edu.jas.gbufd

Class PolyModUtil

java.lang.Object

edu.jas.gbufd.PolyModUtil

public class PolyModUtil
extends java.lang.Object

Package gb and gbufd utilities.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor and Description
PolyModUtil()

Method Summary

Modifier and Type	Method and Description
static <C extends GcdRingElem<C>> GenPolynomial<C>	syzGcd(GenPolynomialRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d) Greatest common divisor.
static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>	syzGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) Greatest common divisor via least common multiple.
static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[]	syzGcdCofactors(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) Greatest common divisor and cofactors via least common multiple and reduction.
static <C extends GcdRingElem<C>> GenPolynomial<C>	syzLcm(GenPolynomialRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d) Least common multiple.
static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>	syzLcm(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) Least common multiple via ideal intersection.
static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>	syzLeftGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) Left greatest common divisor via least common multiple.
static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>	syzRightGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) Right greatest common divisor via least common multiple.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolyModUtil

public PolyModUtil()

Method Detail

syzLcm

public static <C extends GcdRingElem<C>> GenSolvablePolynomial<C> syzLcm(GenSolvablePolynomialRing<C> r,
                                                                         GenSolvablePolynomial<C> n,
                                                                         GenSolvablePolynomial<C> d)

Least common multiple via ideal intersection.

Parameters:

r - solvable polynomial ring.

n - first solvable polynomial.

d - second solvable polynomial.

Returns:

lcm(n,d)

syzGcd

public static <C extends GcdRingElem<C>> GenSolvablePolynomial<C> syzGcd(GenSolvablePolynomialRing<C> r,
                                                                         GenSolvablePolynomial<C> n,
                                                                         GenSolvablePolynomial<C> d)

Greatest common divisor via least common multiple.

Parameters:

r - solvable polynomial ring.

n - first solvable polynomial.

d - second solvable polynomial.

Returns:

gcd(n,d)

syzLeftGcd

public static <C extends GcdRingElem<C>> GenSolvablePolynomial<C> syzLeftGcd(GenSolvablePolynomialRing<C> r,
                                                                             GenSolvablePolynomial<C> n,
                                                                             GenSolvablePolynomial<C> d)

Left greatest common divisor via least common multiple.

Parameters:

r - solvable polynomial ring.

n - first solvable polynomial.

d - second solvable polynomial.

Returns:

gcd(n,d)

syzRightGcd

public static <C extends GcdRingElem<C>> GenSolvablePolynomial<C> syzRightGcd(GenSolvablePolynomialRing<C> r,
                                                                              GenSolvablePolynomial<C> n,
                                                                              GenSolvablePolynomial<C> d)

Right greatest common divisor via least common multiple.

Parameters:

r - solvable polynomial ring.

n - first solvable polynomial.

d - second solvable polynomial.

Returns:

gcd(n,d)

syzGcdCofactors

public static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[] syzGcdCofactors(GenSolvablePolynomialRing<C> r,
                                                                                    GenSolvablePolynomial<C> n,
                                                                                    GenSolvablePolynomial<C> d)

Greatest common divisor and cofactors via least common multiple and reduction.

Parameters:

r - solvable polynomial ring.

n - first solvable polynomial.

d - second solvable polynomial.

Returns:

[ g=gcd(n,d), n/g, d/g ]

syzLcm

public static <C extends GcdRingElem<C>> GenPolynomial<C> syzLcm(GenPolynomialRing<C> r,
                                                                 GenPolynomial<C> n,
                                                                 GenPolynomial<C> d)

Least common multiple. Just for fun, is not efficient.

Parameters:

r - polynomial ring.

n - first polynomial.

d - second polynomial.

Returns:

lcm(n,d)

syzGcd

public static <C extends GcdRingElem<C>> GenPolynomial<C> syzGcd(GenPolynomialRing<C> r,
                                                                 GenPolynomial<C> n,
                                                                 GenPolynomial<C> d)

Greatest common divisor. Just for fun, is not efficient.

Parameters:

r - polynomial ring.

n - first polynomial.

d - second polynomial.

Returns:

gcd(n,d)