Package edu.jas.gb
Class SolvableGroebnerBaseSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.SolvableGroebnerBaseAbstract<C>
edu.jas.gb.SolvableGroebnerBaseSeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SolvableGroebnerBase<C>
,Serializable
Solvable Groebner bases sequential algorithms. Implements common left, right
and twosided Groebner bases and left, right and twosided GB tests.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
private static final org.apache.logging.log4j.Logger
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Constructor Summary
ConstructorsConstructorDescriptionConstructor.Constructor.Constructor.SolvableGroebnerBaseSeq
(SolvableReduction<C> sred, PairList<C> pl) Constructor. -
Method Summary
Modifier and TypeMethodDescriptionextLeftGB
(int modv, List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.boolean
Test if M is a left reduction matrix.leftGB
(int modv, List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.minimalSolvableExtendedGB
(int flen, List<GenSolvablePolynomial<C>> Gp, List<List<GenSolvablePolynomial<C>>> M) Minimal solvable extended groebner basis.normalizeMatrix
(int flen, List<List<GenSolvablePolynomial<C>>> M) Normalize M.rightGB
(int modv, List<GenSolvablePolynomial<C>> F) Right Groebner base via right reduction using pairlist class.twosidedGB
(int modv, List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.Methods inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract
cancel, commonZeroTest, constructUnivariate, constructUnivariate, extLeftGB, extRightGB, extRightGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGBidem, isLeftGBsimple, isLeftReductionMatrix, isRightGB, isRightGB, isRightGB, isRightGB, isRightGBidem, isRightGBidem, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGBidem, isTwosidedGBidem, leftGB, leftGB, leftGB, leftMinimalGB, normalizeZerosOnes, rightGB, rightGB, rightMinimalGB, terminate, twosidedGB, twosidedGB, twosidedGB, univariateDegrees
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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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SolvableGroebnerBaseSeq
public SolvableGroebnerBaseSeq()Constructor. -
SolvableGroebnerBaseSeq
Constructor.- Parameters:
sred
- Solvable reduction engine
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SolvableGroebnerBaseSeq
Constructor.- Parameters:
pl
- pair selection strategy
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SolvableGroebnerBaseSeq
Constructor.- Parameters:
sred
- Solvable reduction enginepl
- pair selection strategy
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Method Details
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leftGB
Left Groebner base using pairlist class.- Parameters:
modv
- number of module variables.F
- solvable polynomial list.- Returns:
- leftGB(F) a left Groebner base of F.
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extLeftGB
Solvable Extended Groebner base using critical pair class.- Specified by:
extLeftGB
in interfaceSolvableGroebnerBase<C extends RingElem<C>>
- Overrides:
extLeftGB
in classSolvableGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
modv
- module variable number.F
- solvable polynomial list.- Returns:
- a container for an extended left Groebner base of F.
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twosidedGB
Twosided 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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normalizeMatrix
public List<List<GenSolvablePolynomial<C>>> normalizeMatrix(int flen, List<List<GenSolvablePolynomial<C>>> M) Normalize M. Make all rows the same size and make certain column elements zero.- Parameters:
M
- a reduction matrix.- Returns:
- normalized M.
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isLeftReductionMatrix
Test if M is a left reduction matrix.- Specified by:
isLeftReductionMatrix
in interfaceSolvableGroebnerBase<C extends RingElem<C>>
- Overrides:
isLeftReductionMatrix
in classSolvableGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
exgb
- an SolvableExtendedGB container.- Returns:
- true, if exgb contains a left reduction matrix, else false.
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minimalSolvableExtendedGB
public SolvableExtendedGB<C> minimalSolvableExtendedGB(int flen, List<GenSolvablePolynomial<C>> Gp, List<List<GenSolvablePolynomial<C>>> M) Minimal solvable extended groebner basis.- Parameters:
Gp
- a left Groebner base.M
- a left reduction matrix, is modified.- Returns:
- a (partially) reduced left Groebner base of Gp in a container.
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rightGB
Right Groebner base via right reduction using pairlist class. Overrides rightGB() via opposite ring.- Specified by:
rightGB
in interfaceSolvableGroebnerBase<C extends RingElem<C>>
- Overrides:
rightGB
in classSolvableGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
modv
- number of module variables.F
- solvable polynomial list.- Returns:
- rightGB(F) a right Groebner base of F.
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