Package dk.jonaslindstrom.ruffini.polynomials.structures

Class PolynomialRingOverRing<E>

java.lang.Object

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

All Implemented Interfaces:

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

Direct Known Subclasses:

PolynomialRing

public class PolynomialRingOverRing<E>
extends Object
implements Ring<Polynomial<E>>

Constructor Summary

Constructors

Constructor	Description
PolynomialRingOverRing(Ring<E> ring)
PolynomialRingOverRing(Ring<E> ring, String variable)

Method Summary

Modifier and Type	Method	Description
Polynomial<E>	add(Polynomial<E> a, Polynomial<E> b)	Return the result of a+b.
Pair<Polynomial<E>,Polynomial<E>>	divisionWithRemainder(Polynomial<E> a, Polynomial<E> b)	Perform polynomial division, eg.
Pair<Polynomial<E>,Polynomial<E>>	divisionWithRemainder(Polynomial<E> a, Polynomial<E> b, E bLeadInverse)	Perform polynomial division, eg.
final Polynomial<E>	element(E... coefficients)
boolean	equals(Polynomial<E> a, Polynomial<E> b)	Returns true if and only if a = b as elements of this set.
Ring<E>	getRing()
Polynomial<E>	identity()	Return the identity element of this monoid.
Polynomial<E>	multiply(Polynomial<E> a, Polynomial<E> b)	Return the result of the product ab in this group.
Polynomial<E>	multiply(E a, Polynomial<E> b)
Polynomial<E>	negate(Polynomial<E> a)	Return -a.
String	toString()
String	toString(Polynomial<E> a)	Returns a human-readable string representation of an element in this set.
Polynomial<E>	zero()	Return the zero element.

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.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

PolynomialRingOverRing

public PolynomialRingOverRing(Ring<E> ring)

PolynomialRingOverRing

public PolynomialRingOverRing(Ring<E> ring,
 String variable)

Method Details

getRing

public Ring<E> getRing()

element

@SafeVarargs
public final Polynomial<E> element(E... coefficients)

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>

multiply

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

identity

public Polynomial<E> identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<E>

toString

public String toString(Polynomial<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>

add

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

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

negate

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

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

zero

public Polynomial<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

equals

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

divisionWithRemainder

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

Perform polynomial division, eg. finding a quotient q and a remainder r with degree smaller than the divisor b s.t. a = qb + r.

Parameters:

a - The dividend.

b - The divisor. It is assumed that this is a monic polynomial.

divisionWithRemainder

public Pair<Polynomial<E>,Polynomial<E>> divisionWithRemainder(Polynomial<E> a,
 Polynomial<E> b,
 E bLeadInverse)

Perform polynomial division, eg. finding a quotient q and a remainder r with degree smaller than b s.t. a = qb + r.

Parameters:

a - The dividend.

b - The divisor.

bLeadInverse - An inverse of the leading coefficient of b.

toString

public String toString()

Overrides:

toString in class Object