HenselMultUtil
edu.jas.ufd

Class HenselMultUtil



  • public class HenselMultUtilextends Object
    Hensel multivariate lifting utilities.
    • Constructor Detail

      • HenselMultUtil

        public HenselMultUtil()
    • Method Detail

      • liftDiophant

        public static <MOD extends GcdRingElem<MOD> & ModularList<GenPolynomial<MOD>> liftDiophant(GenPolynomial<MOD> A,                                                                            GenPolynomial<MOD> B,                                                                            GenPolynomial<MOD> C,                                                                            List<MOD> V,                                                                            long d,                                                                            long k)                                                                               throws NoLiftingException
        Modular diophantine equation solution and lifting algorithm. Let p = A_i.ring.coFac.modul() and assume ggt(A,B) == 1 mod p.
        Parameters:
        A - modular GenPolynomial, mod p^k
        B - modular GenPolynomial, mod p^k
        C - modular GenPolynomial, mod p^k
        V - list of substitution values, mod p^k
        d - desired approximation exponent (x_i-v_i)^d.
        k - desired approximation exponent p^k.
        Returns:
        [s, t] with s A' + t B' = C mod p^k, with A' = B, B' = A.
        Throws:
        NoLiftingException
      • liftDiophant

        public static <MOD extends GcdRingElem<MOD> & ModularList<GenPolynomial<MOD>> liftDiophant(List<GenPolynomial<MOD>> A,                                                                            GenPolynomial<MOD> C,                                                                            List<MOD> V,                                                                            long d,                                                                            long k)                                                                               throws NoLiftingException
        Modular diophantine equation solution and lifting algorithm. Let p = A_i.ring.coFac.modul() and assume ggt(a,b) == 1 mod p, for a, b in A.
        Parameters:
        A - list of modular GenPolynomials, mod p^k
        C - modular GenPolynomial, mod p^k
        V - list of substitution values, mod p^k
        d - desired approximation exponent (x_i-v_i)^d.
        k - desired approximation exponent p^k.
        Returns:
        [s_1,..., s_n] with sum_i s_i A_i' = C mod p^k, with Ai' = prod_{j!=i} A_j.
        Throws:
        NoLiftingException
      • isHenselLift

        @Deprecatedpublic static <MOD extends GcdRingElem<MOD> & Modular> boolean isHenselLift(GenPolynomial<BigInteger> C,                                                                      GenPolynomial<MOD> Cp,                                                                      List<GenPolynomial<MOD>> F,                                                                      long k,                                                                      List<GenPolynomial<MOD>> L)
        Deprecated. use isHenselLift() without parameter k
        Modular Hensel lifting algorithm on coefficients test. Let p = f_i.ring.coFac.modul() and assume C == prod_{0,...,n-1} f_i mod p with gcd(f_i,f_j) == 1 mod p for i != j
        Parameters:
        C - integer polynomial
        Cp - GenPolynomial mod p^k
        F - = [f_0,...,f_{n-1}] list of monic modular polynomials.
        k - approximation exponent.
        L - = [g_0,...,g_{n-1}] list of lifted modular polynomials.
        Returns:
        true if C = prod_{0,...,n-1} g_i mod p^k, else false.
      • isHenselLift

        public static <MOD extends GcdRingElem<MOD> & Modular> boolean isHenselLift(GenPolynomial<BigInteger> C,                                                           GenPolynomial<MOD> Cp,                                                           List<GenPolynomial<MOD>> F,                                                           List<GenPolynomial<MOD>> L)
        Modular Hensel lifting algorithm on coefficients test. Let p = f_i.ring.coFac.modul() and assume C == prod_{0,...,n-1} f_i mod p with gcd(f_i,f_j) == 1 mod p for i != j
        Parameters:
        C - integer polynomial
        Cp - GenPolynomial mod p^k
        F - = [f_0,...,f_{n-1}] list of monic modular polynomials.
        L - = [g_0,...,g_{n-1}] list of lifted modular polynomials.
        Returns:
        true if C = prod_{0,...,n-1} g_i mod p^k, else false.

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