Power
edu.jas.structure

Class Power<C extends RingElem<C>>



  • public class Power<C extends RingElem<C>>extends Object
    Power class to compute powers of RingElem.
    • Constructor Detail

      • Power

        public Power()
        The constructor creates a Power object.
      • Power

        public Power(RingFactory<C> fac)
        The constructor creates a Power object.
        Parameters:
        fac - ring factory
    • Method Detail

      • positivePower

        public static <C extends RingElem<C>> C positivePower(C a,                                      long n)
        power of a to the n-th, n positive.
        Parameters:
        a - element.
        n - integer exponent > 0.
        Returns:
        a^n.
      • positivePower

        public static <C extends RingElem<C>> C positivePower(C a,                                      BigInteger n)
        power of a to the n-th, n positive.
        Parameters:
        a - element.
        n - java.math.BigInteger exponent > 0.
        Returns:
        a^n.
      • modPositivePower

        public static <C extends RingElem<C>> C modPositivePower(C a,                                         long n,                                         C m)
        power of a to the n-th, n positive, modulo m.
        Parameters:
        a - element.
        n - integer exponent > 0.
        m - modulus.
        Returns:
        a^n mod m.
      • power

        public static <C extends RingElem<C>> C power(RingFactory<C> fac,                              C a,                              long n)
        power of a to the n-th.
        Parameters:
        a - element.
        n - integer exponent.
        fac - ring factory.
        Returns:
        a^n, with 0^0 = 0 and a^{-n} = {1/a}^n.
      • power

        public static <C extends MonoidElem<C>> C power(MonoidFactory<C> fac,                                C a,                                long n)
        power of a to the n-th.
        Parameters:
        a - element.
        n - integer exponent.
        fac - monoid factory.
        Returns:
        a^n, with a^{-n} = {1/a}^n.
      • modPower

        public static <C extends MonoidElem<C>> C modPower(MonoidFactory<C> fac,                                   C a,                                   long n,                                   C m)
        power of a to the n-th modulo m.
        Parameters:
        a - element.
        n - integer exponent.
        m - modulus.
        fac - monoid factory.
        Returns:
        a^n mod m, with a^{-n} = {1/a}^n.
      • modPower

        public static <C extends MonoidElem<C>> C modPower(MonoidFactory<C> fac,                                   C a,                                   BigInteger n,                                   C m)
        power of a to the n-th modulo m.
        Parameters:
        a - element.
        n - integer exponent.
        m - modulus.
        fac - monoid factory.
        Returns:
        a^n mod m, with a^{-n} = {1/a}^n.
      • power

        public C power(C a,      long n)
        power of a to the n-th.
        Parameters:
        a - element.
        n - integer exponent.
        Returns:
        a^n, with 0^0 = 0.
      • modPower

        public C modPower(C a,         long n,         C m)
        power of a to the n-th mod m.
        Parameters:
        a - element.
        n - integer exponent.
        m - modulus.
        Returns:
        a^n mod m, with 0^0 = 0.
      • modPower

        public C modPower(C a,         BigInteger n,         C m)
        power of a to the n-th mod m.
        Parameters:
        a - element.
        n - integer exponent.
        m - modulus.
        Returns:
        a^n mod m, with 0^0 = 0.
      • logarithm

        public static <C extends RingElem<C>> long logarithm(C p,                                     C a)
        Logarithm.
        Parameters:
        p - logarithm base.
        a - element.
        Returns:
        k ≥ 1 minimal with p^k ≥ b.
      • multiply

        public static <C extends RingElem<C>> C multiply(RingFactory<C> fac,                                 List<C> A)
        Multiply elements in list.
        Parameters:
        A - list of elements (a_0,...,a_k).
        fac - ring factory.
        Returns:
        prod(i=0,...k) a_i.
      • multiply

        public static <C extends MonoidElem<C>> C multiply(MonoidFactory<C> fac,                                   List<C> A)
        Multiply elements in list.
        Parameters:
        A - list of elements (a_0,...,a_k).
        fac - monoid factory.
        Returns:
        prod(i=0,...k) a_i.
      • sum

        public static <C extends RingElem<C>> C sum(RingFactory<C> fac,                            List<C> A)
        Sum elements in list.
        Parameters:
        A - list of elements (a_0,...,a_k).
        fac - ring factory.
        Returns:
        sum(i=0,...k) a_i.
      • sum

        public static <C extends AbelianGroupElem<C>> C sum(AbelianGroupFactory<C> fac,                                    List<C> A)
        Sum elements in list.
        Parameters:
        A - list of elements (a_0,...,a_k).
        fac - monoid factory.
        Returns:
        sum(i=0,...k) a_i.

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