Ring of polynomials over another ring. More...
#include <polynomi.h>
Classes | |
class | InterpolationFailed |
Public Types | |
typedef T | CoefficientRing |
typedef PolynomialOver< T > | Element |
typedef Element::CoefficientType | CoefficientType |
typedef Element::RandomizationParameter | RandomizationParameter |
Public Member Functions | |
RingOfPolynomialsOver (const CoefficientRing &ring) | |
Element | RandomElement (RandomNumberGenerator &rng, const RandomizationParameter ¶meter) |
bool | Equal (const Element &a, const Element &b) const |
const Element & | Identity () const |
const Element & | Add (const Element &a, const Element &b) const |
Element & | Accumulate (Element &a, const Element &b) const |
const Element & | Inverse (const Element &a) const |
const Element & | Subtract (const Element &a, const Element &b) const |
Element & | Reduce (Element &a, const Element &b) const |
const Element & | Double (const Element &a) const |
const Element & | MultiplicativeIdentity () const |
const Element & | Multiply (const Element &a, const Element &b) const |
const Element & | Square (const Element &a) const |
bool | IsUnit (const Element &a) const |
const Element & | MultiplicativeInverse (const Element &a) const |
const Element & | Divide (const Element &a, const Element &b) const |
const Element & | Mod (const Element &a, const Element &b) const |
void | DivisionAlgorithm (Element &r, Element &q, const Element &a, const Element &d) const |
Element | Interpolate (const CoefficientType x[], const CoefficientType y[], unsigned int n) const |
CoefficientType | InterpolateAt (const CoefficientType &position, const CoefficientType x[], const CoefficientType y[], unsigned int n) const |
virtual const Element & | Gcd (const Element &a, const Element &b) const |
virtual Element | Exponentiate (const Element &a, const Integer &e) const |
virtual Element | CascadeExponentiate (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const |
virtual void | SimultaneousExponentiate (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const |
virtual const AbstractGroup < PolynomialOver< T > > & | MultiplicativeGroup () const |
virtual bool | InversionIsFast () const |
virtual Element | ScalarMultiply (const Element &a, const Integer &e) const |
virtual Element | CascadeScalarMultiply (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const |
virtual void | SimultaneousMultiply (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const |
Protected Member Functions | |
void | CalculateAlpha (std::vector< CoefficientType > &alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n) const |
Protected Attributes | |
CoefficientRing | m_ring |
Element | result |
Ring of polynomials over another ring.
Definition at line 310 of file polynomi.h.