edu.jas.ufd

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>, java.io.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 and Description
protected GreatestCommonDivisorAbstract<MOD>	mengine Gcd engine for modular base coefficients.
protected FactorAbstract<MOD>	mfactor Factorization engine for modular base coefficients.

Fields inherited from class edu.jas.ufd.FactorAbstract

engine, sengine

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
java.util.List<GenPolynomial<BigInteger>>	baseFactorsSquarefree(GenPolynomial<BigInteger> P) GenPolynomial base factorization of a squarefree polynomial.
static <C extends RingElem<C>> long	degreeSum(java.util.List<GenPolynomial<C>> L) Sum of all degrees.
java.util.BitSet	factorDegrees(java.util.List<ExpVector> E, int deg) BitSet for factor degree list.
java.util.List<GenPolynomial<BigInteger>>	factorsSquarefree(GenPolynomial<BigInteger> P) GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting if possible.
java.util.List<GenPolynomial<BigInteger>>	factorsSquarefreeHensel(GenPolynomial<BigInteger> P) GenPolynomial factorization of a multivariate squarefree polynomial, using Hensel lifting.
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 edu.jas.ufd.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 java.lang.Object

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

Field Detail

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 Detail

FactorInteger

public FactorInteger()

No argument constructor.

FactorInteger

public FactorInteger(RingFactory<BigInteger> cfac)

Constructor.

Parameters:

cfac - coefficient ring factory.

Method Detail

isIrreducible

public boolean isIrreducible(GenPolynomial<BigInteger> P)

GenPolynomial test if is irreducible.

Specified by:

isIrreducible in interface Factorization<BigInteger>

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 java.util.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 java.util.BitSet factorDegrees(java.util.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(java.util.List<GenPolynomial<C>> L)

Sum of all degrees.

Parameters:

L - univariate polynomial list.

Returns:

sum deg(p) for p in L.

factorsSquarefree

public java.util.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<BigInteger>

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.

factorsSquarefreeHensel

public java.util.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.