edu.jas.ufd

Interface Squarefree<C extends GcdRingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

SquarefreeAbstract, SquarefreeFieldChar0, SquarefreeFieldCharP, SquarefreeFiniteFieldCharP, SquarefreeInfiniteAlgebraicFieldCharP, SquarefreeInfiniteFieldCharP, SquarefreeRingChar0

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

Squarefree decomposition interface.

See Also:

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

Method Summary

Modifier and Type	Method and Description
java.util.List<GenPolynomial<C>>	coPrimeSquarefree(GenPolynomial<C> a, java.util.List<GenPolynomial<C>> P) GenPolynomial squarefree and co-prime list.
java.util.List<GenPolynomial<C>>	coPrimeSquarefree(java.util.List<GenPolynomial<C>> A) GenPolynomial squarefree and co-prime list.
boolean	isCoPrimeSquarefree(java.util.List<GenPolynomial<C>> B) Test if list of GenPolynomials is squarefree and co-prime.
boolean	isFactorization(GenPolynomial<C> P, java.util.List<GenPolynomial<C>> F) GenPolynomial is (squarefree) factorization.
boolean	isFactorization(GenPolynomial<C> P, java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F) GenPolynomial is (squarefree) factorization.
boolean	isSquarefree(GenPolynomial<C> P) GenPolynomial test if is squarefree.
boolean	isSquarefree(java.util.List<GenPolynomial<C>> L) GenPolynomial list test if 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

squarefreePart

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

GenPolynomial greatest squarefree divisor.

Parameters:

P - GenPolynomial.

Returns:

squarefree(pp(P)).

isSquarefree

boolean isSquarefree(GenPolynomial<C> P)

GenPolynomial test if is squarefree.

Parameters:

P - GenPolynomial.

Returns:

true if P is squarefree, else false.

isSquarefree

boolean isSquarefree(java.util.List<GenPolynomial<C>> L)

GenPolynomial list test if squarefree.

Parameters:

L - list of GenPolynomial.

Returns:

true if each P in L is squarefree, else false.

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 (squarefree) 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 (squarefree) 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.

coPrimeSquarefree

java.util.List<GenPolynomial<C>> coPrimeSquarefree(java.util.List<GenPolynomial<C>> A)

GenPolynomial squarefree and co-prime list.

Parameters:

A - list of GenPolynomials.

Returns:

B with gcd(b,c) = 1 for all b != c in B and for all non-constant a in A there exists b in B with b|a and each b in B is squarefree. B does not contain zero or constant polynomials.

coPrimeSquarefree

java.util.List<GenPolynomial<C>> coPrimeSquarefree(GenPolynomial<C> a,
                                                   java.util.List<GenPolynomial<C>> P)

GenPolynomial squarefree and co-prime list.

Parameters:

a - polynomial.

P - squarefree co-prime list of GenPolynomials.

Returns:

B with gcd(b,c) = 1 for all b != c in B and for non-constant a there exists b in P with b|a. B does not contain zero or constant polynomials.

isCoPrimeSquarefree

boolean isCoPrimeSquarefree(java.util.List<GenPolynomial<C>> B)

Test if list of GenPolynomials is squarefree and co-prime.

Parameters:

B - list of GenPolynomials.

Returns:

true, if for all b != c in B gcd(b,c) = 1 and each b in B is squarefree, else false.