edu.jas.ring
Class Reduction

java.lang.Object
  edu.jas.ring.Reduction

public class Reduction
extends java.lang.Object

Polynomial Reduction class. Implements S-Polynomial, Normalform, Criterion 4 and Irreducible Set.

Constructor Summary

Reduction()

Method Summary

static boolean	GBCriterion4(OrderedPolynomial A, OrderedPolynomial B) GB criterium 4.
static boolean	GBCriterion4(OrderedPolynomial A, OrderedPolynomial B, ExpVector e) GB criterium 4.
static java.util.ArrayList	irreducibleSet(java.util.List Pp) Irreducible set.
static java.util.ArrayList	leftIrreducibleSet(java.util.List Pp) Left irreducible set.
static java.util.List	leftNormalform(java.util.List Pp, java.util.List Ap) Left Normalform Set.
static SolvablePolynomial	leftNormalform(java.util.List Pp, SolvablePolynomial Ap) Left Normalform.
static SolvablePolynomial	leftSPolynomial(SolvablePolynomial Ap, SolvablePolynomial Bp) Left S-Polynomial
static boolean	ModuleCriterion(int modv, OrderedPolynomial A, OrderedPolynomial B) Module criterium.
static java.util.List	normalform(java.util.List Pp, java.util.List Ap) Normalform Set.
static OrderedPolynomial	normalform(java.util.List Pp, OrderedPolynomial Ap) Normalform.
static OrderedPolynomial	normalformMod(DistHashTable Pp, OrderedPolynomial Ap) Normalform.
static OrderedPolynomial	normalformMod(java.util.List Pp, OrderedPolynomial Ap) Normalform.
static OrderedPolynomial	SPolynomial(OrderedPolynomial Ap, OrderedPolynomial Bp) S-Polynomial

Methods inherited from class java.lang.Object

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

Constructor Detail

Reduction

public Reduction()

Method Detail

SPolynomial

public static OrderedPolynomial SPolynomial(OrderedPolynomial Ap,
                                            OrderedPolynomial Bp)

S-Polynomial

leftSPolynomial

public static SolvablePolynomial leftSPolynomial(SolvablePolynomial Ap,
                                                 SolvablePolynomial Bp)

Left S-Polynomial

ModuleCriterion

public static boolean ModuleCriterion(int modv,
                                      OrderedPolynomial A,
                                      OrderedPolynomial B)

Module criterium.

Returns:

true if the module S-polynomial(i,j) is required.

GBCriterion4

public static boolean GBCriterion4(OrderedPolynomial A,
                                   OrderedPolynomial B,
                                   ExpVector e)

GB criterium 4.

Parameters:

e - = lcm(ht(A),ht(B))

Returns:

true if the S-polynomial(i,j) is required.

GBCriterion4

public static boolean GBCriterion4(OrderedPolynomial A,
                                   OrderedPolynomial B)

GB criterium 4.

Returns:

true if the S-polynomial(i,j) is required.

normalform

public static OrderedPolynomial normalform(java.util.List Pp,
                                           OrderedPolynomial Ap)

Normalform.

normalform

public static java.util.List normalform(java.util.List Pp,
                                        java.util.List Ap)

Normalform Set.

leftNormalform

public static SolvablePolynomial leftNormalform(java.util.List Pp,
                                                SolvablePolynomial Ap)

Left Normalform.

leftNormalform

public static java.util.List leftNormalform(java.util.List Pp,
                                            java.util.List Ap)

Left Normalform Set.

normalformMod

public static OrderedPolynomial normalformMod(java.util.List Pp,
                                              OrderedPolynomial Ap)

Normalform. Allows concurrent modification of the list.

normalformMod

public static OrderedPolynomial normalformMod(DistHashTable Pp,
                                              OrderedPolynomial Ap)

Normalform. Allows concurrent modification of the list.

irreducibleSet

public static java.util.ArrayList irreducibleSet(java.util.List Pp)

Irreducible set.

leftIrreducibleSet

public static java.util.ArrayList leftIrreducibleSet(java.util.List Pp)

Left irreducible set.