Package edu.jas.gbufd
Interface RReduction<C extends RegularRingElem<C>>
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- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Reduction<C>
,java.io.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.- Author:
- Heinz Kredel
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description GenPolynomial<C>
booleanClosure(GenPolynomial<C> A)
Boolean closure, compute idempotent(ldcf(A)) A.GenPolynomial<C>
booleanRemainder(GenPolynomial<C> A)
Boolean remainder, compute idemComplement(ldcf(A)) A.boolean
isBooleanClosed(GenPolynomial<C> A)
Is boolean closed, test if A == idempotent(ldcf(A)) A.boolean
isBooleanClosed(java.util.List<GenPolynomial<C>> F)
Is boolean closed, test if all A in F are boolean closed.boolean
isStrongTopReducible(java.util.List<GenPolynomial<C>> P, GenPolynomial<C> A)
Is strong top reducible.java.util.List<GenPolynomial<C>>
reducedBooleanClosure(java.util.List<GenPolynomial<C>> F)
Reduced boolean closure, compute BC(A) for all A in F.java.util.List<GenPolynomial<C>>
reducedBooleanClosure(java.util.List<GenPolynomial<C>> F, GenPolynomial<C> A)
Reduced boolean closure, compute BC(A) modulo F.-
Methods inherited from interface edu.jas.gb.Reduction
criterion4, criterion4, criterion4, irreducibleSet, isNormalform, isNormalform, isReducible, isReductionNF, isTopReducible, moduleCriterion, moduleCriterion, normalform, normalform, normalform, SPolynomial, SPolynomial
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Method Detail
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isStrongTopReducible
boolean isStrongTopReducible(java.util.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:
A
- polynomial.P
- polynomial list.- Returns:
- true if A is string top reducible with respect to P.
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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.
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isBooleanClosed
boolean isBooleanClosed(java.util.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.
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booleanClosure
GenPolynomial<C> booleanClosure(GenPolynomial<C> A)
Boolean closure, compute idempotent(ldcf(A)) A.- Parameters:
A
- polynomial.- Returns:
- bc(A).
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booleanRemainder
GenPolynomial<C> booleanRemainder(GenPolynomial<C> A)
Boolean remainder, compute idemComplement(ldcf(A)) A.- Parameters:
A
- polynomial.- Returns:
- br(A) = A - bc(A).
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reducedBooleanClosure
java.util.List<GenPolynomial<C>> reducedBooleanClosure(java.util.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)).
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reducedBooleanClosure
java.util.List<GenPolynomial<C>> reducedBooleanClosure(java.util.List<GenPolynomial<C>> F, GenPolynomial<C> A)
Reduced boolean closure, compute BC(A) modulo F.- Parameters:
A
- polynomial.F
- polynomial list.- Returns:
- red(bc(A)).
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