SquarefreeAbstract
edu.jas.ufd

Class SquarefreeAbstract<C extends GcdRingElem<C>>

    • Method Detail

      • baseSquarefreePart

        public abstract GenPolynomial<C> baseSquarefreePart(GenPolynomial<C> P)
        GenPolynomial polynomial greatest squarefree divisor.
        Parameters:
        P - GenPolynomial.
        Returns:
        squarefree(pp(P)).
      • baseSquarefreeFactors

        public abstract SortedMap<GenPolynomial<C>,Long> baseSquarefreeFactors(GenPolynomial<C> A)
        GenPolynomial polynomial squarefree factorization.
        Parameters:
        A - GenPolynomial.
        Returns:
        [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.
      • recursiveUnivariateSquarefreePart

        public abstract GenPolynomial<GenPolynomial<C>> recursiveUnivariateSquarefreePart(GenPolynomial<GenPolynomial<C>> P)
        GenPolynomial recursive polynomial greatest squarefree divisor.
        Parameters:
        P - recursive univariate GenPolynomial.
        Returns:
        squarefree(pp(P)).
      • recursiveUnivariateSquarefreeFactors

        public abstract SortedMap<GenPolynomial<GenPolynomial<C>>,Long> recursiveUnivariateSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)
        GenPolynomial recursive univariate polynomial squarefree factorization.
        Parameters:
        P - recursive univariate GenPolynomial.
        Returns:
        [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.
      • isSquarefree

        public boolean isSquarefree(GenPolynomial<C> P)
        GenPolynomial test if is squarefree.
        Specified by:
        isSquarefree in interface Squarefree<C extends GcdRingElem<C>>
        Parameters:
        P - GenPolynomial.
        Returns:
        true if P is squarefree, else false.
      • isSquarefree

        public boolean isSquarefree(List<GenPolynomial<C>> L)
        GenPolynomial list test if squarefree.
        Specified by:
        isSquarefree in interface Squarefree<C extends GcdRingElem<C>>
        Parameters:
        L - list of GenPolynomial.
        Returns:
        true if each P in L is squarefree, else false.
      • isRecursiveSquarefree

        public boolean isRecursiveSquarefree(GenPolynomial<GenPolynomial<C>> P)
        Recursive GenPolynomial test if is squarefree.
        Parameters:
        P - recursive univariate GenPolynomial.
        Returns:
        true if P is squarefree, else false.
      • coPrimeSquarefree

        public List<GenPolynomial<C>> coPrimeSquarefree(List<GenPolynomial<C>> A)
        GenPolynomial squarefree and co-prime list.
        Specified by:
        coPrimeSquarefree in interface Squarefree<C extends GcdRingElem<C>>
        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

        public List<GenPolynomial<C>> coPrimeSquarefree(GenPolynomial<C> a,                                       List<GenPolynomial<C>> P)
        GenPolynomial squarefree and co-prime list.
        Specified by:
        coPrimeSquarefree in interface Squarefree<C extends GcdRingElem<C>>
        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

        public boolean isCoPrimeSquarefree(List<GenPolynomial<C>> B)
        Test if list of GenPolynomials is squarefree and co-prime.
        Specified by:
        isCoPrimeSquarefree in interface Squarefree<C extends GcdRingElem<C>>
        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.
      • normalizeFactorization

        public SortedMap<GenPolynomial<C>,Long> normalizeFactorization(SortedMap<GenPolynomial<C>,Long> F)
        Normalize factorization. p'_i > 0 for i > 1 and p'_1 != 1 if k > 1.
        Parameters:
        F - = [p_1->e_1;, ..., p_k->e_k].
        Returns:
        F' = [p'_1->e_1, ..., p'_k->e_k].
      • factorCount

        public long factorCount(SortedMap<GenPolynomial<C>,Long> F)
        Count number of factors in a (squarefree) factorization.
        Parameters:
        F - = [p_1 -> e_1, ..., p_k -> e_k].
        Returns:
        sum_{i=1,...,k} e_i.
      • recursiveSquarefreeFactors

        public SortedMap<GenPolynomial<GenPolynomial<C>>,Long> recursiveSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)
        GenPolynomial recursive polynomial squarefree factorization.
        Parameters:
        P - recursive GenPolynomial.
        Returns:
        [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.
      • basePartialFraction

        public List<List<GenPolynomial<C>>> basePartialFraction(GenPolynomial<C> A,                                               SortedMap<GenPolynomial<C>,Long> D)
        Univariate GenPolynomial partial fraction decomposition.
        Parameters:
        A - univariate GenPolynomial.
        D - sorted map [d_1 -> e_1, ..., d_k -> e_k] with d_i squarefree.
        Returns:
        [ [Ai0, Ai1,..., Aie_i], i=0,...,k ] with A/prod(D) = A0 + sum( sum ( Aij/di^j ) ) with deg(Aij) < deg(di).
      • isBasePartialFraction

        public boolean isBasePartialFraction(GenPolynomial<C> A,                            SortedMap<GenPolynomial<C>,Long> D,                            List<List<GenPolynomial<C>>> F)
        Test for Univariate GenPolynomial partial fraction decomposition.
        Parameters:
        A - univariate GenPolynomial.
        D - sorted map [d_1 -> e_1, ..., d_k -> e_k] with d_i squarefree.
        F - a list of lists [ [Ai0, Ai1,..., Aie_i], i=0,...,k ]
        Returns:
        true, if A/prod(D) = A0 + sum( sum ( Aij/di^j ) ), else false.
      • squarefreePart

        public C squarefreePart(C P)
        Coefficients greatest squarefree divisor.
        Parameters:
        P - coefficient.
        Returns:
        squarefree part of P.
      • squarefreeFactors

        public abstract SortedMap<C,Long> squarefreeFactors(C P)
        Coefficients squarefree factorization.
        Parameters:
        P - coefficient.
        Returns:
        [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.

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