Package edu.jas.application
Class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>
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- edu.jas.application.ComprehensiveGroebnerBaseSeq<C>
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- Type Parameters:
C
- coefficient type
public class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>> extends java.lang.Object
Comprehensive Groebner Base sequential algorithm. Implements faithful comprehensive Groebner bases via Groebner systems and CGB test.- Author:
- Heinz Kredel
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Field Summary
Fields Modifier and Type Field Description protected RingFactory<C>
cofac
Polynomial coefficient ring factory.protected CReductionSeq<C>
cred
Comprehensive reduction engine.protected SquarefreeAbstract<C>
engine
Squarefree for coefficient content and primitive parts.
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Constructor Summary
Constructors Constructor Description ComprehensiveGroebnerBaseSeq(CReductionSeq<C> red, RingFactory<C> rf)
Constructor.ComprehensiveGroebnerBaseSeq(RingFactory<C> rf)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.util.List<ColoredSystem<C>>
determineAddPairs(ColoredSystem<C> cs, ColorPolynomial<C> A)
Determine polynomial relative to a condition of a colored system and add pairs.java.util.List<GenPolynomial<GenPolynomial<C>>>
GB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive Groebner base via Groebner system.GroebnerSystem<C>
GBsys(java.util.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, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test.boolean
isGB(GroebnerSystem<C> F)
Comprehensive-Groebner system and base test.boolean
isGB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test.boolean
isGBcol(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test using colored systems.boolean
isGBcol(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test using colored systems.boolean
isGBsubst(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test using substitution.boolean
isGBsubst(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test using substitution.boolean
isGBsys(int modv, java.util.List<ColoredSystem<C>> CS)
Comprehensive-Groebner system test.boolean
isGBsys(GroebnerSystem<C> F)
Comprehensive-Groebner system test.boolean
isGBsys(java.util.List<ColoredSystem<C>> CS)
Comprehensive-Groebner system test.ColoredSystem<C>
minimalGB(ColoredSystem<C> cs)
Minimal ordered Groebner basis.
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Field Detail
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engine
protected final SquarefreeAbstract<C extends GcdRingElem<C>> engine
Squarefree for coefficient content and primitive parts.
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cred
protected final CReductionSeq<C extends GcdRingElem<C>> cred
Comprehensive reduction engine.
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cofac
protected final RingFactory<C extends GcdRingElem<C>> cofac
Polynomial coefficient ring factory.
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Constructor Detail
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ComprehensiveGroebnerBaseSeq
public ComprehensiveGroebnerBaseSeq(RingFactory<C> rf)
Constructor.- Parameters:
rf
- base coefficient ring factory.
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ComprehensiveGroebnerBaseSeq
public ComprehensiveGroebnerBaseSeq(CReductionSeq<C> red, RingFactory<C> rf)
Constructor.- Parameters:
red
- C-pseudo-Reduction enginerf
- base coefficient ring factory.
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Method Detail
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isGB
public boolean isGB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive-Groebner base test.- Parameters:
F
- polynomial list.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGB
public boolean isGB(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public boolean isGBcol(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public boolean isGBcol(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public boolean isGBsys(java.util.List<ColoredSystem<C>> CS)
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
public boolean isGBsys(int modv, java.util.List<ColoredSystem<C>> CS)
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
public boolean isGBsubst(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public boolean isGBsubst(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public boolean isGBsys(GroebnerSystem<C> F)
Comprehensive-Groebner system test.- Parameters:
F
- Groebner system.- Returns:
- true, if F is a Comprehensive-Groebner system, else false.
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isCGB
public boolean isCGB(GroebnerSystem<C> F)
Comprehensive-Groebner base test.- Parameters:
F
- Groebner system.- Returns:
- true, if F is a Comprehensive-Groebner base, else false.
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isGB
public boolean isGB(GroebnerSystem<C> F)
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
public GroebnerSystem<C> GBsys(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
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
public java.util.List<ColoredSystem<C>> determineAddPairs(ColoredSystem<C> cs, ColorPolynomial<C> A)
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
public java.util.List<GenPolynomial<GenPolynomial<C>>> GB(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
Comprehensive Groebner base via Groebner system.- Parameters:
F
- polynomial list.- Returns:
- GB(F) a Comprehensive Groebner base of F.
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minimalGB
public ColoredSystem<C> minimalGB(ColoredSystem<C> cs)
Minimal ordered Groebner basis.- Parameters:
cs
- colored system.- Returns:
- a reduced Groebner base of Gp.
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