Package edu.jas.gbufd
Class SolvableGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
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- edu.jas.gb.SolvableGroebnerBaseAbstract<GenPolynomial<C>>
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- edu.jas.gbufd.SolvableGroebnerBasePseudoRecSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SolvableGroebnerBase<GenPolynomial<C>>
,java.io.Serializable
public class SolvableGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>> extends SolvableGroebnerBaseAbstract<GenPolynomial<C>>
Solvable Groebner Base with pseudo reduction sequential algorithm. Implements coefficient fraction free Groebner bases. Coefficients can for example be (commutative) multivariate polynomials.- Author:
- Heinz Kredel
- See Also:
GBAlgorithmBuilder
,GBFactory
, Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected GenPolynomialRing<C>
cofac
Coefficient ring factory.protected GreatestCommonDivisorAbstract<C>
engine
Greatest common divisor engine for coefficient content and primitive parts.protected SolvablePseudoReduction<GenPolynomial<C>>
sred
Pseudo reduction engine.protected SolvablePseudoReduction<C>
sredRec
Pseudo reduction engine.-
Fields inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract
blas, cbb, red, strategy
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Constructor Summary
Constructors Constructor Description SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)
Constructor.SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, PairList<GenPolynomial<C>> pl)
Constructor.SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red)
Constructor.SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red, PairList<GenPolynomial<C>> pl)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description boolean
isLeftGBidem(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base idempotence test.boolean
isLeftGBsimple(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base test.boolean
isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)
Twosided Groebner base test.java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>
leftGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base using pairlist class.java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>
leftMinimalGB(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Gp)
Minimal ordered Solvable Groebner basis.java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>
twosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)
Twosided Solvable Groebner base using pairlist class.-
Methods inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract
cancel, commonZeroTest, constructUnivariate, constructUnivariate, extLeftGB, extLeftGB, extRightGB, extRightGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftReductionMatrix, isLeftReductionMatrix, isRightGB, isRightGB, isRightGB, isRightGB, isRightGBidem, isRightGBidem, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGBidem, isTwosidedGBidem, leftGB, leftGB, leftGB, normalizeZerosOnes, rightGB, rightGB, rightGB, rightMinimalGB, terminate, twosidedGB, twosidedGB, twosidedGB, univariateDegrees
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Field Detail
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engine
protected final GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> engine
Greatest common divisor engine for coefficient content and primitive parts.
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sredRec
protected final SolvablePseudoReduction<C extends GcdRingElem<C>> sredRec
Pseudo reduction engine.
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sred
protected final SolvablePseudoReduction<GenPolynomial<C extends GcdRingElem<C>>> sred
Pseudo reduction engine.
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cofac
protected final GenPolynomialRing<C extends GcdRingElem<C>> cofac
Coefficient ring factory.
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Constructor Detail
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SolvableGroebnerBasePseudoRecSeq
public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)
Constructor.- Parameters:
rf
- coefficient ring factory.
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SolvableGroebnerBasePseudoRecSeq
public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, PairList<GenPolynomial<C>> pl)
Constructor.- Parameters:
rf
- coefficient ring factory.pl
- pair selection strategy
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SolvableGroebnerBasePseudoRecSeq
public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red)
Constructor.- Parameters:
rf
- coefficient ring factory.red
- pseudo reduction engine. Note: red must be an instance of PseudoReductionSeq.
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SolvableGroebnerBasePseudoRecSeq
public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red, PairList<GenPolynomial<C>> pl)
Constructor.- Parameters:
rf
- coefficient ring factory.red
- pseudo reduction engine. Note: red must be an instance of PseudoReductionSeq.pl
- pair selection strategy
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Method Detail
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leftGB
public java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> leftGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base using pairlist class.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- GB(F) a Groebner base of F.
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leftMinimalGB
public java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> leftMinimalGB(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Gp)
Minimal ordered Solvable Groebner basis.- Specified by:
leftMinimalGB
in interfaceSolvableGroebnerBase<C extends GcdRingElem<C>>
- Overrides:
leftMinimalGB
in classSolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
Gp
- a Solvable Groebner base.- Returns:
- a reduced Solvable Groebner base of Gp.
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twosidedGB
public java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> twosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)
Twosided Solvable Groebner base using pairlist class.- Parameters:
modv
- number of module variables.Fp
- solvable polynomial list.- Returns:
- tsGB(Fp) a twosided Groebner base of Fp.
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isLeftGBsimple
public boolean isLeftGBsimple(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base test.- Overrides:
isLeftGBsimple
in classSolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
modv
- number of module variables.F
- solvable polynomial list.- Returns:
- true, if F is a left Groebner base, else false.
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isLeftGBidem
public boolean isLeftGBidem(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)
Left Groebner base idempotence test.- Overrides:
isLeftGBidem
in classSolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
modv
- module variable number.F
- solvable polynomial list.- Returns:
- true, if F is equal to GB(F), else false.
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isTwosidedGB
public boolean isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)
Twosided Groebner base test.- Specified by:
isTwosidedGB
in interfaceSolvableGroebnerBase<C extends GcdRingElem<C>>
- Overrides:
isTwosidedGB
in classSolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
modv
- number of module variables.Fp
- solvable polynomial list.- Returns:
- true, if Fp is a two-sided Groebner base, else false.
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