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

java.lang.Object

edu.jas.ufd.FactorAbstract<MOD>

edu.jas.ufd.FactorAbsolute<MOD>

edu.jas.ufd.FactorModular<MOD>

All Implemented Interfaces:

Factorization<MOD>, Serializable

public class FactorModular<MOD extends GcdRingElem<MOD> & Modular>
extends FactorAbsolute<MOD>

Modular coefficients factorization algorithms. This class implements factorization methods for polynomials over (prime) modular integers.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Constructor	Description
FactorModular(RingFactory<MOD> cfac)	Constructor.

Method Summary

Modifier and Type	Method	Description
SortedMap<Long, GenPolynomial<MOD>>	baseDistinctDegreeFactors(GenPolynomial<MOD> P)	GenPolynomial base distinct degree factorization.
List<GenPolynomial<MOD>>	baseEqualDegreeFactors(GenPolynomial<MOD> P, long deg)	GenPolynomial base equal degree factorization.
List<GenPolynomial<MOD>>	baseFactorsSquarefree(GenPolynomial<MOD> P)	GenPolynomial base factorization of a squarefree polynomial.

Methods inherited from class FactorAbsolute

baseAlgebraicPartialFraction, baseAlgebraicPartialFractionIrreducibleAbsolute, baseFactorsAbsolute, baseFactorsAbsoluteIrreducible, baseFactorsAbsoluteSquarefree, factorsAbsolute, factorsAbsoluteIrreducible, factorsAbsoluteSquarefree, isAbsoluteFactorization, isAbsoluteFactorization, isAbsoluteFactorization, isAbsoluteIrreducible, toString

Methods inherited from class FactorAbstract

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

Methods inherited from class Object

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

Constructor Details

FactorModular

public FactorModular(RingFactory<MOD> cfac)

Constructor.

Parameters:

cfac - coefficient ring factory.

Method Details

baseDistinctDegreeFactors

public SortedMap<Long, GenPolynomial<MOD>> baseDistinctDegreeFactors(GenPolynomial<MOD> P)

GenPolynomial base distinct degree factorization.

Parameters:

P - squarefree and monic GenPolynomial.

Returns:

[e_1 -> p_1, ..., e_k -> p_k] with P = prod_{i=1,...,k} p_i and p_i has only irreducible factors of degree e_i.

baseEqualDegreeFactors

public List<GenPolynomial<MOD>> baseEqualDegreeFactors(GenPolynomial<MOD> P,
 long deg)

GenPolynomial base equal degree factorization.

Parameters:

P - squarefree and monic GenPolynomial.

deg - such that P has only irreducible factors of degree deg.

Returns:

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

baseFactorsSquarefree

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

GenPolynomial base factorization of a squarefree polynomial.

Specified by:

baseFactorsSquarefree in class FactorAbstract<MOD extends GcdRingElem<MOD> & Modular>

Parameters:

P - squarefree and monic! GenPolynomial.

Returns:

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