|
| AbstractRing () |
| Construct an AbstractRing.
|
|
| AbstractRing (const AbstractRing &source) |
| Copy construct an AbstractRing.
|
|
AbstractRing & | operator= (const AbstractRing &source) |
| Assign an AbstractRing.
|
|
virtual bool | IsUnit (const Element &a) const =0 |
| Determines whether an element is a unit in the group.
|
|
virtual const Element & | MultiplicativeIdentity () const =0 |
| Retrieves the multiplicative identity.
|
|
virtual const Element & | Multiply (const Element &a, const Element &b) const =0 |
| Multiplies elements in the group.
|
|
virtual const Element & | MultiplicativeInverse (const Element &a) const =0 |
| Calculate the multiplicative inverse of an element in the group.
|
|
virtual const Element & | Square (const Element &a) const |
| Square an element in the group.
|
|
virtual const Element & | Divide (const Element &a, const Element &b) const |
| Divides elements in the group.
|
|
virtual Element | Exponentiate (const Element &a, const Integer &e) const |
| Raises a base to an exponent in the group.
|
|
virtual Element | CascadeExponentiate (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const |
| TODO.
|
|
virtual void | SimultaneousExponentiate (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const |
| Exponentiates a base to multiple exponents in the Ring.
|
|
virtual const AbstractGroup< T > & | MultiplicativeGroup () const |
| Retrieves the multiplicative group.
|
|
virtual bool | Equal (const Element &a, const Element &b) const =0 |
| Compare two elements for equality.
|
|
virtual const Element & | Identity () const =0 |
| Provides the Identity element.
|
|
virtual const Element & | Add (const Element &a, const Element &b) const =0 |
| Adds elements in the group.
|
|
virtual const Element & | Inverse (const Element &a) const =0 |
| Inverts the element in the group.
|
|
virtual bool | InversionIsFast () const |
| Determine if inversion is fast.
|
|
virtual const Element & | Double (const Element &a) const |
| Doubles an element in the group.
|
|
virtual const Element & | Subtract (const Element &a, const Element &b) const |
| Subtracts elements in the group.
|
|
virtual Element & | Accumulate (Element &a, const Element &b) const |
| TODO.
|
|
virtual Element & | Reduce (Element &a, const Element &b) const |
| Reduces an element in the congruence class.
|
|
virtual Element | ScalarMultiply (const Element &a, const Integer &e) const |
| Performs a scalar multiplication.
|
|
virtual Element | CascadeScalarMultiply (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const |
| TODO.
|
|
virtual void | SimultaneousMultiply (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const |
| Multiplies a base to multiple exponents in a group.
|
|
template<class T>
class AbstractRing< T >
Abstract ring.
- Template Parameters
-
const Element&
returned by member functions are references to internal data members. Since each object may have only one such data member for holding results, the following code will produce incorrect results:
abcd = group.Add(group.Add(a,b), group.Add(c,d));
But this should be fine:
abcd = group.Add(a, group.Add(b, group.Add(c,d));
Definition at line 118 of file algebra.h.