Package edu.jas.ufd

Class FactorFraction<C extends GcdRingElem<C>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>>

java.lang.Object

edu.jas.ufd.FactorFraction<C,D>

public class FactorFraction<C extends GcdRingElem<C>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>>
extends java.lang.Object

Fraction factorization algorithms. This class implements factorization methods for fractions represended as pairs of polynomials.

Author:

Heinz Kredel

Field Summary

Fields

Modifier and Type	Field	Description
protected FactorAbstract<C>	nengine	Factorization engine for normal coefficients.
protected QuotPairFactory<GenPolynomial<C>,D>	qfac	Quotient pairs ring factory.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FactorFraction()	No argument constructor.
	FactorFraction(QuotPairFactory<GenPolynomial<C>,D> fac)	Constructor.
	FactorFraction(QuotPairFactory<GenPolynomial<C>,D> fac, FactorAbstract<C> nengine)	Constructor.

Method Summary

Modifier and Type	Method	Description
java.util.SortedMap<D,java.lang.Long>	factors(D P)	Quotient pair factorization.
boolean	isFactorization(D P, java.util.SortedMap<D,java.lang.Long> F)	Test quotient pair factorization.
boolean	isIrreducible(D P)	Test if a quotient pair is irreducible.
boolean	isReducible(D P)	Test if a non trivial factorization exists.
java.lang.String	toString()	Get the String representation.

Methods inherited from class java.lang.Object

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

Field Detail

qfac

protected final QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>> qfac

Quotient pairs ring factory. D == QuotPair<GenPolynomial<C>> must hold.

nengine

protected final FactorAbstract<C extends GcdRingElem<C>> nengine

Factorization engine for normal coefficients.

Constructor Detail

FactorFraction

protected FactorFraction()

No argument constructor.

FactorFraction

public FactorFraction(QuotPairFactory<GenPolynomial<C>,D> fac)

Constructor.

Parameters:

fac - coefficient quotient ring factory.

FactorFraction

public FactorFraction(QuotPairFactory<GenPolynomial<C>,D> fac,
                      FactorAbstract<C> nengine)

Constructor.

Parameters:

fac - coefficient quotient ring factory.

nengine - factorization engine for polynomials over base coefficients.

Method Detail

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

isIrreducible

public boolean isIrreducible(D P)

Test if a quotient pair is irreducible.

Parameters:

P - quotient pair (num,den), with gcd(num,den) == 1.

Returns:

true if P is irreducible, else false.

isReducible

public boolean isReducible(D P)

Test if a non trivial factorization exists.

Parameters:

P - quotient pair (num,den), with gcd(num,den) == 1.

Returns:

true if P is reducible, else false.

factors

public java.util.SortedMap<D,java.lang.Long> factors(D P)

Quotient pair factorization.

Parameters:

P - quotient pair (num,den), with gcd(num,den) == 1.

Returns:

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

isFactorization

public boolean isFactorization(D P,
                               java.util.SortedMap<D,java.lang.Long> F)

Test quotient pair factorization.

Parameters:

P - quotient pair.

F - = [p_1 -> e_1, ..., p_k -> e_k].

Returns:

true if P = prod_{i=1,...,k} p_i**e_i, else false.