edu.jas.ufd

Interface Factorization<C extends GcdRingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

FactorAbsolute, FactorAbstract, FactorAlgebraic, FactorAlgebraicPrim, FactorComplex, FactorInteger, FactorModular, FactorQuotient, FactorRational, FactorRealAlgebraic, FactorRealReal

public interface Factorization<C extends GcdRingElem<C>>
extends java.io.Serializable

Factorization algorithms interface.

See Also:

FactorFactory.getImplementation(edu.jas.arith.ModIntegerRing)

Method Summary

Modifier and Type	Method and Description
java.util.SortedMap<GenPolynomial<C>,java.lang.Long>	factors(GenPolynomial<C> P) GenPolynomial factorization.
java.util.List<GenPolynomial<C>>	factorsRadical(GenPolynomial<C> P) GenPolynomial factorization ignoring multiplicities.
java.util.List<GenPolynomial<C>>	factorsSquarefree(GenPolynomial<C> P) GenPolynomial factorization of a squarefree polynomial.
boolean	isFactorization(GenPolynomial<C> P, java.util.List<GenPolynomial<C>> F) GenPolynomial is factorization.
boolean	isFactorization(GenPolynomial<C> P, java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F) GenPolynomial is factorization.
boolean	isIrreducible(GenPolynomial<C> P) GenPolynomial test if is irreducible.
boolean	isReducible(GenPolynomial<C> P) GenPolynomial test if a non trivial factorization exsists.
boolean	isSquarefree(GenPolynomial<C> P) GenPolynomial test if is squarefree.
java.util.SortedMap<GenPolynomial<C>,java.lang.Long>	squarefreeFactors(GenPolynomial<C> P) GenPolynomial squarefree factorization.
GenPolynomial<C>	squarefreePart(GenPolynomial<C> P) GenPolynomial greatest squarefree divisor.

Method Detail

isIrreducible

boolean isIrreducible(GenPolynomial<C> P)

GenPolynomial test if is irreducible.

Parameters:

P - GenPolynomial.

Returns:

true if P is irreducible, else false.

isReducible

boolean isReducible(GenPolynomial<C> P)

GenPolynomial test if a non trivial factorization exsists.

Parameters:

P - GenPolynomial.

Returns:

true if P is reducible, else false.

isSquarefree

boolean isSquarefree(GenPolynomial<C> P)

GenPolynomial test if is squarefree.

Parameters:

P - GenPolynomial.

Returns:

true if P is squarefree, else false.

factorsSquarefree

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

GenPolynomial factorization of a squarefree polynomial.

Parameters:

P - squarefree and primitive! or monic! GenPolynomial.

Returns:

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

factors

java.util.SortedMap<GenPolynomial<C>,java.lang.Long> factors(GenPolynomial<C> P)

GenPolynomial factorization.

Parameters:

P - GenPolynomial.

Returns:

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

factorsRadical

java.util.List<GenPolynomial<C>> factorsRadical(GenPolynomial<C> P)

GenPolynomial factorization ignoring multiplicities.

Parameters:

P - GenPolynomial.

Returns:

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

squarefreePart

GenPolynomial<C> squarefreePart(GenPolynomial<C> P)

GenPolynomial greatest squarefree divisor.

Parameters:

P - GenPolynomial.

Returns:

squarefree(P).

squarefreeFactors

java.util.SortedMap<GenPolynomial<C>,java.lang.Long> squarefreeFactors(GenPolynomial<C> P)

GenPolynomial squarefree factorization.

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 squarefree.

isFactorization

boolean isFactorization(GenPolynomial<C> P,
                        java.util.List<GenPolynomial<C>> F)

GenPolynomial is factorization.

Parameters:

P - GenPolynomial

F - = [p_1,...,p_k].

Returns:

true if P = prod_{i=1,...,r} p_i, else false.

isFactorization

boolean isFactorization(GenPolynomial<C> P,
                        java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F)

GenPolynomial is factorization.

Parameters:

P - GenPolynomial.

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

Returns:

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