Package edu.jas.gb
Interface SolvableReduction<C extends RingElem<C>>
- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Serializable
- All Known Subinterfaces:
SolvablePseudoReduction<C>
- All Known Implementing Classes:
SolvablePseudoReductionSeq
,SolvableReductionAbstract
,SolvableReductionPar
,SolvableReductionSeq
Solvable polynomial Reduction interface. Defines S-Polynomial, normalform and
irreducible set.
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Method Summary
Modifier and TypeMethodDescriptionboolean
isLeftReductionNF
(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np) Is reduction of normal form.boolean
Is in normalform.boolean
Is reducible.boolean
isRightReductionNF
(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np) Is right reduction of normal form.boolean
Is top reducible.Left irreducible set.leftNormalform
(List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) Left Normalform.leftNormalform
(List<GenSolvablePolynomial<C>> Pp, List<GenSolvablePolynomial<C>> Ap) Left Normalform Set.leftNormalform
(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) LeftNormalform with recording.Left S-Polynomial.leftSPolynomial
(List<GenSolvablePolynomial<C>> S, int i, GenSolvablePolynomial<C> Ap, int j, GenSolvablePolynomial<C> Bp) S-Polynomial with recording.normalform
(List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) Two-sided Normalform.rightNormalform
(List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) Right Normalform.rightNormalform
(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) RightNormalform with recording.Right S-Polynomial.
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Method Details
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leftSPolynomial
Left S-Polynomial.- Parameters:
Ap
- solvable polynomial.Bp
- solvable polynomial.- Returns:
- left-spol(Ap,Bp) the left S-polynomial of Ap and Bp.
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leftSPolynomial
GenSolvablePolynomial<C> leftSPolynomial(List<GenSolvablePolynomial<C>> S, int i, GenSolvablePolynomial<C> Ap, int j, GenSolvablePolynomial<C> Bp) S-Polynomial with recording.- Parameters:
S
- recording matrix, is modified.i
- index of Ap in basis list.Ap
- a polynomial.j
- index of Bp in basis list.Bp
- a polynomial.- Returns:
- leftSpol(Ap, Bp), the left S-Polynomial for Ap and Bp.
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leftNormalform
GenSolvablePolynomial<C> leftNormalform(List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) Left Normalform.- Parameters:
Pp
- solvable polynomial list.Ap
- solvable polynomial.- Returns:
- left-nf(Ap) with respect to Pp.
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leftNormalform
GenSolvablePolynomial<C> leftNormalform(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) LeftNormalform with recording.- Parameters:
row
- recording matrix, is modified.Pp
- a polynomial list for reduction.Ap
- a polynomial.- Returns:
- nf(Pp,Ap), the left normal form of Ap wrt. Pp.
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leftNormalform
List<GenSolvablePolynomial<C>> leftNormalform(List<GenSolvablePolynomial<C>> Pp, List<GenSolvablePolynomial<C>> Ap) Left Normalform Set.- Parameters:
Pp
- solvable polynomial list.Ap
- solvable polynomial list.- Returns:
- list of left-nf(a) with respect to Pp for all a in Ap.
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leftIrreducibleSet
Left irreducible set.- Parameters:
Pp
- solvable polynomial list.- Returns:
- a list P of solvable polynomials which are in normalform wrt. P.
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isLeftReductionNF
boolean isLeftReductionNF(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np) Is reduction of normal form.- Parameters:
row
- recording matrix, is modified.Pp
- a solvable polynomial list for reduction.Ap
- a solvable polynomial.Np
- nf(Pp,Ap), a left normal form of Ap wrt. Pp.- Returns:
- true, if Np + sum( row[i]*Pp[i] ) == Ap, else false.
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rightSPolynomial
Right S-Polynomial.- Parameters:
Ap
- solvable polynomial.Bp
- solvable polynomial.- Returns:
- right-spol(Ap,Bp) the right S-polynomial of Ap and Bp.
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rightNormalform
GenSolvablePolynomial<C> rightNormalform(List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) Right Normalform.- Parameters:
Pp
- solvable polynomial list.Ap
- solvable polynomial.- Returns:
- right-nf(Ap) with respect to Pp.
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rightNormalform
GenSolvablePolynomial<C> rightNormalform(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap) RightNormalform with recording.- Parameters:
row
- recording matrix, is modified.Pp
- a polynomial list for reduction.Ap
- a polynomial.- Returns:
- nf(Pp,Ap), the right normal form of Ap wrt. Pp.
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isTopReducible
Is top reducible. Condition is lt(B) | lt(A) for some B in F. Is left right symmetric.- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is top reducible with respect to P.
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isReducible
Is reducible. Is left right symmetric.- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is reducible with respect to P.
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isNormalform
Is in normalform. Is left right symmetric.- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is in normalform with respect to P.
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isRightReductionNF
boolean isRightReductionNF(List<GenSolvablePolynomial<C>> row, List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np) Is right reduction of normal form.- Parameters:
row
- recording matrix, is modified.Pp
- a solvable polynomial list for reduction.Ap
- a solvable polynomial.Np
- nf(Pp,Ap), a right normal form of Ap wrt. Pp.- Returns:
- true, if Np + sum( Pp[i]*row[i] ) == Ap, else false.
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normalform
Two-sided Normalform.- Parameters:
Pp
- solvable polynomial list.Ap
- solvable polynomial.- Returns:
- two-sided-nf(Ap) with respect to Pp.
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