Package edu.jas.application
Class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.application.ComprehensiveGroebnerBaseSeq<C>
- Type Parameters:
C
- coefficient type
Comprehensive Groebner Base sequential algorithm. Implements faithful
comprehensive Groebner bases via Groebner systems and CGB test.
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected final RingFactory
<C> Polynomial coefficient ring factory.protected final CReductionSeq
<C> Comprehensive reduction engine.private static final boolean
protected final SquarefreeAbstract
<C> Squarefree for coefficient content and primitive parts.private static final org.apache.logging.log4j.Logger
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Constructor Summary
ConstructorsConstructorDescriptionComprehensiveGroebnerBaseSeq
(CReductionSeq<C> red, RingFactory<C> rf) Constructor.Constructor. -
Method Summary
Modifier and TypeMethodDescriptiondetermineAddPairs
(ColoredSystem<C> cs, ColorPolynomial<C> A) Determine polynomial relative to a condition of a colored system and add pairs.GB
(List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive Groebner base via Groebner system.GBsys
(List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive Groebner base system using pairlist class.boolean
isCGB
(GroebnerSystem<C> F) Comprehensive-Groebner base test.boolean
isGB
(int modv, List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test.boolean
isGB
(GroebnerSystem<C> F) Comprehensive-Groebner system and base test.boolean
isGB
(List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test.boolean
isGBcol
(int modv, List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using colored systems.boolean
isGBcol
(List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using colored systems.boolean
isGBsubst
(int modv, List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using substitution.boolean
isGBsubst
(List<GenPolynomial<GenPolynomial<C>>> F) Comprehensive-Groebner base test using substitution.boolean
isGBsys
(int modv, List<ColoredSystem<C>> CS) Comprehensive-Groebner system test.boolean
isGBsys
(GroebnerSystem<C> F) Comprehensive-Groebner system test.boolean
isGBsys
(List<ColoredSystem<C>> CS) Comprehensive-Groebner system test.minimalGB
(ColoredSystem<C> cs) Minimal ordered Groebner basis.
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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 -
engine
Squarefree for coefficient content and primitive parts. -
cred
Comprehensive reduction engine. -
cofac
Polynomial coefficient ring factory.
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Constructor Details
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ComprehensiveGroebnerBaseSeq
Constructor.- Parameters:
rf
- base coefficient ring factory.
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ComprehensiveGroebnerBaseSeq
Constructor.- Parameters:
red
- C-pseudo-Reduction enginerf
- base coefficient ring factory.
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Method Details
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isGB
Comprehensive-Groebner base test.- Parameters:
F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGB
Comprehensive-Groebner base test.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGBcol
Comprehensive-Groebner base test using colored systems.- Parameters:
F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGBcol
Comprehensive-Groebner base test using colored systems.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGBsys
Comprehensive-Groebner system test.- Parameters:
CS
- list of colored systems.- Returns:
- true, if CS is a Comprehensive-Groebner system, else false.
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isGBsys
Comprehensive-Groebner system test.- Parameters:
modv
- module variable number, unused.CS
- list of colored systems.- Returns:
- true, if CS is a Comprehensive-Groebner system, else false.
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isGBsubst
Comprehensive-Groebner base test using substitution.- Parameters:
F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGBsubst
Comprehensive-Groebner base test using substitution.- Parameters:
modv
- module variable number, unused.F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGBsys
Comprehensive-Groebner system test.- Parameters:
F
- Groebner system.- Returns:
- true, if F is a Comprehensive-Groebner system, else false.
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isCGB
Comprehensive-Groebner base test.- Parameters:
F
- Groebner system.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGB
Comprehensive-Groebner system and base test.- Parameters:
F
- Groebner system.- Returns:
- true, if F is a Comprehensive-Groebner system and base, else false.
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GBsys
Comprehensive Groebner base system using pairlist class.- Parameters:
F
- polynomial list.- Returns:
- GBsys(F) a Comprehensive Groebner system of F.
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determineAddPairs
Determine polynomial relative to a condition of a colored system and add pairs.- Parameters:
cs
- a colored system.A
- color polynomial.- Returns:
- list of colored systems, the conditions extending the condition of cs.
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GB
Comprehensive Groebner base via Groebner system.- Parameters:
F
- polynomial list.- Returns:
- GB(F) a Comprehensive Groebner base of F.
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minimalGB
Minimal ordered Groebner basis.- Parameters:
cs
- colored system.- Returns:
- a reduced Groebner base of Gp.
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