Squarefree
edu.jas.ufd

## Interface Squarefree<C extends GcdRingElem<C>>

• ### Method Summary

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

`SortedMap<GenPolynomial<C>,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,                      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,                      SortedMap<GenPolynomial<C>,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

`List<GenPolynomial<C>> coPrimeSquarefree(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

`List<GenPolynomial<C>> coPrimeSquarefree(GenPolynomial<C> a,                                       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(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.