Class FactorInteger<MOD extends GcdRingElem<MOD> & Modular>

java.lang.Object

edu.jas.ufd.FactorAbstract<BigInteger>

edu.jas.ufd.FactorInteger<MOD>

Type Parameters:

MOD -

All Implemented Interfaces:

Factorization<BigInteger>, Serializable

public class FactorInteger<MOD extends GcdRingElem<MOD> & Modular>
extends FactorAbstract<BigInteger>

Integer coefficients factorization algorithms. This class implements factorization methods for polynomials over integers.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final GreatestCommonDivisorAbstract<MOD>	mengine	Gcd engine for modular base coefficients.
protected final FactorAbstract<MOD>	mfactor	Factorization engine for modular base coefficients.

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Constructor	Description
FactorInteger()	No argument constructor.
FactorInteger(RingFactory<BigInteger> cfac)	Constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<BigInteger>>	baseFactorsSquarefree(GenPolynomial<BigInteger> P)	GenPolynomial base factorization of a squarefree polynomial.
static <C extends RingElem<C>> long	degreeSum(List<GenPolynomial<C>> L)	Sum of all degrees.
BitSet	factorDegrees(List<ExpVector> E, int deg)	BitSet for factor degree list.
List<GenPolynomial<BigInteger>>	factorsSquarefree(GenPolynomial<BigInteger> P)	GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting if possible.
List<GenPolynomial<BigInteger>>	factorsSquarefreeHensel(GenPolynomial<BigInteger> P)	GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting.
List<GenPolynomial<BigInteger>>	factorsSquarefreeOptions(GenPolynomial<BigInteger> P, boolean opti, boolean tlex)	GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting if possible.
boolean	isIrreducible(GenPolynomial<BigInteger> P)	GenPolynomial test if is irreducible.
boolean	isIrreducibleEisenstein(GenPolynomial<BigInteger> P)	GenPolynomial test if is irreducible with Eisenstein criterion.

Methods inherited from class FactorAbstract

baseFactors, baseFactorsRadical, basePrimitivePart, factors, factorsDegree, factorsRadical, factorsRadical, factorsSquarefreeKronecker, factorsSquarefreeOptimize, isFactorization, isFactorization, isRecursiveFactorization, isReducible, isSquarefree, normalizeFactorization, primitivePart, recursiveFactors, recursiveFactorsSquarefree, squarefreeFactors, squarefreePart, toString

Methods inherited from class Object

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

Field Details

mfactor

protected final FactorAbstract<MOD extends GcdRingElem<MOD> & Modular> mfactor

Factorization engine for modular base coefficients.

mengine

protected final GreatestCommonDivisorAbstract<MOD extends GcdRingElem<MOD> & Modular> mengine

Gcd engine for modular base coefficients.

Constructor Details

FactorInteger

public FactorInteger()

No argument constructor.

FactorInteger

public FactorInteger(RingFactory<BigInteger> cfac)

Constructor.

Parameters:

cfac - coefficient ring factory.

Method Details

isIrreducible

public boolean isIrreducible(GenPolynomial<BigInteger> P)

GenPolynomial test if is irreducible.

Specified by:

isIrreducible in interface Factorization<MOD extends GcdRingElem<MOD> & Modular>

Overrides:

isIrreducible in class FactorAbstract<BigInteger>

Parameters:

P - GenPolynomial.

Returns:

true if P is irreducible, else false.

isIrreducibleEisenstein

public boolean isIrreducibleEisenstein(GenPolynomial<BigInteger> P)

GenPolynomial test if is irreducible with Eisenstein criterion.

Parameters:

P - univariate polynomial.

Returns:

true if P is irreducible, else false if it is unknown.

baseFactorsSquarefree

public List<GenPolynomial<BigInteger>> baseFactorsSquarefree(GenPolynomial<BigInteger> P)

GenPolynomial base factorization of a squarefree polynomial.

Specified by:

baseFactorsSquarefree in class FactorAbstract<BigInteger>

Parameters:

P - squarefree and primitive! GenPolynomial.

Returns:

[p_1,...,p_k] with P = prod_{i=1, ..., k} p_i.

factorDegrees

public BitSet factorDegrees(List<ExpVector> E,
 int deg)

BitSet for factor degree list.

Parameters:

E - exponent vector list.

Returns:

{b_0,...,b_k} a BitSet of possible factor degrees.

degreeSum

public static <C extends RingElem<C>> long degreeSum(List<GenPolynomial<C>> L)

Sum of all degrees.

Parameters:

L - univariate polynomial list.

Returns:

sum deg(p) for p in L.

factorsSquarefree

public List<GenPolynomial<BigInteger>> factorsSquarefree(GenPolynomial<BigInteger> P)

GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting if possible.

Specified by:

factorsSquarefree in interface Factorization<MOD extends GcdRingElem<MOD> & Modular>

Overrides:

factorsSquarefree in class FactorAbstract<BigInteger>

Parameters:

P - squarefree and primitive! (respectively monic) multivariate GenPolynomial over the integers.

Returns:

[p_1,...,p_k] with P = prod_{i=1,...,r} p_i.

factorsSquarefreeOptions

public List<GenPolynomial<BigInteger>> factorsSquarefreeOptions(GenPolynomial<BigInteger> P,
 boolean opti,
 boolean tlex)

GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting if possible.

Parameters:

P - squarefree and primitive! (respectively monic) multivariate GenPolynomial over the integers.

opti - true, if polynomial variables should be optimized, else false.

tlex - true, if INVLEX term order should be forced, else false.

Returns:

[p_1,...,p_k] with P = prod_{i=1,...,r} p_i.

factorsSquarefreeHensel

public List<GenPolynomial<BigInteger>> factorsSquarefreeHensel(GenPolynomial<BigInteger> P)

GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting.

Parameters:

P - squarefree and primitive! (respectively monic) multivariate GenPolynomial over the integers.

Returns:

[p_1,...,p_k] with P = prod_{i=1,...,r} p_i.