Package dk.jonaslindstrom.ruffini.polynomials.structures

Class PolynomialRing<E>

java.lang.Object

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

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

Direct Known Subclasses:

PolynomialRingKaratsuba

public class PolynomialRing<E>
extends PolynomialRingOverRing<E>
implements EuclideanDomain<Polynomial<E>>

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

Field Summary

Fields

Modifier and Type	Field	Description
protected final Field<E>	field

Constructor Summary

Constructors

Constructor	Description
PolynomialRing(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.
Field<E>	getBaseField()
BigInteger	norm(Polynomial<E> a)	The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of EuclideanDomain.divide(E, E).
String	toString()

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

add, divisionWithRemainder, divisionWithRemainder, element, equals, getRing, identity, multiply, 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, 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

Field Details

field

protected final Field<E> field

Constructor Details

PolynomialRing

public PolynomialRing(Field<E> field)

Method Details

getBaseField

public Field<E> getBaseField()

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>

norm

public BigInteger norm(Polynomial<E> a)

Description copied from interface: EuclideanDomain

The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of EuclideanDomain.divide(E, E).

Specified by:

norm in interface EuclideanDomain<E>

toString

public String toString()

Overrides:

toString in class PolynomialRingOverRing<E>