edu.jas.module
Class Syzygy

java.lang.Object
  edu.jas.module.Syzygy

public class Syzygy
extends java.lang.Object

Syzygy class. Implements Syzygy computations and tests.

Constructor Summary

Syzygy()

Method Summary

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

Methods inherited from class java.lang.Object

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

Constructor Detail

Syzygy

public Syzygy()

Method Detail

zeroRelations

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

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

zeroRelations

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

zeroRelations

public static ModuleList zeroRelations(ModuleList M)

SPolynomial

public static OrderedPolynomial SPolynomial(java.util.ArrayList S,
                                            int i,
                                            OrderedPolynomial Ap,
                                            int j,
                                            OrderedPolynomial Bp)

S-Polynomial

normalform

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

Normalform.

isZeroRelation

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

Test if sysygy

scalarProduct

public static OrderedPolynomial scalarProduct(java.util.List r,
                                              java.util.List F)

Scalar product of vectors of polynomials.

isZeroRelation

public static boolean isZeroRelation(ModuleList Z,
                                     ModuleList F)

Test if sysygy of modules

scalarProduct

public static java.util.List scalarProduct(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.

scalarProduct

public static java.util.List scalarProduct(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.