Package edu.jas.ps
Class ReductionSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.ps.ReductionSeq<C>
- Type Parameters:
C
- coefficient type
Multivariate power series reduction sequential use algorithm. Implements Mora
normal-form algorithm.
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Field Summary
Fields -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionboolean
contains
(List<MultiVarPowerSeries<C>> S, List<MultiVarPowerSeries<C>> B) Ideal containment.boolean
criterion4
(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B, ExpVector e) GB criterion 4.boolean
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.normalform
(List<MultiVarPowerSeries<C>> Pp, MultiVarPowerSeries<C> Ap) Top normal-form with Mora's algorithm.S-Power-series, S-polynomial.Total reduced normalform with Mora's algorithm.Total reduced normal-form with Mora's algorithm.
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug
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Constructor Details
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ReductionSeq
public ReductionSeq()Constructor.
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Method Details
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moduleCriterion
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.
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moduleCriterion
Module criterion.- Parameters:
modv
- number of module variables.ei
- ExpVector.ej
- ExpVector.- Returns:
- true if the module S-power-series(i,j) is required.
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criterion4
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.
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SPolynomial
S-Power-series, S-polynomial.- Parameters:
A
- power series.B
- power series.- Returns:
- spol(A,B) the S-power-series of A and B.
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normalform
public MultiVarPowerSeries<C> normalform(List<MultiVarPowerSeries<C>> Pp, MultiVarPowerSeries<C> Ap) Top normal-form with Mora's algorithm.- Parameters:
Pp
- power series list.Ap
- power series.- Returns:
- top-nf(Ap) with respect to Pp.
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totalNormalform
public MultiVarPowerSeries<C> totalNormalform(List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A) Total reduced normal-form with Mora's algorithm.- Parameters:
P
- power series list.A
- power series.- Returns:
- total-nf(A) with respect to P.
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totalNormalform
Total reduced normalform with Mora's algorithm.- Parameters:
P
- power series list.- Returns:
- total-nf(p) for p with respect to P\{p}.
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isTopReducible
Is top reducible.- Parameters:
P
- power series list.A
- power series.- Returns:
- true if A is top reducible with respect to P.
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contains
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
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