASEuclideanDomain.hpp>

Simplified semantic inheritance diagram for BPASEuclideanDomain< Derived >:

Full inheritance diagram for BPASEuclideanDomain< Derived >:

Public Member Functions
virtual Integer	euclideanSize () const =0
	Get the euclidean size of *this.

virtual Derived	euclideanDivision (const Derived &b, Derived *q=NULL) const =0
	Perform the eucldiean division of *this and b. More...

virtual Derived	extendedEuclidean (const Derived &b, Derived s=NULL, Derived t=NULL) const =0
	Perform the extended euclidean division on *this and b. More...

virtual Derived	quotient (const Derived &b) const =0
	Get the quotient of *this and b. More...

virtual Derived	remainder (const Derived &b) const =0
	Get the remainder of *this and b. More...

virtual Derived	operator% (const Derived &b) const =0
	Get the remainder of *this and b;. More...

virtual Derived &	operator%= (const Derived &b)=0
	Assign this to be the remainder of this and b. More...

Public Member Functions inherited from BPASGCDDomain< Derived >
virtual Derived	gcd (const Derived &other) const =0
	Get GCD of *this and other. More...

virtual Factors< Derived >	squareFree () const =0
	Compute squarefree factorization of *this. More...

Public Member Functions inherited from BPASIntegralDomain< Derived >
virtual Derived	operator/ (const Derived &d) const =0
	Exact division. More...

virtual Derived &	operator/= (const Derived &d)=0
	Exact division assignment. More...

Public Member Functions inherited from BPASRing< Derived >
virtual mpz_class	getCharacteristic () const
	The characteristic of this ring class.

virtual bool	isZero () const =0
	Determine if *this ring element is zero, that is the additive identity. More...

virtual void	zero ()=0
	Make *this ring element zero.

virtual bool	isOne () const =0
	Determine if *this ring element is one, that is the multiplication identity. More...

virtual void	one ()=0
	Make *this ring element one.

virtual Derived	unitCanonical (Derived u=NULL, Derived v=NULL) const =0
	Obtain the unit normal (a.k.a canonical associate) of an element. More...

virtual Derived &	operator= (const Derived &)=0
	Copy assignment.

virtual Derived	operator+ (const Derived &) const =0
	Addition.

virtual Derived &	operator+= (const Derived &)=0
	Addition assignment.

virtual Derived	operator- (const Derived &) const =0
	Subtraction.

virtual Derived &	operator-= (const Derived &)=0
	Subtraction assignment.

virtual Derived	operator- () const =0
	Negation.

virtual Derived	operator* (const Derived &) const =0
	Multiplication.

virtual Derived &	operator*= (const Derived &)=0
	Multiplication assignment.

virtual Derived	operator^ (long long int e) const =0
	Exponentiation.

virtual Derived &	operator^= (long long int e)=0
	Exponentiation assignment.

virtual bool	operator== (const Derived &) const =0
	Equality test,. More...

virtual bool	operator!= (const Derived &) const =0
	Inequality test,. More...

virtual void	print (std::ostream &ostream) const
	Print the Ring element. More...

virtual std::string	toString () const
	Convert the Ring element to a string. More...

Public Member Functions inherited from ExpressionTreeConvert
virtual ExpressionTree	convertToExpressionTree () const =0
	Convert this to an expression tree. More...

Detailed Description

template<class Derived>
class BPASEuclideanDomain< Derived >

An abstract class defining the interface of a Euclidean domain.

Member Function Documentation

◆ euclideanDivision()

template<class Derived>

virtual Derived BPASEuclideanDomain< Derived >::euclideanDivision	(	const Derived &	b,
		Derived *	q = `NULL`
	)		const

pure virtual

Perform the eucldiean division of *this and b.

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

Parameters

	b	the divisor.
[out]	q	a pointer to store the quotient in.

Returns: the remainder.

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ extendedEuclidean()

template<class Derived>

virtual Derived BPASEuclideanDomain< Derived >::extendedEuclidean	(	const Derived &	b,
		Derived *	s = `NULL`,
		Derived *	t = `NULL`
	)		const

pure 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.

Parameters

	b	the divisor.
[out]	s	the bezout coefficient of this.
[out]	t	the bezout coefficient of b.

Returns: the remainder.

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ operator%()

template<class Derived>

virtual Derived BPASEuclideanDomain< Derived >::operator% ( const Derived & b ) const

pure virtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, GeneralizedFermatPrimeField, BigPrimeField, Integer, RationalNumber, ComplexRationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ operator%=()

template<class Derived>

virtual Derived& BPASEuclideanDomain< Derived >::operator%= ( const Derived & b )

pure virtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, GeneralizedFermatPrimeField, BigPrimeField, Integer, RationalNumber, ComplexRationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ quotient()

template<class Derived>

virtual Derived BPASEuclideanDomain< Derived >::quotient ( const Derived & b ) const

pure virtual

Get the quotient of *this and b.

Parameters

b	the divisor

Returns: the quotient

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ remainder()

template<class Derived>

virtual Derived BPASEuclideanDomain< Derived >::remainder ( const Derived & b ) const

pure virtual

Get the remainder of *this and b.

Parameters

b	the divisor

Returns: the remainder

Implemented in DenseUnivariatePolynomial< Field >, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

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

include/Ring/BPASEuclideanDomain.hpp

Public Member Functions

Detailed Description

template<class Derived> class BPASEuclideanDomain< Derived >

Member Function Documentation

◆ euclideanDivision()

◆ extendedEuclidean()

◆ operator%()

◆ operator%=()

◆ quotient()

◆ remainder()

template<class Derived>
class BPASEuclideanDomain< Derived >