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QuotientRing< T > Class Template Reference

Quotient ring. More...

#include <algebra.h>

Inheritance diagram for QuotientRing< T >:
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Collaboration diagram for QuotientRing< T >:
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Public Types

typedef T EuclideanDomain
 
typedef T::Element Element
 
- Public Types inherited from AbstractRing< T::Element >
typedef T Element
 
- Public Types inherited from AbstractGroup< T >
typedef T Element
 

Public Member Functions

 QuotientRing (const EuclideanDomain &domain, const Element &modulus)
 
const EuclideanDomainGetDomain () const
 
const ElementGetModulus () const
 
bool Equal (const Element &a, const Element &b) const
 Compare two elements for equality. More...
 
const ElementIdentity () const
 Provides the Identity element. More...
 
const ElementAdd (const Element &a, const Element &b) const
 Adds elements in the group. More...
 
ElementAccumulate (Element &a, const Element &b) const
 TODO. More...
 
const ElementInverse (const Element &a) const
 Inverts the element in the group. More...
 
const ElementSubtract (const Element &a, const Element &b) const
 Subtracts elements in the group. More...
 
ElementReduce (Element &a, const Element &b) const
 Reduces an element in the congruence class. More...
 
const ElementDouble (const Element &a) const
 Doubles an element in the group. More...
 
bool IsUnit (const Element &a) const
 Determines whether an element is a unit in the group. More...
 
const ElementMultiplicativeIdentity () const
 Retrieves the multiplicative identity. More...
 
const ElementMultiply (const Element &a, const Element &b) const
 Multiplies elements in the group. More...
 
const ElementSquare (const Element &a) const
 Square an element in the group. More...
 
const ElementMultiplicativeInverse (const Element &a) const
 Calculate the multiplicative inverse of an element in the group. More...
 
bool operator== (const QuotientRing< T > &rhs) const
 
- Public Member Functions inherited from AbstractRing< T::Element >
 AbstractRing ()
 Construct an AbstractRing. More...
 
 AbstractRing (const AbstractRing &source)
 Copy construct an AbstractRing. More...
 
AbstractRingoperator= (const AbstractRing &source)
 Assign an AbstractRing. More...
 
virtual const ElementDivide (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 ~AbstractGroup ()
 
virtual bool InversionIsFast () const
 Determine if inversion is fast. 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...
 

Protected Attributes

EuclideanDomain m_domain
 
Element m_modulus
 

Detailed Description

template<class T>
class QuotientRing< T >

Quotient 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 386 of file algebra.h.

Member Typedef Documentation

template<class T>
typedef T::Element QuotientRing< T >::Element

Definition at line 390 of file algebra.h.

template<class T>
typedef T QuotientRing< T >::EuclideanDomain

Definition at line 389 of file algebra.h.

Constructor & Destructor Documentation

template<class T>
QuotientRing< T >::QuotientRing ( const EuclideanDomain domain,
const Element modulus 
)
inline

Definition at line 392 of file algebra.h.

Member Function Documentation

template<class T>
Element& QuotientRing< T >::Accumulate ( Element a,
const Element b 
) const
inlinevirtual

TODO.

Parameters
afirst element
bsecond element
Returns
TODO

Reimplemented from AbstractGroup< T >.

Definition at line 410 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Add ( const Element a,
const Element b 
) const
inlinevirtual

Adds elements in the group.

Parameters
afirst element
bsecond element
Returns
the sum of a and b

Implements AbstractGroup< T >.

Definition at line 407 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Double ( const Element a) const
inlinevirtual

Doubles an element in the group.

Parameters
athe element
Returns
the element doubled

Reimplemented from AbstractGroup< T >.

Definition at line 422 of file algebra.h.

template<class T>
bool QuotientRing< T >::Equal ( const Element a,
const Element b 
) const
inlinevirtual

Compare two elements for equality.

Parameters
afirst element
bsecond element
Returns
true if the elements are equal, false otherwise

Equal() tests the elements for equality using a==b

Implements AbstractGroup< T >.

Definition at line 401 of file algebra.h.

template<class T>
const EuclideanDomain& QuotientRing< T >::GetDomain ( ) const
inline

Definition at line 395 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::GetModulus ( ) const
inline

Definition at line 398 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Identity ( ) const
inlinevirtual

Provides the Identity element.

Returns
the Identity element

Implements AbstractGroup< T >.

Definition at line 404 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Inverse ( const Element a) const
inlinevirtual

Inverts the element in the group.

Parameters
afirst element
Returns
the inverse of the element

Implements AbstractGroup< T >.

Definition at line 413 of file algebra.h.

template<class T>
bool QuotientRing< T >::IsUnit ( const Element a) const
inlinevirtual

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.

Implements AbstractRing< T::Element >.

Definition at line 425 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::MultiplicativeIdentity ( ) const
inlinevirtual

Retrieves the multiplicative identity.

Returns
the multiplicative identity

Implements AbstractRing< T::Element >.

Definition at line 428 of file algebra.h.

template<class T >
const QuotientRing< T >::Element & QuotientRing< T >::MultiplicativeInverse ( const Element a) const
virtual

Calculate the multiplicative inverse of an element in the group.

Parameters
athe element

Implements AbstractRing< T::Element >.

Definition at line 70 of file algebra.cpp.

template<class T>
const Element& QuotientRing< T >::Multiply ( const Element a,
const Element b 
) const
inlinevirtual

Multiplies elements in the group.

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

Implements AbstractRing< T::Element >.

Definition at line 431 of file algebra.h.

template<class T>
bool QuotientRing< T >::operator== ( const QuotientRing< T > &  rhs) const
inline

Definition at line 439 of file algebra.h.

template<class T>
Element& QuotientRing< T >::Reduce ( Element a,
const Element b 
) const
inlinevirtual

Reduces an element in the congruence class.

Parameters
aelement to reduce
bthe congruence class
Returns
the reduced element

Reimplemented from AbstractGroup< T >.

Definition at line 419 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Square ( const Element a) const
inlinevirtual

Square an element in the group.

Parameters
athe element
Returns
the element squared

Reimplemented from AbstractRing< T::Element >.

Definition at line 434 of file algebra.h.

template<class T>
const Element& QuotientRing< T >::Subtract ( const Element a,
const Element b 
) const
inlinevirtual

Subtracts elements in the group.

Parameters
afirst element
bsecond element
Returns
the difference of a and b. The element a must provide a Subtract member function.

Reimplemented from AbstractGroup< T >.

Definition at line 416 of file algebra.h.

Member Data Documentation

template<class T>
EuclideanDomain QuotientRing< T >::m_domain
protected

Definition at line 443 of file algebra.h.

template<class T>
Element QuotientRing< T >::m_modulus
protected

Definition at line 444 of file algebra.h.


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