edu.jas.ps
Class ReductionSeq<C extends RingElem<C>>

java.lang.Object
  edu.jas.ps.ReductionSeq<C>

Type Parameters:

C - coefficient type

public class ReductionSeq<C extends RingElem<C>>
extends java.lang.Object

Multivariate power series reduction sequential use algorithm. Implements Mora normal-form algorithm.

Author:

Heinz Kredel

Constructor Summary

ReductionSeq()
Constructor.

Method Summary

boolean	contains(java.util.List<MultiVarPowerSeries<C>> S, java.util.List<MultiVarPowerSeries<C>> B) Ideal containment.
boolean	criterion4(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B, ExpVector e) GB criterion 4.
boolean	isTopReducible(java.util.List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A) Is top reducible.
boolean	moduleCriterion(int modv, ExpVector ei, ExpVector ej) Module criterion.
boolean	moduleCriterion(int modv, MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B) Module criterium.
MultiVarPowerSeries<C>	normalform(java.util.List<MultiVarPowerSeries<C>> Pp, MultiVarPowerSeries<C> Ap) Top normal-form with Mora's algorithm.
MultiVarPowerSeries<C>	SPolynomial(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B) S-Power-series, S-polynomial.
java.util.List<MultiVarPowerSeries<C>>	totalNormalform(java.util.List<MultiVarPowerSeries<C>> P) Total reduced normalform with Mora's algorithm.
MultiVarPowerSeries<C>	totalNormalform(java.util.List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A) Total reduced normal-form with Mora's algorithm.

Methods inherited from class java.lang.Object

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

Constructor Detail

ReductionSeq

public ReductionSeq()

Constructor.

Method Detail

moduleCriterion

public boolean moduleCriterion(int modv,
                               MultiVarPowerSeries<C> A,
                               MultiVarPowerSeries<C> B)

Module criterium.

Parameters:

modv - number of module variables.

A - power series.

B - power series.

Returns:

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

moduleCriterion

public boolean moduleCriterion(int modv,
                               ExpVector ei,
                               ExpVector ej)

Module criterion.

Parameters:

modv - number of module variables.

ei - ExpVector.

ej - ExpVector.

Returns:

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

criterion4

public boolean criterion4(MultiVarPowerSeries<C> A,
                          MultiVarPowerSeries<C> B,
                          ExpVector e)

GB criterion 4. Use only for commutative power series rings.

Parameters:

A - power series.

B - power series.

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

Returns:

true if the S-power-series(i,j) is required, else false.

SPolynomial

public MultiVarPowerSeries<C> SPolynomial(MultiVarPowerSeries<C> A,
                                          MultiVarPowerSeries<C> B)

S-Power-series, S-polynomial.

Parameters:

A - power series.

B - power series.

Returns:

spol(A,B) the S-power-series of A and B.

normalform

public MultiVarPowerSeries<C> normalform(java.util.List<MultiVarPowerSeries<C>> Pp,
                                         MultiVarPowerSeries<C> Ap)

Top normal-form with Mora's algorithm.

Parameters:

Ap - power series.

Pp - power series list.

Returns:

top-nf(Ap) with respect to Pp.

totalNormalform

public MultiVarPowerSeries<C> totalNormalform(java.util.List<MultiVarPowerSeries<C>> P,
                                              MultiVarPowerSeries<C> A)

Total reduced normal-form with Mora's algorithm.

Parameters:

A - power series.

P - power series list.

Returns:

total-nf(A) with respect to P.

totalNormalform

public java.util.List<MultiVarPowerSeries<C>> totalNormalform(java.util.List<MultiVarPowerSeries<C>> P)

Total reduced normalform with Mora's algorithm.

Parameters:

P - power series list.

Returns:

total-nf(p) for p with respect to P\{p}.

isTopReducible

public boolean isTopReducible(java.util.List<MultiVarPowerSeries<C>> P,
                              MultiVarPowerSeries<C> A)

Is top reducible.

Parameters:

A - power series.

P - power series list.

Returns:

true if A is top reducible with respect to P.

contains

public boolean contains(java.util.List<MultiVarPowerSeries<C>> S,
                        java.util.List<MultiVarPowerSeries<C>> B)

Ideal containment. Test if each b in B is contained in ideal S.

Parameters:

S - standard base.

B - list of power series

Returns:

true, if each b in B is contained in ideal(S), else false