edu.jas.ufd

Class FactorComplex<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.FactorAbstract<C>

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

edu.jas.ufd.FactorComplex<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Factorization<Complex<C>>, java.io.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 and Description
AlgebraicNumberRing<C>	afac Complex algebraic factory.
FactorAbstract<AlgebraicNumber<C>>	factorAlgeb Factorization engine for algebraic coefficients.

Fields inherited from class edu.jas.ufd.FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor and 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

Methods

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

Methods inherited from class edu.jas.ufd.FactorAbsolute

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

Methods inherited from class edu.jas.ufd.FactorAbstract

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

Methods inherited from class java.lang.Object

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

Field Detail

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 Detail

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 Detail

baseFactorsSquarefree

public java.util.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.