edu.jas.gbufd

Class GroebnerBaseWalk<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gbufd.GroebnerBaseWalk<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, java.io.Serializable

public class GroebnerBaseWalk<C extends GcdRingElem<C>>
extends GroebnerBaseAbstract<C>

Groebner Base sequential Groebner Walk algorithm. Implements Groebner base computation via Groebner Walk algorithm. See "The generic Groebner walk" by Fukuda, Jensen, Lauritzen, Thomas, 2005. The start term order t1 can be set by a constructor. The target term order t2 is taken from the input polynomials term order.

Author:

Heinz Kredel

See Also:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected GroebnerBaseAbstract<C>	sgb The backing GB algorithm implementation.
protected TermOrder	startTO The start term order t1.

Fields inherited from class edu.jas.gb.GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor and Description
GroebnerBaseWalk() Constructor.
GroebnerBaseWalk(GroebnerBaseAbstract<C> gb) Constructor.
GroebnerBaseWalk(GroebnerBaseAbstract<C> gb, TermOrder t1) Constructor.
GroebnerBaseWalk(RingFactory<C> coFac) Constructor.
GroebnerBaseWalk(RingFactory<C> coFac, TermOrder t1) Constructor.

Method Summary

Modifier and Type	Method and Description
int	cancel() Cancel ThreadPool.
ExpVector	facetNormal(TermOrder t1, TermOrder t2, java.util.Set<ExpVector> delta, ExpVector zero, long[][] t2weight) Determine new facet normal.
java.util.List<GenPolynomial<C>>	GB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base using Groebner Walk algorithm.
java.util.List<GenPolynomial<C>>	liftReductas(java.util.List<Monomial<C>> M, java.util.List<Monomial<C>> Mp, java.util.List<GenPolynomial<C>> G, java.util.List<GenPolynomial<C>> A) Lift leading polynomials to full Groebner base with respect to term order.
void	terminate() Cleanup and terminate ThreadPool.
java.lang.String	toString() Get the String representation with GB engine.
java.util.List<GenPolynomial<C>>	walkGroebnerToTarget(int modv, java.util.List<GenPolynomial<C>> Gl, GenPolynomialRing<C> ufac) Converts Groebner bases w.r.t. total degree / start term order to Groebner base w.r.t to inverse lexicographical / target term order.

Methods inherited from class edu.jas.gb.GroebnerBaseAbstract

commonZeroTest, constructUnivariate, extGB, extGB, GB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isReductionMatrix, isReductionMatrix, minimalExtendedGB, minimalGB, normalizeMatrix, normalizeZerosOnes, univariateDegrees

Methods inherited from class java.lang.Object

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

Field Detail

sgb

protected GroebnerBaseAbstract<C extends GcdRingElem<C>> sgb

The backing GB algorithm implementation.

startTO

protected TermOrder startTO

The start term order t1.

Constructor Detail

GroebnerBaseWalk

public GroebnerBaseWalk()

Constructor.

GroebnerBaseWalk

public GroebnerBaseWalk(RingFactory<C> coFac)

Constructor.

Parameters:

coFac - coefficient ring of polynomial ring.

GroebnerBaseWalk

public GroebnerBaseWalk(RingFactory<C> coFac,
                        TermOrder t1)

Constructor.

Parameters:

coFac - coefficient ring of polynomial ring.

t1 - start term order.

GroebnerBaseWalk

public GroebnerBaseWalk(GroebnerBaseAbstract<C> gb)

Constructor.

Parameters:

gb - backing GB algorithm.

GroebnerBaseWalk

public GroebnerBaseWalk(GroebnerBaseAbstract<C> gb,
                        TermOrder t1)

Constructor.

Parameters:

gb - backing GB algorithm.

t1 - start term order.

Method Detail

toString

public java.lang.String toString()

Get the String representation with GB engine.

Overrides:

toString in class GroebnerBaseAbstract<C extends GcdRingElem<C>>

See Also:

Object.toString()

GB

public java.util.List<GenPolynomial<C>> GB(int modv,
                                           java.util.List<GenPolynomial<C>> F)

Groebner base using Groebner Walk algorithm.

Parameters:

modv - module variable number.

F - polynomial list in target term order.

Returns:

GB(F) a INVLEX / target term order Groebner base of F.

walkGroebnerToTarget

public java.util.List<GenPolynomial<C>> walkGroebnerToTarget(int modv,
                                                             java.util.List<GenPolynomial<C>> Gl,
                                                             GenPolynomialRing<C> ufac)

Converts Groebner bases w.r.t. total degree / start term order to Groebner base w.r.t to inverse lexicographical / target term order.

Parameters:

modv - module variable number.

Gl - Groebner base with respect to graded / start term order.

ufac - target polynomial ring and term order.

Returns:

Groebner base w.r.t inverse lexicographical / target term order

facetNormal

public ExpVector facetNormal(TermOrder t1,
                             TermOrder t2,
                             java.util.Set<ExpVector> delta,
                             ExpVector zero,
                             long[][] t2weight)

Determine new facet normal.

Parameters:

t1 - old term order.

t2 - new term order.

delta - exponent vectors deltas.

zero - exponent vector.

t2weight - weight representation of t2.

Returns:

new facet normal v or null if no new facet normal exists.

terminate

public void terminate()

Cleanup and terminate ThreadPool.

Overrides:

terminate in class GroebnerBaseAbstract<C extends GcdRingElem<C>>

cancel

public int cancel()

Cancel ThreadPool.

Overrides:

cancel in class GroebnerBaseAbstract<C extends GcdRingElem<C>>

liftReductas

public java.util.List<GenPolynomial<C>> liftReductas(java.util.List<Monomial<C>> M,
                                                     java.util.List<Monomial<C>> Mp,
                                                     java.util.List<GenPolynomial<C>> G,
                                                     java.util.List<GenPolynomial<C>> A)

Lift leading polynomials to full Groebner base with respect to term order.

Parameters:

M - new leading monomial list of polynomials as marks.

Mp - old leading monomial list of polynomials as marks.

G - Groebner base polynomials for lift.

A - polynomial list of leading omega polynomials to lift.

Returns:

lift(A) a Groebner base wrt M of ideal(G).