Class FactorComplex<C extends GcdRingElem<C>>

java.lang.Object

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

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

edu.jas.ufd.FactorComplex<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Factorization<Complex<C>>, Serializable

public class FactorComplex<C extends GcdRingElem<C>>
extends FactorAbsolute<Complex<C>>

Complex coefficients factorization algorithms. This class implements factorization methods for polynomials over Complex numbers via the algebraic number C(i) over rational numbers or over (prime) modular integers. Note: Decomposition to linear factors is only via absolute factorization since Complex are not the analytic complex numbers.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final AlgebraicNumberRing<C>	afac	Complex algebraic factory.
final FactorAbstract<AlgebraicNumber<C>>	factorAlgeb	Factorization engine for algebraic coefficients.

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FactorComplex()	No argument constructor.
	FactorComplex(ComplexRing<C> fac)	Constructor.
	FactorComplex(ComplexRing<C> fac, FactorAbstract<AlgebraicNumber<C>> factorAlgeb)	Constructor.
	FactorComplex(RingFactory<Complex<C>> fac)	Constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<Complex<C>>>	baseFactorsSquarefree(GenPolynomial<Complex<C>> P)	GenPolynomial base factorization of a squarefree polynomial.
List<GenPolynomial<Complex<C>>>	factorsSquarefree(GenPolynomial<Complex<C>> P)	GenPolynomial 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, 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

factorAlgeb

public final FactorAbstract<AlgebraicNumber<C extends GcdRingElem<C>>> factorAlgeb

Factorization engine for algebraic coefficients.

afac

public final AlgebraicNumberRing<C extends GcdRingElem<C>> afac

Complex algebraic factory.

Constructor Details

FactorComplex

protected FactorComplex()

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

FactorComplex

public FactorComplex(RingFactory<Complex<C>> fac)

Constructor.

Parameters:

fac - complex number factory.

FactorComplex

public FactorComplex(ComplexRing<C> fac)

Constructor.

Parameters:

fac - complex number factory.

FactorComplex

public FactorComplex(ComplexRing<C> fac,
 FactorAbstract<AlgebraicNumber<C>> factorAlgeb)

Constructor.

Parameters:

fac - complex number factory.

factorAlgeb - factorization engine for polynomials over algebraic coefficients.

Method Details

baseFactorsSquarefree

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

GenPolynomial base factorization of a squarefree polynomial.

Specified by:

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

Parameters:

P - squarefree GenPolynomial<AlgebraicNumber<C>>.

Returns:

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

factorsSquarefree

public List<GenPolynomial<Complex<C>>> factorsSquarefree(GenPolynomial<Complex<C>> P)

GenPolynomial factorization of a squarefree polynomial.

Specified by:

factorsSquarefree in interface Factorization<C extends GcdRingElem<C>>

Overrides:

factorsSquarefree in class FactorAbstract<Complex<C extends GcdRingElem<C>>>

Parameters:

P - squarefree GenPolynomial<AlgebraicNumber<C>>.

Returns:

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