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RingOfPolynomialsOver< T > Class Template Reference

Ring of polynomials over another ring. More...

#include <polynomi.h>

Inheritance diagram for RingOfPolynomialsOver< T >:
AbstractEuclideanDomain< PolynomialOver< T > > AbstractRing< T > AbstractGroup< T >

Classes

class  InterpolationFailed
 

Public Types

typedef T CoefficientRing
 
typedef PolynomialOver< T > Element
 
typedef Element::CoefficientType CoefficientType
 
typedef Element::RandomizationParameter RandomizationParameter
 
- Public Types inherited from AbstractEuclideanDomain< PolynomialOver< T > >
typedef PolynomialOver< T > Element
 
- Public Types inherited from AbstractRing< T >
typedef T Element
 
- Public Types inherited from AbstractGroup< T >
typedef T Element
 

Public Member Functions

 RingOfPolynomialsOver (const CoefficientRing &ring)
 
Element RandomElement (RandomNumberGenerator &rng, const RandomizationParameter &parameter)
 
bool Equal (const Element &a, const Element &b) const
 
const ElementIdentity () const
 Provides the Identity element.
 
const ElementAdd (const Element &a, const Element &b) const
 
ElementAccumulate (Element &a, const Element &b) const
 
const ElementInverse (const Element &a) const
 
const ElementSubtract (const Element &a, const Element &b) const
 
ElementReduce (Element &a, const Element &b) const
 
const ElementDouble (const Element &a) const
 
const ElementMultiplicativeIdentity () const
 Retrieves the multiplicative identity.
 
const ElementMultiply (const Element &a, const Element &b) const
 
const ElementSquare (const Element &a) const
 
bool IsUnit (const Element &a) const
 
const ElementMultiplicativeInverse (const Element &a) const
 
const ElementDivide (const Element &a, const Element &b) const
 
const ElementMod (const Element &a, const Element &b) const
 Performs a modular reduction in the ring.
 
void DivisionAlgorithm (Element &r, Element &q, const Element &a, const Element &d) const
 Performs the division algorithm on two elements in the ring.
 
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
 
- Public Member Functions inherited from AbstractEuclideanDomain< PolynomialOver< T > >
virtual const ElementGcd (const Element &a, const Element &b) const
 Calculates the greatest common denominator in the ring.
 
- Public Member Functions inherited from AbstractRing< T >
 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.
 

Protected Member Functions

void CalculateAlpha (std::vector< CoefficientType > &alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n) const
 

Protected Attributes

CoefficientRing m_ring
 
- Protected Attributes inherited from AbstractEuclideanDomain< PolynomialOver< T > >
Element result
 

Detailed Description

template<class T>
class RingOfPolynomialsOver< T >

Ring of polynomials over another ring.

Definition at line 314 of file polynomi.h.

Member Typedef Documentation

◆ CoefficientRing

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

Definition at line 317 of file polynomi.h.

◆ CoefficientType

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

Definition at line 319 of file polynomi.h.

◆ Element

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

Definition at line 318 of file polynomi.h.

◆ RandomizationParameter

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

Definition at line 320 of file polynomi.h.

Constructor & Destructor Documentation

◆ RingOfPolynomialsOver()

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

Definition at line 322 of file polynomi.h.

Member Function Documentation

◆ Accumulate()

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

Definition at line 336 of file polynomi.h.

◆ Add()

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

Definition at line 333 of file polynomi.h.

◆ CalculateAlpha()

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

Definition at line 456 of file polynomi.cpp.

◆ Divide()

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

Definition at line 366 of file polynomi.h.

◆ DivisionAlgorithm()

template<class T >
void RingOfPolynomialsOver< T >::DivisionAlgorithm ( Element r,
Element q,
const Element a,
const Element d 
) const
inlinevirtual

Performs the division algorithm on two elements in the ring.

Parameters
rthe remainder
qthe quotient
athe dividend
dthe divisor

Implements AbstractEuclideanDomain< PolynomialOver< T > >.

Definition at line 372 of file polynomi.h.

◆ Double()

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

Definition at line 348 of file polynomi.h.

◆ Equal()

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

Definition at line 327 of file polynomi.h.

◆ Identity()

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

Provides the Identity element.

Returns
the Identity element

Implements AbstractGroup< T >.

Definition at line 330 of file polynomi.h.

◆ Interpolate()

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

Definition at line 476 of file polynomi.cpp.

◆ InterpolateAt()

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 498 of file polynomi.cpp.

◆ Inverse()

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

Definition at line 339 of file polynomi.h.

◆ IsUnit()

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

Definition at line 360 of file polynomi.h.

◆ Mod()

template<class T >
const Element & RingOfPolynomialsOver< T >::Mod ( const Element a,
const Element b 
) const
inlinevirtual

Performs a modular reduction in the ring.

Parameters
athe element
bthe modulus
Returns
the result of ab.

Implements AbstractEuclideanDomain< PolynomialOver< T > >.

Definition at line 369 of file polynomi.h.

◆ MultiplicativeIdentity()

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

Retrieves the multiplicative identity.

Returns
the multiplicative identity

Implements AbstractRing< T >.

Definition at line 351 of file polynomi.h.

◆ MultiplicativeInverse()

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

Definition at line 363 of file polynomi.h.

◆ Multiply()

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

Definition at line 354 of file polynomi.h.

◆ RandomElement()

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

Definition at line 324 of file polynomi.h.

◆ Reduce()

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

Definition at line 345 of file polynomi.h.

◆ Square()

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

Definition at line 357 of file polynomi.h.

◆ Subtract()

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

Definition at line 342 of file polynomi.h.

Member Data Documentation

◆ m_ring

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

Definition at line 393 of file polynomi.h.


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