Basic Polynomial Algebra Subprograms (BPAS)  v. 1.548
Public Member Functions | Static Public Attributes | Friends | List of all members
BPASRing< Derived > Class Template Referenceabstract

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 >:
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Public Member Functions

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

Static Public Attributes

static RingProperties properties
 Static element describing the properties of this ring class.
 

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

◆ isZero()

template<class Derived>
virtual bool BPASRing< Derived >::isZero ( ) const
pure virtual

◆ operator!=()

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

◆ operator==()

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

◆ 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 >, DenseUnivariateRationalPolynomial, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, ComplexRationalNumber, SmartFraction< Domain >, and Fraction< Domain >.

◆ 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, DenseUnivariateRationalPolynomial, 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.


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