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

  • Field Details

    • logger

      private static final org.apache.logging.log4j.Logger logger

    • debug

      private static final boolean debug

  • Constructor Details

    • ReductionSeq

      public ReductionSeq()
      Constructor.

  • Method Details

    • 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(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.

    • 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.

    • totalNormalform

      public List<MultiVarPowerSeries<C>> totalNormalform(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(List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A)
      Is top reducible.
      Parameters:
      P - power series list.
      A - power series.
      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