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AbstractRing< T > Class Template Referenceabstract

Abstract ring. More...

+ Inheritance diagram for AbstractRing< T >:

Public Types

typedef T Element
 
- Public Types inherited from AbstractGroup< T >
typedef T Element
 

Public Member Functions

 AbstractRing ()
 Construct an AbstractRing.
 
 AbstractRing (const AbstractRing &source)
 Copy construct an AbstractRing. More...
 
AbstractRingoperator= (const AbstractRing &source)
 Assign an AbstractRing. More...
 
virtual bool IsUnit (const Element &a) const =0
 Determines whether an element is a unit in the group. More...
 
virtual const Element & MultiplicativeIdentity () const =0
 Retrieves the multiplicative identity. More...
 
virtual const Element & Multiply (const Element &a, const Element &b) const =0
 Multiplies elements in the group. More...
 
virtual const Element & MultiplicativeInverse (const Element &a) const =0
 Calculate the multiplicative inverse of an element in the group. More...
 
virtual const Element & Square (const Element &a) const
 Square an element in the group. More...
 
virtual const Element & Divide (const Element &a, const Element &b) const
 Divides elements in the group. More...
 
virtual Element Exponentiate (const Element &a, const Integer &e) const
 Raises a base to an exponent in the group. More...
 
virtual Element CascadeExponentiate (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
 TODO. More...
 
virtual void SimultaneousExponentiate (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
 Exponentiates a base to multiple exponents in the Ring. More...
 
virtual const AbstractGroup< T > & MultiplicativeGroup () const
 Retrieves the multiplicative group. More...
 
- Public Member Functions inherited from AbstractGroup< T >
virtual bool Equal (const Element &a, const Element &b) const =0
 Compare two elements for equality. More...
 
virtual const Element & Identity () const =0
 Provides the Identity element. More...
 
virtual const Element & Add (const Element &a, const Element &b) const =0
 Adds elements in the group. More...
 
virtual const Element & Inverse (const Element &a) const =0
 Inverts the element in the group. More...
 
virtual bool InversionIsFast () const
 Determine if inversion is fast. More...
 
virtual const Element & Double (const Element &a) const
 Doubles an element in the group. More...
 
virtual const Element & Subtract (const Element &a, const Element &b) const
 Subtracts elements in the group. More...
 
virtual Element & Accumulate (Element &a, const Element &b) const
 TODO. More...
 
virtual Element & Reduce (Element &a, const Element &b) const
 Reduces an element in the congruence class. More...
 
virtual Element ScalarMultiply (const Element &a, const Integer &e) const
 Performs a scalar multiplication. More...
 
virtual Element CascadeScalarMultiply (const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
 TODO. More...
 
virtual void SimultaneousMultiply (Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
 Multiplies a base to multiple exponents in a group. More...
 

Detailed Description

template<class T>
class AbstractRing< T >

Abstract ring.

Template Parameters
Telement class or type

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.

Constructor & Destructor Documentation

template<class T>
AbstractRing< T >::AbstractRing ( const AbstractRing< T > &  source)
inline

Copy construct an AbstractRing.

Parameters
sourceother AbstractRing

Definition at line 128 of file algebra.h.

Member Function Documentation

template<class T>
AbstractRing& AbstractRing< T >::operator= ( const AbstractRing< T > &  source)
inline

Assign an AbstractRing.

Parameters
sourceother AbstractRing

Definition at line 133 of file algebra.h.

template<class T>
virtual bool AbstractRing< T >::IsUnit ( const Element &  a) const
pure virtual

Determines whether an element is a unit in the group.

Parameters
athe element
Returns
true if the element is a unit after reduction, false otherwise.

Implemented in QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, GF2NP, ModularArithmetic, and GFP2_ONB< F >.

template<class T>
virtual const Element& AbstractRing< T >::MultiplicativeIdentity ( ) const
pure virtual
template<class T>
virtual const Element& AbstractRing< T >::Multiply ( const Element &  a,
const Element &  b 
) const
pure virtual

Multiplies elements in the group.

Parameters
athe multiplicand
bthe multiplier
Returns
the product of a and b

Implemented in QuotientRing< T >, QuotientRing< EuclideanDomainOf< PolynomialMod2 > >, RingOfPolynomialsOver< T >, EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, GF2NT, MontgomeryRepresentation, ModularArithmetic, and GFP2_ONB< F >.

template<class T>
virtual const Element& AbstractRing< T >::MultiplicativeInverse ( const Element &  a) const
pure virtual
template<class T >
const T & AbstractRing< T >::Square ( const Element &  a) const
virtual
template<class T >
const T & AbstractRing< T >::Divide ( const Element &  a,
const Element &  b 
) const
virtual

Divides elements in the group.

Parameters
athe dividend
bthe divisor
Returns
the quotient

Reimplemented in RingOfPolynomialsOver< T >, EuclideanDomainOf< T >, EuclideanDomainOf< PolynomialMod2 >, and ModularArithmetic.

Definition at line 42 of file algebra.cpp.

template<class T >
T AbstractRing< T >::Exponentiate ( const Element &  a,
const Integer e 
) const
virtual

Raises a base to an exponent in the group.

Parameters
athe base
ethe exponent
Returns
the exponentiation

Reimplemented in GFP2_ONB< F >.

Definition at line 316 of file algebra.cpp.

template<class T >
T AbstractRing< T >::CascadeExponentiate ( const Element &  x,
const Integer e1,
const Element &  y,
const Integer e2 
) const
virtual

TODO.

Parameters
xfirst element
e1first exponent
ysecond element
e2second exponent
Returns
TODO

Reimplemented in MontgomeryRepresentation, and ModularArithmetic.

Definition at line 323 of file algebra.cpp.

template<class T >
void AbstractRing< T >::SimultaneousExponentiate ( Element *  results,
const Element &  base,
const Integer exponents,
unsigned int  exponentsCount 
) const
virtual

Exponentiates a base to multiple exponents in the Ring.

Parameters
resultsan array of Elements
basethe base to raise to the exponents
exponentsan array of exponents
exponentsCountthe number of exponents in the array

SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the result at the respective position in the results array.

SimultaneousExponentiate() must be implemented in a derived class.

Precondition
COUNTOF(results) == exponentsCount
COUNTOF(exponents) == exponentsCount

Reimplemented in MontgomeryRepresentation, and ModularArithmetic.

Definition at line 334 of file algebra.cpp.

template<class T>
virtual const AbstractGroup<T>& AbstractRing< T >::MultiplicativeGroup ( ) const
inlinevirtual

Retrieves the multiplicative group.

Returns
the multiplicative group

Definition at line 194 of file algebra.h.


The documentation for this class was generated from the following files: