Class FactorAlgebraic<C extends GcdRingElem<C>>

java.lang.Object

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

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

edu.jas.ufd.FactorAlgebraic<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Factorization<AlgebraicNumber<C>>, 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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
final FactorAbstract<C>	factorCoeff	Factorization engine for base coefficients.
private static final org.apache.logging.log4j.Logger	logger

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor	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	Description
List<GenPolynomial<AlgebraicNumber<C>>>	baseFactorsSquarefree(GenPolynomial<AlgebraicNumber<C>> P)	GenPolynomial base factorization of a squarefree polynomial.
List<GenPolynomial<AlgebraicNumber<C>>>	factorsSquarefree(GenPolynomial<AlgebraicNumber<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, 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

factorCoeff

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

Factorization engine for base coefficients.

Constructor Details

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 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.

factorsSquarefree

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

GenPolynomial factorization of a squarefree polynomial.

Specified by:

factorsSquarefree in interface Factorization<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.