Package cc.redberry.rings.poly.multivar

Class MultivariateSquareFreeFactorization

java.lang.Object

cc.redberry.rings.poly.multivar.MultivariateSquareFreeFactorization

public final class MultivariateSquareFreeFactorization
extends Object

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> boolean	isSquareFree(Poly poly)	Tests whether the given poly is square free.
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> PolynomialFactorDecomposition<Poly>	SquareFreeFactorization(Poly poly)	Performs square-free factorization of a {@code poly. @param poly the polynomial @return square-free decomposition
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> PolynomialFactorDecomposition<Poly>	SquareFreeFactorizationBernardin(Poly poly)	Performs square-free factorization of a poly over finite field using Bernardin's algorithm (see Factorization of multivariate polynomials over finite fields, 1999, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.5310&rep=rep1&type=pdf).
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> PolynomialFactorDecomposition<Poly>	SquareFreeFactorizationMusserZeroCharacteristics(Poly poly)	Performs square-free factorization of a poly which coefficient ring has zero characteristic using Musser's algorithm.
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> PolynomialFactorDecomposition<Poly>	SquareFreeFactorizationYunZeroCharacteristics(Poly poly)	Performs square-free factorization of a poly which coefficient ring has zero characteristic using Yun's algorithm.
static <Term extends AMonomial<Term>, Poly extends AMultivariatePolynomial<Term, Poly>> Poly	SquareFreePart(Poly poly)	Returns square-free part of the poly

Methods inherited from class java.lang.Object

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

Method Details

SquareFreeFactorization

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
PolynomialFactorDecomposition<Poly> SquareFreeFactorization(Poly poly)

Performs square-free factorization of a {@code poly. @param poly the polynomial @return square-free decomposition

isSquareFree

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
boolean isSquareFree(Poly poly)

Tests whether the given poly is square free.

Parameters:

poly - the polynomial

Returns:

whether the given poly is square free

SquareFreePart

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
Poly SquareFreePart(Poly poly)

Returns square-free part of the poly

Parameters:

poly - the polynomial

Returns:

square free part

SquareFreeFactorizationYunZeroCharacteristics

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
PolynomialFactorDecomposition<Poly> SquareFreeFactorizationYunZeroCharacteristics(Poly poly)

Performs square-free factorization of a poly which coefficient ring has zero characteristic using Yun's algorithm.

Parameters:

poly - the polynomial

Returns:

square-free decomposition

SquareFreeFactorizationMusserZeroCharacteristics

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
PolynomialFactorDecomposition<Poly> SquareFreeFactorizationMusserZeroCharacteristics(Poly poly)

Performs square-free factorization of a poly which coefficient ring has zero characteristic using Musser's algorithm.

Parameters:

poly - the polynomial

Returns:

square-free decomposition

SquareFreeFactorizationBernardin

public static <Term extends AMonomial<Term>,
Poly extends AMultivariatePolynomial<Term,
Poly>>
PolynomialFactorDecomposition<Poly> SquareFreeFactorizationBernardin(Poly poly)

Performs square-free factorization of a poly over finite field using Bernardin's algorithm (see Factorization of multivariate polynomials over finite fields, 1999, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.5310&rep=rep1&type=pdf).

Parameters:

poly - the polynomial

Returns:

square-free decomposition