Package dk.jonaslindstrom.ruffini.finitefields

Class AlgebraicFieldExtension<E,F extends Field<E>>

java.lang.Object

dk.jonaslindstrom.ruffini.common.structures.QuotientRing<Polynomial<E>>

dk.jonaslindstrom.ruffini.finitefields.AlgebraicFieldExtension<E,F>

All Implemented Interfaces:

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

Direct Known Subclasses:

GaussianRationals, QuadraticField

public class AlgebraicFieldExtension<E,F extends Field<E>>
extends QuotientRing<Polynomial<E>>
implements Field<Polynomial<E>>

Field Summary

Fields inherited from class dk.jonaslindstrom.ruffini.common.structures.QuotientRing

mod, ring

Constructor Summary

Constructors

Constructor	Description
AlgebraicFieldExtension(F field, String element, Polynomial<E> minimalPolynomial)

Method Summary

Modifier and Type	Method	Description
Polynomial<E>	embed(E value)
F	getBaseField()
Polynomial<E>	invert(Polynomial<E> a)	Return the inverse a-1.
String	toString()
String	toString(Polynomial<E> p)	Returns a human-readable string representation of an element in this set.

Methods inherited from class dk.jonaslindstrom.ruffini.common.structures.QuotientRing

add, equals, identity, multiply, negate, 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.Field

divideInt

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

divide

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

Constructor Details

AlgebraicFieldExtension

public AlgebraicFieldExtension(F field,
 String element,
 Polynomial<E> minimalPolynomial)

Method Details

invert

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

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<E>

getBaseField

public F getBaseField()

embed

public Polynomial<E> embed(E value)

toString

public String toString(Polynomial<E> p)

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 QuotientRing<Polynomial<E>>

toString

public String toString()

Overrides:

toString in class QuotientRing<Polynomial<E>>