 |
Basic Polynomial Algebra Subprograms (BPAS)
v. 1.652
|
|
Basic Polynomial Algebra Subprograms (BPAS)
v. 1.652
|
An abstract class defining the interface of a Euclidean domain. More...
#include <BPASEuclideanDomain.hpp>
Full inheritance diagram for BPASEuclideanDomain< Derived >:Public Member Functions | |
| virtual Derived | 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 |
| Perofrm the extended euclidean division on *this and b. More... | |
| virtual Derived | quotient (const Derived &b) const =0 |
| Get the quotient of *this and b. | |
| virtual Derived | remainder (const Derived &b) const =0 |
| Get the remainder of *this and b. | |
| virtual Derived | operator% (const Derived &b) const =0 |
| Get the remainder of *this and b;. | |
| virtual Derived & | operator%= (const Derived &b)=0 |
| Assign *this to be the remainder of *this and b. | |
| Public Member Functions inherited from BPASGCDDomain< Derived > | |
| virtual Derived | gcd (const Derived &other) const =0 |
| Get GCD of *this and other. | |
| virtual Factors< Derived > | squareFree () const =0 |
| Compute squarefree factorization of *this. | |
| Public Member Functions inherited from BPASIntegralDomain< Derived > | |
| virtual Derived | operator/ (const Derived &) const =0 |
| Exact division. | |
| virtual Derived & | operator/= (const Derived &)=0 |
| Exact division assignment. | |
| Public Member Functions inherited from BPASRing< Derived > | |
| 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... | |
Additional Inherited Members | |
| Static Public Attributes inherited from BPASRing< Derived > | |
| static RingProperties | properties |
| Static element describing the properties of this ring class. | |
An abstract class defining the interface of a Euclidean domain.
|
pure virtual |
Perform the eucldiean division of *this and b.
Returns the remainder. If q is not NULL, then returns the quotient in q.
Implemented in DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.
|
pure virtual |
Perofrm the extended euclidean division on *this and b.
Returns the GCD. If s and t are not NULL, returns the bezout coefficients in them.
Implemented in DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, SmallPrimeField, GeneralizedFermatPrimeField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field >, BigPrimeField, Integer, ComplexRationalNumber, RationalNumber, SmartFraction< Domain >, and Fraction< Domain >.
1.8.13