edu.jas.structure
Class Power<C extends RingElem<C>>

java.lang.Object
  edu.jas.structure.Power<C>

public class Power<C extends RingElem<C>>
extends java.lang.Object

Power class to compute powers of RingElem.

Author:

Heinz Kredel

Constructor Summary

Power()
The constructor creates a Power object.

Power(RingFactory<C> fac)
The constructor creates a Power object.

Method Summary

static <C extends RingElem<C>> long	logarithm(C p, C a) Logarithm.
static <C extends RingElem<C>> C	modPositivePower(C a, long n, C m) power of a to the n-th, n positive, modulo m.
C	modPower(C a, java.math.BigInteger n, C m) power of a to the n-th mod m.
C	modPower(C a, long n, C m) power of a to the n-th mod m.
static <C extends MonoidElem<C>> C	modPower(MonoidFactory<C> fac, C a, java.math.BigInteger n, C m) power of a to the n-th modulo m.
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.
static <C extends MonoidElem<C>> C	multiply(MonoidFactory<C> fac, java.util.List<C> A) Multiply elements in list.
static <C extends RingElem<C>> C	multiply(RingFactory<C> fac, java.util.List<C> A) Multiply elements in list.
static <C extends RingElem<C>> C	positivePower(C a, java.math.BigInteger n) power of a to the n-th, n positive.
static <C extends RingElem<C>> C	positivePower(C a, long n) power of a to the n-th, n positive.
C	power(C a, long n) power of a to the n-th.
static <C extends MonoidElem<C>> C	power(MonoidFactory<C> fac, C a, long n) power of a to the n-th.
static <C extends RingElem<C>> C	power(RingFactory<C> fac, C a, long n) power of a to the n-th.
static <C extends AbelianGroupElem<C>> C	sum(AbelianGroupFactory<C> fac, java.util.List<C> A) Sum elements in list.
static <C extends RingElem<C>> C	sum(RingFactory<C> fac, java.util.List<C> A) Sum elements in list.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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,
                                                      java.math.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,
                                                   java.math.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,
                  java.math.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,
                                                 java.util.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,
                                                   java.util.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,
                                            java.util.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,
                                                    java.util.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.