Package dk.jonaslindstrom.ruffini.polynomials.structures

Class PolynomialRingFFT<E>

java.lang.Object

dk.jonaslindstrom.ruffini.polynomials.structures.PolynomialRingFFT<E>

All Implemented Interfaces:

AdditiveGroup<PolynomialRingFFT<E>.TransformedPolynomial>, CommutativeMonoid<PolynomialRingFFT<E>.TransformedPolynomial>, Monoid<PolynomialRingFFT<E>.TransformedPolynomial>, Ring<PolynomialRingFFT<E>.TransformedPolynomial>, Semigroup<PolynomialRingFFT<E>.TransformedPolynomial>, SemiRing<PolynomialRingFFT<E>.TransformedPolynomial>, Set<PolynomialRingFFT<E>.TransformedPolynomial>

public class PolynomialRingFFT<E>
extends Object
implements Ring<PolynomialRingFFT<E>.TransformedPolynomial>

This class implements the ring of polynomials K[x] over a field K.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
class	PolynomialRingFFT.TransformedPolynomial

Constructor Summary

Constructors

Constructor	Description
PolynomialRingFFT(Field<E> field, E rootOfUnity, int n)

Method Summary

Modifier and Type	Method	Description
PolynomialRingFFT<E>.TransformedPolynomial	add(PolynomialRingFFT<E>.TransformedPolynomial a, PolynomialRingFFT<E>.TransformedPolynomial b)	Return the result of a+b.
boolean	equals(PolynomialRingFFT<E>.TransformedPolynomial a, PolynomialRingFFT<E>.TransformedPolynomial b)	Returns true if and only if a = b as elements of this set.
PolynomialRingFFT<E>.TransformedPolynomial	fromConstant(E a)
PolynomialRingFFT<E>.TransformedPolynomial	fromFourierCoefficients(Vector<E> a)
PolynomialRingFFT<E>.TransformedPolynomial	fromPolynomial(Polynomial<E> a)
Field<E>	getField()
PolynomialRingFFT<E>.TransformedPolynomial	identity()	Return the identity element of this monoid.
PolynomialRingFFT<E>.TransformedPolynomial	monomial(int m)	Transformation of x^m
PolynomialRingFFT<E>.TransformedPolynomial	multiply(PolynomialRingFFT<E>.TransformedPolynomial a, PolynomialRingFFT<E>.TransformedPolynomial b)	Return the result of the product ab in this group.
PolynomialRingFFT<E>.TransformedPolynomial	negate(PolynomialRingFFT<E>.TransformedPolynomial a)	Return -a.
PolynomialRingFFT<E>.TransformedPolynomial	scale(PolynomialRingFFT<E>.TransformedPolynomial a, E b)
Polynomial<E>	toPolynomial(PolynomialRingFFT<E>.TransformedPolynomial a)
String	toString(PolynomialRingFFT<E>.TransformedPolynomial a)	Returns a human-readable string representation of an element in this set.
PolynomialRingFFT<E>.TransformedPolynomial	zero()	Return the zero element.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.AdditiveGroup

doubling, isZero, scale, scale, subtract, sum

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.CommutativeMonoid

add, add

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Monoid

isIdentity, power

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Semigroup

multiply, multiply

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.SemiRing

integer, multiply, multiply

Constructor Details

PolynomialRingFFT

public PolynomialRingFFT(Field<E> field,
 E rootOfUnity,
 int n)

Method Details

getField

public Field<E> getField()

monomial

public PolynomialRingFFT<E>.TransformedPolynomial monomial(int m)

Transformation of x^m

fromConstant

public PolynomialRingFFT<E>.TransformedPolynomial fromConstant(E a)

scale

public PolynomialRingFFT<E>.TransformedPolynomial scale(PolynomialRingFFT<E>.TransformedPolynomial a,
 E b)

fromPolynomial

public PolynomialRingFFT<E>.TransformedPolynomial fromPolynomial(Polynomial<E> a)

fromFourierCoefficients

public PolynomialRingFFT<E>.TransformedPolynomial fromFourierCoefficients(Vector<E> a)

toPolynomial

public Polynomial<E> toPolynomial(PolynomialRingFFT<E>.TransformedPolynomial a)

negate

public PolynomialRingFFT<E>.TransformedPolynomial negate(PolynomialRingFFT<E>.TransformedPolynomial a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

add

public PolynomialRingFFT<E>.TransformedPolynomial add(PolynomialRingFFT<E>.TransformedPolynomial a,
 PolynomialRingFFT<E>.TransformedPolynomial b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

zero

public PolynomialRingFFT<E>.TransformedPolynomial zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

identity

public PolynomialRingFFT<E>.TransformedPolynomial identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<E>

multiply

public PolynomialRingFFT<E>.TransformedPolynomial multiply(PolynomialRingFFT<E>.TransformedPolynomial a,
 PolynomialRingFFT<E>.TransformedPolynomial b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<E>

toString

public String toString(PolynomialRingFFT<E>.TransformedPolynomial a)

Description copied from interface: Set

Returns a human-readable string representation of an element in this set.

Specified by:

toString in interface Set<E>

equals

public boolean equals(PolynomialRingFFT<E>.TransformedPolynomial a,
 PolynomialRingFFT<E>.TransformedPolynomial b)

Description copied from interface: Set

Returns true if and only if a = b as elements of this set.

Specified by:

equals in interface Set<E>