Package cc.redberry.rings.poly.univar

Class IrreduciblePolynomials

java.lang.Object

cc.redberry.rings.poly.univar.IrreduciblePolynomials

public final class IrreduciblePolynomials
extends Object

Irreducibility tests and generators for random irreducible polynomials.

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static <Poly extends IUnivariatePolynomial<Poly>> boolean	finiteFieldIrreducibleBenOr(Poly poly)	Tests whether poly is irreducible over the finite field
static <Poly extends IUnivariatePolynomial<Poly>> boolean	finiteFieldIrreducibleQ(Poly poly)	Tests whether poly is irreducible over the finite field
static <Poly extends IUnivariatePolynomial<Poly>> boolean	finiteFieldIrreducibleViaModularComposition(Poly poly)	Tests whether poly is irreducible over the finite field
static <Poly extends IUnivariatePolynomial<Poly>> boolean	irreducibleQ(Poly poly)	Tests whether poly is irreducible
static UnivariatePolynomialZp64	randomIrreduciblePolynomial(long modulus, int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible Zp polynomial of degree degree
static <E> UnivariatePolynomial<E>	randomIrreduciblePolynomial(Ring<E> ring, int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible polynomial over specified ring of degree degree
static <Poly extends IUnivariatePolynomial<Poly>> Poly	randomIrreduciblePolynomial(Poly factory, int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible polynomial of degree degree
static UnivariatePolynomial<BigInteger>	randomIrreduciblePolynomialOverZ(int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible polynomial over Z

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

irreducibleQ

public static <Poly extends IUnivariatePolynomial<Poly>> boolean irreducibleQ(Poly poly)

Tests whether poly is irreducible

Parameters:

poly - the polynomial

Returns:

whether poly is an irreducible polynomial

finiteFieldIrreducibleQ

public static <Poly extends IUnivariatePolynomial<Poly>> boolean finiteFieldIrreducibleQ(Poly poly)

Tests whether poly is irreducible over the finite field

Parameters:

poly - the polynomial over finite field

Returns:

whether poly is an irreducible polynomial

finiteFieldIrreducibleViaModularComposition

public static <Poly extends IUnivariatePolynomial<Poly>> boolean finiteFieldIrreducibleViaModularComposition(Poly poly)

Tests whether poly is irreducible over the finite field

Parameters:

poly - the polynomial over finite field

Returns:

whether poly is an irreducible polynomial

finiteFieldIrreducibleBenOr

public static <Poly extends IUnivariatePolynomial<Poly>> boolean finiteFieldIrreducibleBenOr(Poly poly)

Tests whether poly is irreducible over the finite field

Parameters:

poly - the polynomial over finite field

Returns:

whether poly is an irreducible polynomial

randomIrreduciblePolynomial

public static UnivariatePolynomialZp64 randomIrreduciblePolynomial(long modulus,
                                                                   int degree,
                                                                   org.apache.commons.math3.random.RandomGenerator rnd)

Generated random irreducible Zp polynomial of degree degree

Parameters:

modulus - the modulus

degree - the degree

rnd - random source

Returns:

irreducible polynomial

randomIrreduciblePolynomial

public static <E> UnivariatePolynomial<E> randomIrreduciblePolynomial(Ring<E> ring,
                                                                      int degree,
                                                                      org.apache.commons.math3.random.RandomGenerator rnd)

Generated random irreducible polynomial over specified ring of degree degree

Parameters:

ring - coefficient ring

degree - the degree

rnd - random source

Returns:

irreducible polynomial

randomIrreduciblePolynomialOverZ

public static UnivariatePolynomial<BigInteger> randomIrreduciblePolynomialOverZ(int degree,
                                                                                org.apache.commons.math3.random.RandomGenerator rnd)

Generated random irreducible polynomial over Z

Parameters:

degree - the degree

rnd - random source

Returns:

irreducible polynomial over Z

randomIrreduciblePolynomial

public static <Poly extends IUnivariatePolynomial<Poly>> Poly randomIrreduciblePolynomial(Poly factory,
                                                                                          int degree,
                                                                                          org.apache.commons.math3.random.RandomGenerator rnd)

Generated random irreducible polynomial of degree degree

Parameters:

factory - type marker

degree - the degree

rnd - random source

Returns:

irreducible polynomial