Ring of polynomials over another ring. More...

#include <polynomi.h>

Inheritance diagram for RingOfPolynomialsOver< 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 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

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

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
	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 Element &	Gcd (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.

AbstractRing &	operator= (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 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.

◆ Element

template<class T >

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

Definition at line 318 of file polynomi.h.

◆ CoefficientType

template<class T >

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

Definition at line 319 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

◆ RandomElement()

template<class T >

Element RingOfPolynomialsOver< T >::RandomElement	(	RandomNumberGenerator &	rng,
		const RandomizationParameter &	parameter
	)

inline

Definition at line 324 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.

◆ 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.

◆ Accumulate()

template<class T >

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

inline

Definition at line 336 of file polynomi.h.

◆ Inverse()

template<class T >

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

inline

Definition at line 339 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.

◆ Reduce()

template<class T >

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

inline

Definition at line 345 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.

◆ 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.

◆ 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.

◆ Square()

template<class T >

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

inline

Definition at line 357 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.

◆ MultiplicativeInverse()

template<class T >

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

inline

Definition at line 363 of file polynomi.h.

◆ 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.

◆ 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

a	the element
b	the modulus

Returns: the result of ab.

Implements AbstractEuclideanDomain< PolynomialOver< T > >.

Definition at line 369 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

r	the remainder
q	the quotient
a	the dividend
d	the divisor

Implements AbstractEuclideanDomain< PolynomialOver< T > >.

Definition at line 372 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.

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

Classes

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ CoefficientRing

◆ Element

◆ CoefficientType

◆ RandomizationParameter

Constructor & Destructor Documentation

◆ RingOfPolynomialsOver()

Member Function Documentation

◆ RandomElement()

◆ Equal()

◆ Identity()

◆ Add()

◆ Accumulate()

◆ Inverse()

◆ Subtract()

◆ Reduce()

◆ Double()

◆ MultiplicativeIdentity()

◆ Multiply()

◆ Square()

◆ IsUnit()

◆ MultiplicativeInverse()

◆ Divide()

◆ Mod()

◆ DivisionAlgorithm()

◆ Interpolate()

◆ InterpolateAt()