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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
private static final org.apache.logging.log4j.Logger	logger

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor	Description
private	FactorModular()	No argument constructor, do not use.
	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, removeOnce, squarefreeFactors, squarefreePart

Methods inherited from class Object

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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

Constructor Details

FactorModular

private FactorModular()

No argument constructor, do not use.

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.