edu.jas.ufd

Class FactorAlgebraic<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.FactorAbstract<C>

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

edu.jas.ufd.FactorAlgebraic<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Factorization<AlgebraicNumber<C>>, java.io.Serializable

public class FactorAlgebraic<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.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

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

Fields inherited from class edu.jas.ufd.FactorAbstract

engine, sengine

Constructor Summary

Constructors

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

Method Summary

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

Methods inherited from class edu.jas.ufd.FactorAbsolute

baseAlgebraicPartialFraction, 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, factorsSquarefreeKronecker, factorsSquarefreeOptimize, 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

factorCoeff

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

Factorization engine for base coefficients.

Constructor Detail

FactorAlgebraic

protected FactorAlgebraic()

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

FactorAlgebraic

public FactorAlgebraic(AlgebraicNumberRing<C> fac)

Constructor.

Parameters:

fac - algebraic number factory.

FactorAlgebraic

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

Constructor.

Parameters:

fac - algebraic number factory.

factorCoeff - factorization engine for polynomials over base coefficients.

Method Detail

baseFactorsSquarefree

public java.util.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.

factorsSquarefree

public java.util.List<GenPolynomial<AlgebraicNumber<C>>> factorsSquarefree(GenPolynomial<AlgebraicNumber<C>> P)

GenPolynomial factorization of a squarefree polynomial.

Specified by:

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

Overrides:

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

Parameters:

P - squarefree and primitive! (respectively monic) GenPolynomial<AlgebraicNumber<C>>.

Returns:

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