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Public Types | Public Member Functions | List of all members
QuotientRing< T > Class Template Reference

Quotient ring. More...

#include <algebra.h>

+ Inheritance diagram for QuotientRing< T >:

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 EuclideanDomain & GetDomain () const
 
const Element & GetModulus () const
 
bool Equal (const Element &a, const Element &b) const
 
const Element & Identity () const
 Provides the Identity element.
 
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
 Retrieves the multiplicative identity.
 
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
 
- Public Member Functions inherited from AbstractRing< T::Element >
 AbstractRing ()
 Construct an AbstractRing.
 
 AbstractRing (const AbstractRing &source)
 Copy construct an AbstractRing.
 
AbstractRingoperator= (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 & 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.
 
- Public Member Functions inherited from AbstractGroup< T >
virtual bool Equal (const Element &a, const Element &b) const =0
 Compare two elements for equality.
 
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.
 

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

◆ EuclideanDomain

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

Definition at line 389 of file algebra.h.

◆ Element

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

Definition at line 390 of file algebra.h.

Constructor & Destructor Documentation

◆ QuotientRing()

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

Definition at line 392 of file algebra.h.

Member Function Documentation

◆ GetDomain()

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

Definition at line 395 of file algebra.h.

◆ GetModulus()

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

Definition at line 398 of file algebra.h.

◆ Equal()

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

Definition at line 401 of file algebra.h.

◆ Identity()

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.

◆ Add()

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

Definition at line 407 of file algebra.h.

◆ Accumulate()

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

Definition at line 410 of file algebra.h.

◆ Inverse()

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

Definition at line 413 of file algebra.h.

◆ Subtract()

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

Definition at line 416 of file algebra.h.

◆ Reduce()

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

Definition at line 419 of file algebra.h.

◆ Double()

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

Definition at line 422 of file algebra.h.

◆ IsUnit()

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

Definition at line 425 of file algebra.h.

◆ MultiplicativeIdentity()

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.

◆ Multiply()

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

Definition at line 431 of file algebra.h.

◆ Square()

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

Definition at line 434 of file algebra.h.

◆ MultiplicativeInverse()

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

Definition at line 70 of file algebra.cpp.

◆ operator==()

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

Definition at line 439 of file algebra.h.


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