Package edu.jas.gbufd
Interface Syzygy<C extends RingElem<C>>
- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Serializable
- All Known Implementing Classes:
SyzygyAbstract
,SyzygySeq
Syzygy interface. Defines Syzygy computations and tests.
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Method Summary
Modifier and TypeMethodDescriptionboolean
isZeroRelation
(ModuleList<C> Z, ModuleList<C> F) Test if sysygy of modules.boolean
isZeroRelation
(List<List<GenPolynomial<C>>> Z, List<GenPolynomial<C>> F) Test if sysygy.resolution
(ModuleList<C> M) Resolution of a module.Resolution of a polynomial list.Resolution of a module.Resolution of a polynomial list.List
<List<GenPolynomial<C>>> zeroRelations
(int modv, GenVector<GenPolynomial<C>> v) Syzygy module from Groebner base.List
<List<GenPolynomial<C>>> zeroRelations
(int modv, List<GenPolynomial<C>> F) Syzygy module from Groebner base.zeroRelations
(ModuleList<C> M) Syzygy module from module Groebner base.List
<List<GenPolynomial<C>>> zeroRelations
(List<GenPolynomial<C>> F) Syzygy module from Groebner base.List
<List<GenPolynomial<C>>> zeroRelationsArbitrary
(int modv, List<GenPolynomial<C>> F) Syzygy module from arbitrary base.Syzygy module from arbitrary module base.List
<List<GenPolynomial<C>>> Syzygy module from arbitrary base.
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Method Details
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zeroRelations
Syzygy module from Groebner base. F must be a Groebner base.- Parameters:
F
- a Groebner base.- Returns:
- syz(F), a basis for the module of syzygies for F.
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zeroRelations
Syzygy module from Groebner base. F must be a Groebner base.- Parameters:
modv
- number of module variables.F
- a Groebner base.- Returns:
- syz(F), a basis for the module of syzygies for F.
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zeroRelations
Syzygy module from Groebner base. v must be a Groebner base.- Parameters:
modv
- number of module variables.v
- a Groebner base.- Returns:
- syz(v), a basis for the module of syzygies for v.
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zeroRelations
Syzygy module from module Groebner base. M must be a module Groebner base.- Parameters:
M
- a module Groebner base.- Returns:
- syz(M), a basis for the module of syzygies for M.
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isZeroRelation
Test if sysygy.- Parameters:
Z
- list of sysygies.F
- a polynomial list.- Returns:
- true, if Z is a list of syzygies for F, else false.
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isZeroRelation
Test if sysygy of modules.- Parameters:
Z
- list of sysygies.F
- a module list.- Returns:
- true, if Z is a list of syzygies for F, else false.
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resolution
Resolution of a module. Only with direct GBs.- Parameters:
M
- a module list of a Groebner basis.- Returns:
- a resolution of M.
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resolution
Resolution of a polynomial list. Only with direct GBs.- Parameters:
F
- a polynomial list of a Groebner basis.- Returns:
- a resolution of F.
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resolutionArbitrary
Resolution of a polynomial list.- Parameters:
F
- a polynomial list of an arbitrary basis.- Returns:
- a resolution of F.
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resolutionArbitrary
Resolution of a module.- Parameters:
M
- a module list of an arbitrary basis.- Returns:
- a resolution of M.
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zeroRelationsArbitrary
Syzygy module from arbitrary base.- Parameters:
F
- a polynomial list.- Returns:
- syz(F), a basis for the module of syzygies for F.
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zeroRelationsArbitrary
Syzygy module from arbitrary base.- Parameters:
modv
- number of module variables.F
- a polynomial list.- Returns:
- syz(F), a basis for the module of syzygies for F.
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zeroRelationsArbitrary
Syzygy module from arbitrary module base.- Parameters:
M
- an arbitrary module base.- Returns:
- syz(M), a basis for the module of syzygies for M.
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