ReductionSeq
edu.jas.ps

Class ReductionSeq<C extends RingElem<C>>

  • Type Parameters:
    C - coefficient type


    public class ReductionSeq<C extends RingElem<C>>extends Object
    Multivariate power series reduction sequential use algorithm. Implements Mora normal-form 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.
      • isTopReducible

        public boolean isTopReducible(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(List<MultiVarPowerSeries<C>> S,               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

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