Basic Polynomial Algebra Subprograms (BPAS)
v. 1.652

An abstract class defining the interface of a commutative ring. More...
#include <BPASRing.hpp>
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) 
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 subclasses of BPASRing.

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 >, DenseUnivariateRationalPolynomial, DenseUnivariatePolynomial< Field >, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, SmartFraction< Domain >, GeneralizedFermatPrimeField, Integer, BigPrimeField, RationalNumber, ComplexRationalNumber, and Fraction< Domain >.

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 >, DenseUnivariateRationalPolynomial, DenseUnivariatePolynomial< Field >, SmartFraction< Domain >, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, GeneralizedFermatPrimeField, Integer, BigPrimeField, RationalNumber, Fraction< Domain >, and ComplexRationalNumber.

pure virtual 
Inequality test,.
returns true iff not equal.
Implemented in SmallPrimeField, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, Integer, DenseUnivariateRationalPolynomial, DenseUnivariatePolynomial< Field >, RationalNumber, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, SmartFraction< Domain >, BigPrimeField, ComplexRationalNumber, and Fraction< Domain >.

pure virtual 
Equality test,.
returns true iff equal
Implemented in SmallPrimeField, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial, Integer, DenseUnivariateRationalPolynomial, DenseUnivariatePolynomial< Field >, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, RationalNumber, GeneralizedFermatPrimeField, SmartFraction< Domain >, ComplexRationalNumber, BigPrimeField, and Fraction< Domain >.

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 >.

pure virtual 
Obtain the unit normal (a.k.a canonical associate) of an element.
If either parameters u, v, are nonNULL 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.

friend 
Output operator.
Defines a to string conversion.