Package edu.jas.gbufd

Interface RReduction<C extends RegularRingElem<C>>

Type Parameters:
C - coefficient type
All Superinterfaces:
Reduction<C>, Serializable
All Known Subinterfaces:
RPseudoReduction<C>
All Known Implementing Classes:
RPseudoReductionSeq, RReductionSeq

public interface RReduction<C extends RegularRingElem<C>> extends Reduction<C>
Polynomial R Reduction interface. Defines additionally boolean closure methods.
  • Method Details

    • isStrongTopReducible

      boolean isStrongTopReducible(List<GenPolynomial<C>> P, GenPolynomial<C> A)
      Is strong top reducible. Condition is idempotent(a) == idempotent(b), for a=ldcf(A) and b=ldcf(B) and lt(B) | lt(A) for some B in F.
      Parameters:
      P - polynomial list.
      A - polynomial.
      Returns:
      true if A is string top reducible with respect to P.
    • isBooleanClosed

      boolean isBooleanClosed(GenPolynomial<C> A)
      Is boolean closed, test if A == idempotent(ldcf(A)) A.
      Parameters:
      A - polynomial.
      Returns:
      true if A is boolean closed, else false.
    • isBooleanClosed

      boolean isBooleanClosed(List<GenPolynomial<C>> F)
      Is boolean closed, test if all A in F are boolean closed.
      Parameters:
      F - polynomial list.
      Returns:
      true if F is boolean closed, else false.
    • booleanClosure

      GenPolynomial<C> booleanClosure(GenPolynomial<C> A)
      Boolean closure, compute idempotent(ldcf(A)) A.
      Parameters:
      A - polynomial.
      Returns:
      bc(A).
    • booleanRemainder

      GenPolynomial<C> booleanRemainder(GenPolynomial<C> A)
      Boolean remainder, compute idemComplement(ldcf(A)) A.
      Parameters:
      A - polynomial.
      Returns:
      br(A) = A - bc(A).
    • reducedBooleanClosure

      List<GenPolynomial<C>> reducedBooleanClosure(List<GenPolynomial<C>> F)
      Reduced boolean closure, compute BC(A) for all A in F.
      Parameters:
      F - polynomial list.
      Returns:
      red(bc(F)) = bc(red(F)).
    • reducedBooleanClosure

      List<GenPolynomial<C>> reducedBooleanClosure(List<GenPolynomial<C>> F, GenPolynomial<C> A)
      Reduced boolean closure, compute BC(A) modulo F.
      Parameters:
      F - polynomial list.
      A - polynomial.
      Returns:
      red(bc(A)).