Package dk.jonaslindstrom.ruffini.polynomials.structures

Class MultivariatePolynomialRing<E>

java.lang.Object

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

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

All Implemented Interfaces:

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

public class MultivariatePolynomialRing<E>
extends MultivariatePolynomialRingOverRing<E>
implements EuclideanDomain<MultivariatePolynomial<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.MultivariatePolynomialRingOverRing

variables

Constructor Summary

Constructors

Constructor	Description
MultivariatePolynomialRing(Field<E> field, int variables)
MultivariatePolynomialRing(Field<E> field, int variables, Comparator<Monomial> ordering)

Method Summary

Modifier and Type	Method	Description
MultivariatePolynomial<E>	add(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)	Return the result of a+b.
Pair<MultivariatePolynomial<E>,MultivariatePolynomial<E>>	divide(MultivariatePolynomial<E> a, MultivariatePolynomial<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.
boolean	equals(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)	Returns true if and only if a = b as elements of this set.
Field<E>	getField()
MultivariatePolynomial<E>	identity()	Return the identity element of this monoid.
MultivariatePolynomial<E>	multiply(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)	Return the result of the product ab in this group.
MultivariatePolynomial<E>	negate(MultivariatePolynomial<E> a)	Return -a.
BigInteger	norm(MultivariatePolynomial<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()
String	toString(MultivariatePolynomial<E> a)	Returns a human-readable string representation of an element in this set.
MultivariatePolynomial<E>	zero()	Return the zero element.

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

getRing

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, 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.EuclideanDomain

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

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

MultivariatePolynomialRing

public MultivariatePolynomialRing(Field<E> field,
 int variables,
 Comparator<Monomial> ordering)

MultivariatePolynomialRing

public MultivariatePolynomialRing(Field<E> field,
 int variables)

Method Details

getField

public Field<E> getField()

toString

public String toString()

Overrides:

toString in class MultivariatePolynomialRingOverRing<E>

identity

public MultivariatePolynomial<E> identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<E>

Overrides:

identity in class MultivariatePolynomialRingOverRing<E>

multiply

public MultivariatePolynomial<E> multiply(MultivariatePolynomial<E> a,
 MultivariatePolynomial<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 MultivariatePolynomialRingOverRing<E>

toString

public String toString(MultivariatePolynomial<E> 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>

Overrides:

toString in class MultivariatePolynomialRingOverRing<E>

equals

public boolean equals(MultivariatePolynomial<E> a,
 MultivariatePolynomial<E> 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>

Overrides:

equals in class MultivariatePolynomialRingOverRing<E>

add

public MultivariatePolynomial<E> add(MultivariatePolynomial<E> a,
 MultivariatePolynomial<E> b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

Overrides:

add in class MultivariatePolynomialRingOverRing<E>

negate

public MultivariatePolynomial<E> negate(MultivariatePolynomial<E> a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

Overrides:

negate in class MultivariatePolynomialRingOverRing<E>

zero

public MultivariatePolynomial<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

Overrides:

zero in class MultivariatePolynomialRingOverRing<E>

divide

public Pair<MultivariatePolynomial<E>,MultivariatePolynomial<E>> divide(MultivariatePolynomial<E> a,
 MultivariatePolynomial<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(MultivariatePolynomial<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>