Package edu.jas.gb
Class ReductionAbstract<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.ReductionAbstract<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
Reduction<C>
,Serializable
- Direct Known Subclasses:
DReductionSeq
,PseudoReductionPar
,PseudoReductionSeq
,ReductionPar
,ReductionSeq
,RReductionSeq
public abstract class ReductionAbstract<C extends RingElem<C>>
extends Object
implements Reduction<C>
Polynomial Reduction abstract class. Implements common S-Polynomial,
normalform, criterion 4 module criterion and irreducible set.
- See Also:
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Field Summary
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionboolean
criterion4
(ExpVector ei, ExpVector ej, ExpVector e) GB criterium 4.boolean
criterion4
(GenPolynomial<C> A, GenPolynomial<C> B) GB criterium 4.boolean
criterion4
(GenPolynomial<C> A, GenPolynomial<C> B, ExpVector e) GB criterium 4.irreducibleSet
(List<GenPolynomial<C>> Pp) Irreducible set.boolean
isNormalform
(List<GenPolynomial<C>> Pp) Is in Normalform.boolean
isNormalform
(List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Is in Normalform.boolean
isReducible
(List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Is reducible.boolean
isReductionNF
(List<GenPolynomial<C>> row, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap, GenPolynomial<C> Np) Is reduction of normal form.boolean
isTopReducible
(List<GenPolynomial<C>> P, GenPolynomial<C> A) Is top reducible.boolean
moduleCriterion
(int modv, ExpVector ei, ExpVector ej) Module criterium.boolean
moduleCriterion
(int modv, GenPolynomial<C> A, GenPolynomial<C> B) Module criterium.normalform
(ModuleList<C> Pp, ModuleList<C> Ap) Module normalform set.normalform
(ModuleList<C> Pp, ModuleList<C> Ap, boolean top) Module normalform set.normalform
(List<GenPolynomial<C>> Pp, List<GenPolynomial<C>> Ap) Normalform Set.normalformMarked
(List<Monomial<C>> Mp, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with respect to marked head terms.SPolynomial
(GenPolynomial<C> A, GenPolynomial<C> B) S-Polynomial.SPolynomial
(List<GenPolynomial<C>> S, int i, GenPolynomial<C> A, int j, GenPolynomial<C> B) S-Polynomial with recording.Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface edu.jas.gb.Reduction
normalform, normalform
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug
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Constructor Details
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ReductionAbstract
public ReductionAbstract()Constructor.
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Method Details
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SPolynomial
S-Polynomial.- Specified by:
SPolynomial
in interfaceReduction<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.- Returns:
- spol(A,B) the S-polynomial of A and B.
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SPolynomial
public GenPolynomial<C> SPolynomial(List<GenPolynomial<C>> S, int i, GenPolynomial<C> A, int j, GenPolynomial<C> B) S-Polynomial with recording.- Specified by:
SPolynomial
in interfaceReduction<C extends RingElem<C>>
- Parameters:
S
- recording matrix, is modified. Note the negative S-polynomial is recorded as required by all applications.i
- index of A in basis list.A
- a polynomial.j
- index of B in basis list.B
- a polynomial.- Returns:
- Spol(A, B), the S-Polynomial for A and B.
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moduleCriterion
Module criterium.- Specified by:
moduleCriterion
in interfaceReduction<C extends RingElem<C>>
- Parameters:
modv
- number of module variables.A
- polynomial.B
- polynomial.- Returns:
- true if the module S-polynomial(i,j) is required.
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moduleCriterion
Module criterium.- Specified by:
moduleCriterion
in interfaceReduction<C extends RingElem<C>>
- Parameters:
modv
- number of module variables.ei
- ExpVector.ej
- ExpVector.- Returns:
- true if the module S-polynomial(i,j) is required.
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criterion4
GB criterium 4. Use only for commutative polynomial rings.- Specified by:
criterion4
in interfaceReduction<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.e
- = lcm(ht(A),ht(B))- Returns:
- true if the S-polynomial(i,j) is required, else false.
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criterion4
GB criterium 4. Use only for commutative polynomial rings.- Specified by:
criterion4
in interfaceReduction<C extends RingElem<C>>
- Parameters:
ei
- exponent vector.ej
- exponent vector.e
- = lcm(ei,ej)- Returns:
- true if the S-polynomial(i,j) is required, else false.
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criterion4
GB criterium 4.- Specified by:
criterion4
in interfaceReduction<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.- Returns:
- true if the S-polynomial(i,j) is required, else false.
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normalformMarked
public GenPolynomial<C> normalformMarked(List<Monomial<C>> Mp, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with respect to marked head terms.- Parameters:
Mp
- leading monomial list.Pp
- polynomial list.Ap
- polynomial.- Returns:
- nf(Ap) with respect to Mp+Pp.
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normalform
Normalform Set.- Specified by:
normalform
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial list.- Returns:
- list of nf(a) with respect to Pp for all a in Ap.
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normalform
Module normalform set.- Parameters:
Pp
- module list.Ap
- module list.- Returns:
- list of nf(a) with respect to Pp for all a in Ap.
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normalform
Module normalform set.- Parameters:
Pp
- module list.Ap
- module list.top
- true for TOP term order, false for POT term order.- Returns:
- list of nf(a) with respect to Pp for all a in Ap.
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isTopReducible
Is top reducible.- Specified by:
isTopReducible
in interfaceReduction<C extends RingElem<C>>
- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is top reducible with respect to P.
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isReducible
Is reducible.- Specified by:
isReducible
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- true if Ap is reducible with respect to Pp.
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isNormalform
Is in Normalform.- Specified by:
isNormalform
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- true if Ap is in normalform with respect to Pp.
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isNormalform
Is in Normalform.- Specified by:
isNormalform
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- true if each Ap in Pp is in normalform with respect to Pp\{Ap}.
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irreducibleSet
Irreducible set.- Specified by:
irreducibleSet
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- a list P of monic polynomials which are in normalform wrt. P and with ideal(Pp) = ideal(P).
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isReductionNF
public boolean isReductionNF(List<GenPolynomial<C>> row, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap, GenPolynomial<C> Np) Is reduction of normal form.- Specified by:
isReductionNF
in interfaceReduction<C extends RingElem<C>>
- Parameters:
row
- recording matrix.Pp
- a polynomial list for reduction.Ap
- a polynomial.Np
- = nf(Pp,Ap), a normal form of Ap wrt. Pp.- Returns:
- true, if Ap == sum( row[i]*Pp[i] ) + Np, else false. //??
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