Squarefree
edu.jas.ufd

Interface Squarefree<C extends GcdRingElem<C>>

    • 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.

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