Package 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
Constructors Constructor Description ReductionSeq()
Constructor.
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description 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.
-
-
-
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
-
-