edu.jas.module
Class SolvableSyzygy

java.lang.Object
  edu.jas.module.SolvableSyzygy

public class SolvableSyzygy
extends java.lang.Object

Syzygy class for solvable polynomials. Implements Syzygy computations and tests.

Constructor Summary

SolvableSyzygy()

Method Summary

static boolean	isLeftZeroRelation(java.util.List Z, java.util.List F) Test if sysygy
static boolean	isLeftZeroRelation(ModuleList Z, ModuleList F) Test if sysygy of modules
static boolean	isZero(java.util.List a) test vector of zero polynomials.
static SolvablePolynomial	leftNormalform(java.util.ArrayList row, java.util.List Pp, SolvablePolynomial Ap) LeftNormalform.
static SolvablePolynomial	leftScalarProduct(java.util.List r, java.util.List F) Scalar product of vectors of polynomials.
static java.util.List	leftScalarProduct(java.util.List r, ModuleList F) product of vector and matrix of polynomials.
static java.util.List	leftScalarProduct(OrderedPolynomial p, java.util.List F) Scalar product of polynomial with vector of polynomials.
static SolvablePolynomial	leftSPolynomial(java.util.ArrayList S, int i, SolvablePolynomial Ap, int j, SolvablePolynomial Bp) S-Polynomial
static java.util.List	leftZeroRelations(int modv, java.util.List F)
static java.util.List	leftZeroRelations(java.util.List F) Solvable Syzygy module from Groebner base F must be a Groebner base.
static ModuleList	leftZeroRelations(ModuleList M)
static java.util.List	resolution(ModuleList M) Resolution of a module.
static java.util.List	resolution(PolynomialList F) Resolution of a polynomial list.
static java.util.List	vectorAdd(java.util.List a, java.util.List b) Addition of vectors of polynomials.

Methods inherited from class java.lang.Object

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

Constructor Detail

SolvableSyzygy

public SolvableSyzygy()

Method Detail

leftZeroRelations

public static java.util.List leftZeroRelations(java.util.List F)

Solvable Syzygy module from Groebner base F must be a Groebner base.

leftZeroRelations

public static java.util.List leftZeroRelations(int modv,
                                               java.util.List F)

leftZeroRelations

public static ModuleList leftZeroRelations(ModuleList M)

leftSPolynomial

public static SolvablePolynomial leftSPolynomial(java.util.ArrayList S,
                                                 int i,
                                                 SolvablePolynomial Ap,
                                                 int j,
                                                 SolvablePolynomial Bp)

S-Polynomial

leftNormalform

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

LeftNormalform.

isLeftZeroRelation

public static boolean isLeftZeroRelation(java.util.List Z,
                                         java.util.List F)

Test if sysygy

leftScalarProduct

public static SolvablePolynomial leftScalarProduct(java.util.List r,
                                                   java.util.List F)

Scalar product of vectors of polynomials.

isLeftZeroRelation

public static boolean isLeftZeroRelation(ModuleList Z,
                                         ModuleList F)

Test if sysygy of modules

leftScalarProduct

public static java.util.List leftScalarProduct(java.util.List r,
                                               ModuleList F)

product of vector and matrix of polynomials.

vectorAdd

public static java.util.List vectorAdd(java.util.List a,
                                       java.util.List b)

Addition of vectors of polynomials.

isZero

public static boolean isZero(java.util.List a)

test vector of zero polynomials.

leftScalarProduct

public static java.util.List leftScalarProduct(OrderedPolynomial p,
                                               java.util.List F)

Scalar product of polynomial with vector of polynomials.

resolution

public static java.util.List resolution(ModuleList M)

Resolution of a module. Only with direct GBs.

resolution

public static java.util.List resolution(PolynomialList F)

Resolution of a polynomial list. Only with direct GBs.