Basic Polynomial Algebra Subprograms (BPAS)
v. 1.791
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An abstract class defining the interface of a commutative ring. More...
#include <BPASRing.hpp>
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) |
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.
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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 >.
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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.
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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 >.
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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 >.
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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 >.
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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.
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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.
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friend |
Output operator.
Defines a to string conversion.