Package edu.jas.gb
Interface SolvableGroebnerBase<C extends RingElem<C>>
- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Serializable
- All Known Implementing Classes:
SGBProxy
,SolvableGroebnerBaseAbstract
,SolvableGroebnerBaseParallel
,SolvableGroebnerBasePseudoRecSeq
,SolvableGroebnerBasePseudoSeq
,SolvableGroebnerBaseSeq
,SolvableGroebnerBaseSeqPairParallel
Solvable Groebner Bases interface. Defines methods for left, right and
twosided Groebner bases and left, right and twosided GB tests.
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Method Summary
Modifier and TypeMethodDescriptionextLeftGB
(int modv, List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.Solvable Extended Groebner base using critical pair class.boolean
isLeftGB
(int modv, List<GenSolvablePolynomial<C>> F) Left Groebner base test.boolean
isLeftGB
(ModuleList<C> M) Module left Groebner base test.boolean
Left Groebner base test.boolean
Test if left reduction matrix.boolean
isLeftReductionMatrix
(List<GenSolvablePolynomial<C>> F, List<GenSolvablePolynomial<C>> G, List<List<GenSolvablePolynomial<C>>> Mf, List<List<GenSolvablePolynomial<C>>> Mg) Test if left reduction matrix.boolean
isRightGB
(int modv, List<GenSolvablePolynomial<C>> F) Right Groebner base test.boolean
isRightGB
(ModuleList<C> M) Module right Groebner base test.boolean
Right Groebner base test.boolean
isTwosidedGB
(int modv, List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base test.boolean
isTwosidedGB
(ModuleList<C> M) Module twosided Groebner base test.boolean
Twosided Groebner base test.leftGB
(int modv, List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.leftGB
(ModuleList<C> M) Left Groebner base using pairlist class.leftGB
(List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.Left minimal ordered groebner basis.rightGB
(int modv, List<GenSolvablePolynomial<C>> F) Right Groebner base using opposite ring left GB.rightGB
(ModuleList<C> M) Right Groebner base using pairlist class.Right Groebner base using opposite ring left GB.twosidedGB
(int modv, List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.twosidedGB
(ModuleList<C> M) Twosided Groebner base using pairlist class.twosidedGB
(List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.
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Method Details
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isLeftGB
Left Groebner base test.- Parameters:
F
- solvable polynomial list.- Returns:
- true, if F is a left Groebner base, else false.
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isLeftGB
Left Groebner base test.- 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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isTwosidedGB
Twosided Groebner base test.- Parameters:
Fp
- solvable polynomial list.- Returns:
- true, if Fp is a two-sided Groebner base, else false.
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isTwosidedGB
Twosided Groebner base test.- 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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isRightGB
Right Groebner base test.- Parameters:
F
- solvable polynomial list.- Returns:
- true, if F is a right Groebner base, else false.
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isRightGB
Right Groebner base test.- Parameters:
modv
- number of module variables.F
- solvable polynomial list.- Returns:
- true, if F is a right Groebner base, else false.
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leftGB
Left Groebner base using pairlist class.- Parameters:
F
- solvable polynomial list.- Returns:
- leftGB(F) a left Groebner base of F.
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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.- Parameters:
F
- solvable polynomial list.- Returns:
- a container for an extended left Groebner base of F.
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extLeftGB
Solvable Extended Groebner base using critical pair class.- Parameters:
modv
- module variable number.F
- solvable polynomial list.- Returns:
- a container for an extended left Groebner base of F.
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leftMinimalGB
Left minimal ordered groebner basis.- Parameters:
Gp
- a left Groebner base.- Returns:
- leftGBmi(F) a minimal left Groebner base of Gp.
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twosidedGB
Twosided Groebner base using pairlist class.- Parameters:
Fp
- solvable polynomial list.- Returns:
- tsGB(Fp) a twosided Groebner base of Fp.
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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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rightGB
Right Groebner base using opposite ring left GB.- Parameters:
F
- solvable polynomial list.- Returns:
- rightGB(F) a right Groebner base of F.
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rightGB
Right Groebner base using opposite ring left GB.- Parameters:
modv
- number of module variables.F
- solvable polynomial list.- Returns:
- rightGB(F) a right Groebner base of F.
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isLeftReductionMatrix
Test if left reduction matrix.- Parameters:
exgb
- an SolvableExtendedGB container.- Returns:
- true, if exgb contains a left reduction matrix, else false.
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isLeftReductionMatrix
boolean isLeftReductionMatrix(List<GenSolvablePolynomial<C>> F, List<GenSolvablePolynomial<C>> G, List<List<GenSolvablePolynomial<C>>> Mf, List<List<GenSolvablePolynomial<C>>> Mg) Test if left reduction matrix.- Parameters:
F
- a solvable polynomial list.G
- a left Groebner base.Mf
- a possible left reduction matrix.Mg
- a possible left reduction matrix.- Returns:
- true, if Mg and Mf are left reduction matrices, else false.
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isLeftGB
Module left Groebner base test.- Parameters:
M
- a module basis.- Returns:
- true, if M is a left Groebner base, else false.
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leftGB
Left Groebner base using pairlist class.- Parameters:
M
- a module basis.- Returns:
- leftGB(M) a left Groebner base for M.
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isTwosidedGB
Module twosided Groebner base test.- Parameters:
M
- a module basis.- Returns:
- true, if M is a twosided Groebner base, else false.
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twosidedGB
Twosided Groebner base using pairlist class.- Parameters:
M
- a module basis.- Returns:
- tsGB(M) a twosided Groebner base for M.
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isRightGB
Module right Groebner base test.- Parameters:
M
- a module basis.- Returns:
- true, if M is a right Groebner base, else false.
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rightGB
Right Groebner base using pairlist class.- Parameters:
M
- a module basis.- Returns:
- rightGB(M) a right Groebner base for M.
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