Package dk.jonaslindstrom.ruffini.polynomials.structures

Class PolynomialRingKaratsuba<E>

java.lang.Object

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

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

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

All Implemented Interfaces:

AdditiveGroup<Polynomial<E>>, CommutativeMonoid<Polynomial<E>>, EuclideanDomain<Polynomial<E>>, Monoid<Polynomial<E>>, Ring<Polynomial<E>>, Semigroup<Polynomial<E>>, SemiRing<Polynomial<E>>, Set<Polynomial<E>>

public class PolynomialRingKaratsuba<E>
extends PolynomialRing<E>

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

Field Summary

Fields inherited from class dk.jonaslindstrom.ruffini.polynomials.structures.PolynomialRing

field

Constructor Summary

Constructors

Constructor	Description
PolynomialRingKaratsuba(Field<E> field)

Method Summary

Modifier and Type	Method	Description
Pair<Polynomial<E>,Polynomial<E>>	divide(Polynomial<E> a, Polynomial<E> b)	Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see EuclideanDomain.norm(E) for this domain.
Polynomial<E>	multiply(Polynomial<E> a, Polynomial<E> b)	Return the result of the product ab in this group.

Methods inherited from class dk.jonaslindstrom.ruffini.polynomials.structures.PolynomialRing

getBaseField, norm, toString

Methods inherited from class dk.jonaslindstrom.ruffini.polynomials.structures.PolynomialRingOverRing

add, divisionWithRemainder, divisionWithRemainder, element, equals, getRing, identity, multiply, negate, toString, zero

Methods inherited from class java.lang.Object

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

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

doubling, isZero, negate, scale, scale, subtract, sum

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

add, add, add, zero

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

abs, divide, divideExact, divideExact, divides, mod, mod

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

identity, 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

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

equals, toString

Constructor Details

PolynomialRingKaratsuba

public PolynomialRingKaratsuba(Field<E> field)

Method Details

multiply

public Polynomial<E> multiply(Polynomial<E> a,
 Polynomial<E> b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<E>

Overrides:

multiply in class PolynomialRingOverRing<E>

divide

public Pair<Polynomial<E>,Polynomial<E>> divide(Polynomial<E> a,
 Polynomial<E> b)

Description copied from interface: EuclideanDomain

Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see EuclideanDomain.norm(E) for this domain.

Specified by:

divide in interface EuclideanDomain<E>

Overrides:

divide in class PolynomialRing<E>