Class FactorRational

java.lang.Object

edu.jas.ufd.FactorAbstract<BigRational>

edu.jas.ufd.FactorAbsolute<BigRational>

edu.jas.ufd.FactorRational

All Implemented Interfaces:

Factorization<BigRational>, Serializable

public class FactorRational
extends FactorAbsolute<BigRational>

Rational number coefficients factorization algorithms. This class implements factorization methods for polynomials over rational numbers.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final FactorAbstract<BigInteger>	iengine	Factorization engine for integer base coefficients.

Fields inherited from class FactorAbstract

engine, sengine

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FactorRational()	No argument constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<BigRational>>	baseFactorsSquarefree(GenPolynomial<BigRational> P)	GenPolynomial base factorization of a squarefree polynomial.
SortedMap<GenPolynomial<BigRational>, Long>	factors(GenPolynomial<BigRational> P)	GenPolynomial factorization of a polynomial.
List<GenPolynomial<BigRational>>	factorsSquarefree(GenPolynomial<BigRational> 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, 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

iengine

protected final FactorAbstract<BigInteger> iengine

Factorization engine for integer base coefficients.

Constructor Details

FactorRational

protected FactorRational()

No argument constructor.

Method Details

baseFactorsSquarefree

public List<GenPolynomial<BigRational>> baseFactorsSquarefree(GenPolynomial<BigRational> P)

GenPolynomial base factorization of a squarefree polynomial.

Specified by:

baseFactorsSquarefree in class FactorAbstract<BigRational>

Parameters:

P - squarefree GenPolynomial.

Returns:

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

factorsSquarefree

public List<GenPolynomial<BigRational>> factorsSquarefree(GenPolynomial<BigRational> P)

GenPolynomial factorization of a squarefree polynomial.

Specified by:

factorsSquarefree in interface Factorization<BigRational>

Overrides:

factorsSquarefree in class FactorAbstract<BigRational>

Parameters:

P - squarefree GenPolynomial.

Returns:

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

factors

public SortedMap<GenPolynomial<BigRational>, Long> factors(GenPolynomial<BigRational> P)

GenPolynomial factorization of a polynomial.

Specified by:

factors in interface Factorization<BigRational>

Overrides:

factors in class FactorAbstract<BigRational>

Parameters:

P - GenPolynomial.

Returns:

[p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i**e_i and p_i irreducible.