edu.jas.gbufd

Interface RReduction<C extends RegularRingElem<C>>

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

Method Summary

Modifier and Type	Method and 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

Method Detail

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.

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(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.

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

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)).

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)).