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RingOfPolynomialsOver Class Template Reference

Ring of polynomials over another ring. More...

#include <polynomi.h>

Inheritance diagram for RingOfPolynomialsOver:

List of all members.

Public Types
typedef T	CoefficientRing
typedef PolynomialOver<T>	Element
typedef Element::CoefficientType	CoefficientType
typedef Element::RandomizationParameter	RandomizationParameter
Public Methods
	RingOfPolynomialsOver (const CoefficientRing &ring)
Element	RandomElement (RandomNumberGenerator &rng,const RandomizationParameter &parameter)
bool	Equal (const Element &a,const Element &b)const
const Element&	Zero ()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
const Element&	One ()const
const Element&	Multiply (const Element &a,const Element &b)const
const Element&	Square (const Element &a)const
bool	IsUnit (const Element &a)const
const Element&	MultiplicativeInverse (const Element &a)const
const Element&	Divide (const Element &a,const Element &b)const
const Element&	Mod (const Element &a,const Element &b)const
void	DivisionAlgorithm (Element &r,Element &q,const Element &a,const Element &d)const
Element	Interpolate (const CoefficientType x[],const CoefficientType y[],unsigned int n)const
CoefficientType	InterpolateAt (const CoefficientType &position,const CoefficientType x[],const CoefficientType y[],unsigned int n)const
Protected Methods
void	CalculateAlpha (::vector< CoefficientType > &alpha,const CoefficientType x[],const CoefficientType y[],unsigned int n)const
Protected Attributes
CoefficientRing	m_ring

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Detailed Description

template<class T> class RingOfPolynomialsOver

Ring of polynomials over another ring.

Definition at line 302 of file polynomi.h.

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Member Typedef Documentation

template<class T> typedef T RingOfPolynomialsOver<T>::CoefficientRing

Definition at line 305 of file polynomi.h.

template<class T> typedef Element::CoefficientType RingOfPolynomialsOver<T>::CoefficientType

Definition at line 307 of file polynomi.h.

template<class T> typedef PolynomialOver< T > RingOfPolynomialsOver<T>::Element

Reimplemented from AbstractEuclideanDomain. Definition at line 306 of file polynomi.h.

template<class T> typedef Element::RandomizationParameter RingOfPolynomialsOver<T>::RandomizationParameter

Definition at line 308 of file polynomi.h.

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Constructor & Destructor Documentation

template<class T> RingOfPolynomialsOver<T>::RingOfPolynomialsOver<T> ( const CoefficientRing & ring ) [inline]

Definition at line 310 of file polynomi.h.

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Member Function Documentation

template<class T> Element & RingOfPolynomialsOver<T>::Accumulate ( Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 324 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Add ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 321 of file polynomi.h.

template<class T> void RingOfPolynomialsOver< T >::CalculateAlpha ( ::vector< CoefficientType > & alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n ) const [protected]

Definition at line 455 of file polynomi.cpp.

template<class T> const Element & RingOfPolynomialsOver<T>::Divide ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 355 of file polynomi.h.

template<class T> void RingOfPolynomialsOver<T>::DivisionAlgorithm ( Element & r, Element & q, const Element & a, const Element & d ) const [inline, virtual]

Reimplemented from AbstractEuclideanDomain. Definition at line 361 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Double ( const Element & a ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 336 of file polynomi.h.

template<class T> bool RingOfPolynomialsOver<T>::Equal ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 315 of file polynomi.h.

template<class T> RingOfPolynomialsOver< T >::Element RingOfPolynomialsOver< T >::Interpolate ( const CoefficientType x[], const CoefficientType y[], unsigned int n ) const

Definition at line 475 of file polynomi.cpp.

template<class T> RingOfPolynomialsOver< T >::CoefficientType RingOfPolynomialsOver< T >::InterpolateAt ( const CoefficientType & position, const CoefficientType x[], const CoefficientType y[], unsigned int n ) const

Definition at line 497 of file polynomi.cpp.

template<class T> const Element & RingOfPolynomialsOver<T>::Inverse ( const Element & a ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 327 of file polynomi.h.

template<class T> bool RingOfPolynomialsOver<T>::IsUnit ( const Element & a ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 349 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Mod ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractEuclideanDomain. Definition at line 358 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::MultiplicativeInverse ( const Element & a ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 352 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Multiply ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 343 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::One ( ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 340 of file polynomi.h.

template<class T> Element RingOfPolynomialsOver<T>::RandomElement ( RandomNumberGenerator & rng, const RandomizationParameter & parameter ) [inline]

Definition at line 312 of file polynomi.h.

template<class T> Element & RingOfPolynomialsOver<T>::Reduce ( Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 333 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Square ( const Element & a ) const [inline, virtual]

Reimplemented from AbstractRing. Definition at line 346 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Subtract ( const Element & a, const Element & b ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 330 of file polynomi.h.

template<class T> const Element & RingOfPolynomialsOver<T>::Zero ( ) const [inline, virtual]

Reimplemented from AbstractGroup. Definition at line 318 of file polynomi.h.

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Member Data Documentation

template<class T> CoefficientRing RingOfPolynomialsOver<T>::m_ring [protected]

Definition at line 382 of file polynomi.h.

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

• polynomi.h
• polynomi.cpp

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