Class FactorAlgebraicPrim<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.FactorAbstract<AlgebraicNumber<C>>

edu.jas.ufd.FactorAbsolute<AlgebraicNumber<C>>

edu.jas.application.FactorAlgebraicPrim<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Factorization<AlgebraicNumber<C>>, Serializable

public class FactorAlgebraicPrim<C extends GcdRingElem<C>>
extends FactorAbsolute<AlgebraicNumber<C>>

Algebraic number coefficients factorization algorithms. This class implements factorization methods for polynomials over algebraic numbers over rational numbers or over (prime) modular integers. The algorithm uses zero dimensional ideal prime decomposition.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final FactorAbstract<C>	factorCoeff	Factorization engine for base coefficients.

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FactorAlgebraicPrim()	No argument constructor.
	FactorAlgebraicPrim(AlgebraicNumberRing<C> fac)	Constructor.
	FactorAlgebraicPrim(AlgebraicNumberRing<C> fac, FactorAbstract<C> factorCoeff)	Constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<AlgebraicNumber<C>>>	baseFactorsSquarefree(GenPolynomial<AlgebraicNumber<C>> 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

Field Details

factorCoeff

public final FactorAbstract<C extends GcdRingElem<C>> factorCoeff

Factorization engine for base coefficients.

Constructor Details

FactorAlgebraicPrim

protected FactorAlgebraicPrim()

No argument constructor. Note: can't use this constructor.

FactorAlgebraicPrim

public FactorAlgebraicPrim(AlgebraicNumberRing<C> fac)

Constructor.

Parameters:

fac - algebraic number factory.

FactorAlgebraicPrim

public FactorAlgebraicPrim(AlgebraicNumberRing<C> fac,
 FactorAbstract<C> factorCoeff)

Constructor.

Parameters:

fac - algebraic number factory.

factorCoeff - factorization engine for polynomials over base coefficients.

Method Details

baseFactorsSquarefree

public List<GenPolynomial<AlgebraicNumber<C>>> baseFactorsSquarefree(GenPolynomial<AlgebraicNumber<C>> P)

GenPolynomial base factorization of a squarefree polynomial.

Specified by:

baseFactorsSquarefree in class FactorAbstract<AlgebraicNumber<C extends GcdRingElem<C>>>

Parameters:

P - squarefree GenPolynomial<AlgebraicNumber<C>>.

Returns:

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