Quotient Ring. More...
#include <algebra.h>
Public Types | |
typedef T | EuclideanDomain |
typedef T::Element | Element |
Public Member Functions | |
QuotientRing (const EuclideanDomain &domain, const Element &modulus) | |
const EuclideanDomain & | GetDomain () const |
const Element & | GetModulus () const |
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 |
bool | IsUnit (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 |
const Element & | MultiplicativeInverse (const Element &a) const |
bool | operator== (const QuotientRing< T > &rhs) const |
virtual const Element & | Divide (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< 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 Attributes | |
EuclideanDomain | m_domain |
Element | m_modulus |
Quotient Ring.
Definition at line 218 of file algebra.h.