BPASRing< Derived > Class Template Reference

An abstract class defining the interface of a commutative ring. More...

#include <BPASRing.hpp>

Simplified semantic inheritance diagram for BPASRing< Derived >:

 Full inheritance diagram for BPASRing< Derived >:

Public Member Functions
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...

Friends
std::ostream &	operator<< (std::ostream &ostream, const Derived &d)
	Output operator. More...
std::ostream &	operator<< (std::ostream &ostream, Derived &&d)

Detailed Description

template<class Derived>
class BPASRing< Derived >

An abstract class defining the interface of a commutative ring.

The template Derived is a concrete class derived from (implemeneting the interface of) BPASRing. This is the "curiously recurring template pattern" (CTRP). This pattern is used among all sub-classes of BPASRing.

Member Function Documentation

isOne()

template<class Derived>

virtual bool BPASRing< Derived >::isOne ( ) const

pure virtual

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

returns true iff *this is one.

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

isZero()

template<class Derived>

virtual bool BPASRing< Derived >::isZero ( ) const

pure virtual

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

returns true iff *this is zero.

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

operator!=()

template<class Derived>

virtual bool BPASRing< Derived >::operator!= ( const Derived &  ) const

pure virtual

Inequality test,.

returns true iff not equal.

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

operator==()

template<class Derived>

virtual bool BPASRing< Derived >::operator== ( const Derived &  ) const

pure virtual

Equality test,.

returns true iff equal

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

print()

template<class Derived>

virtual void BPASRing< Derived >::print ( std::ostream &  ostream ) const

inlinevirtual

Print the Ring element.

Derived classes may override this to get custom printing that may be more expressive (and prettier) than expression tree printing.

Reimplemented in DenseUnivariatePolynomial< Field >, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, ComplexRationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

toString()

template<class Derived>

virtual std::string BPASRing< Derived >::toString ( ) const

inlinevirtual

Convert the Ring element to a string.

Simple delegation of printing to a stringstream to obtain a string. Overriding the print method is sufficient for sub-classes to make use of this method.

returns the string representation of the Ring element.

unitCanonical()

template<class Derived>

virtual Derived BPASRing< Derived >::unitCanonical ( Derived *  u = NULL, Derived *  v = NULL  ) const

pure 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.

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

Friends And Related Function Documentation

operator<<

template<class Derived>

std::ostream& operator<< ( std::ostream &  ostream, const Derived &  d  )

friend

Output operator.

Defines a to string conversion.

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

• include/Ring/BPASRing.hpp