Package dk.jonaslindstrom.ruffini.finitefields

Class FiniteField

java.lang.Object

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

dk.jonaslindstrom.ruffini.finitefields.FiniteField

All Implemented Interfaces:

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

public class FiniteField
extends QuotientRing<Polynomial<Integer>>
implements Field<Polynomial<Integer>>

Field Summary

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

mod, ring

Constructor Summary

Constructors

Constructor	Description
FiniteField(int p, int n)	Create a new finite field of order pn using default representation.
FiniteField(PrimeField baseField, Polynomial<Integer> mod)	Create a finite field as a field of prime order module an irreducible polynomial.

Method Summary

Modifier and Type	Method	Description
Polynomial<Integer>	createElement(Integer... c)
Polynomial<Integer>	element(Integer... coefficients)
int	getExponent()
int	getPrime()
Polynomial<Integer>	invert(Polynomial<Integer> a)	Return the inverse a-1.
String	toString()

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

add, equals, 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.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, toString

Constructor Details

FiniteField

public FiniteField(int p,
 int n)

Create a new finite field of order pⁿ using default representation.

FiniteField

public FiniteField(PrimeField baseField,
 Polynomial<Integer> mod)

Create a finite field as a field of prime order module an irreducible polynomial.

Method Details

element

public Polynomial<Integer> element(Integer... coefficients)

invert

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

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<Polynomial<Integer>>

toString

public String toString()

Overrides:

toString in class QuotientRing<Polynomial<Integer>>

getPrime

public int getPrime()

getExponent

public int getExponent()

createElement

public Polynomial<Integer> createElement(Integer... c)