Package edu.jas.gb
Interface SolvableGroebnerBase<C extends RingElem<C>>
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- Type Parameters:
C
- coefficient type
- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
SGBProxy
,SolvableGroebnerBaseAbstract
,SolvableGroebnerBaseParallel
,SolvableGroebnerBasePseudoRecSeq
,SolvableGroebnerBasePseudoSeq
,SolvableGroebnerBaseSeq
,SolvableGroebnerBaseSeqPairParallel
public interface SolvableGroebnerBase<C extends RingElem<C>> extends java.io.Serializable
Solvable Groebner Bases interface. Defines methods for left, right and twosided Groebner bases and left, right and twosided GB tests.- Author:
- Heinz Kredel
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description SolvableExtendedGB<C>
extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Solvable Extended Groebner base using critical pair class.SolvableExtendedGB<C>
extLeftGB(java.util.List<GenSolvablePolynomial<C>> F)
Solvable Extended Groebner base using critical pair class.boolean
isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Left Groebner base test.boolean
isLeftGB(ModuleList<C> M)
Module left Groebner base test.boolean
isLeftGB(java.util.List<GenSolvablePolynomial<C>> F)
Left Groebner base test.boolean
isLeftReductionMatrix(SolvableExtendedGB<C> exgb)
Test if left reduction matrix.boolean
isLeftReductionMatrix(java.util.List<GenSolvablePolynomial<C>> F, java.util.List<GenSolvablePolynomial<C>> G, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg)
Test if left reduction matrix.boolean
isRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Right Groebner base test.boolean
isRightGB(ModuleList<C> M)
Module right Groebner base test.boolean
isRightGB(java.util.List<GenSolvablePolynomial<C>> F)
Right Groebner base test.boolean
isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)
Twosided Groebner base test.boolean
isTwosidedGB(ModuleList<C> M)
Module twosided Groebner base test.boolean
isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)
Twosided Groebner base test.java.util.List<GenSolvablePolynomial<C>>
leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Left Groebner base using pairlist class.ModuleList<C>
leftGB(ModuleList<C> M)
Left Groebner base using pairlist class.java.util.List<GenSolvablePolynomial<C>>
leftGB(java.util.List<GenSolvablePolynomial<C>> F)
Left Groebner base using pairlist class.java.util.List<GenSolvablePolynomial<C>>
leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)
Left minimal ordered groebner basis.java.util.List<GenSolvablePolynomial<C>>
rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Right Groebner base using opposite ring left GB.ModuleList<C>
rightGB(ModuleList<C> M)
Right Groebner base using pairlist class.java.util.List<GenSolvablePolynomial<C>>
rightGB(java.util.List<GenSolvablePolynomial<C>> F)
Right Groebner base using opposite ring left GB.java.util.List<GenSolvablePolynomial<C>>
twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)
Twosided Groebner base using pairlist class.ModuleList<C>
twosidedGB(ModuleList<C> M)
Twosided Groebner base using pairlist class.java.util.List<GenSolvablePolynomial<C>>
twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)
Twosided Groebner base using pairlist class.
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Method Detail
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isLeftGB
boolean isLeftGB(java.util.List<GenSolvablePolynomial<C>> F)
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
boolean isLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
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
boolean isTwosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)
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
boolean isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)
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
boolean isRightGB(java.util.List<GenSolvablePolynomial<C>> F)
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
boolean isRightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
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
java.util.List<GenSolvablePolynomial<C>> leftGB(java.util.List<GenSolvablePolynomial<C>> F)
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
java.util.List<GenSolvablePolynomial<C>> leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
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
SolvableExtendedGB<C> extLeftGB(java.util.List<GenSolvablePolynomial<C>> F)
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
SolvableExtendedGB<C> extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
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
java.util.List<GenSolvablePolynomial<C>> leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)
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
java.util.List<GenSolvablePolynomial<C>> twosidedGB(java.util.List<GenSolvablePolynomial<C>> Fp)
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
java.util.List<GenSolvablePolynomial<C>> twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)
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
java.util.List<GenSolvablePolynomial<C>> rightGB(java.util.List<GenSolvablePolynomial<C>> F)
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
java.util.List<GenSolvablePolynomial<C>> rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)
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
boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)
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(java.util.List<GenSolvablePolynomial<C>> F, java.util.List<GenSolvablePolynomial<C>> G, java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf, java.util.List<java.util.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
boolean isLeftGB(ModuleList<C> M)
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
ModuleList<C> leftGB(ModuleList<C> M)
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
boolean isTwosidedGB(ModuleList<C> M)
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
ModuleList<C> twosidedGB(ModuleList<C> M)
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
boolean isRightGB(ModuleList<C> M)
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
ModuleList<C> rightGB(ModuleList<C> M)
Right Groebner base using pairlist class.- Parameters:
M
- a module basis.- Returns:
- rightGB(M) a right Groebner base for M.
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