Package edu.jas.gbufd
Interface Syzygy<C extends RingElem<C>>
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- Type Parameters:
C
- coefficient type
- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
SyzygyAbstract
,SyzygySeq
public interface Syzygy<C extends RingElem<C>> extends java.io.Serializable
Syzygy interface. Defines Syzygy computations and tests.- Author:
- Heinz Kredel
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description boolean
isZeroRelation(ModuleList<C> Z, ModuleList<C> F)
Test if sysygy of modules.boolean
isZeroRelation(java.util.List<java.util.List<GenPolynomial<C>>> Z, java.util.List<GenPolynomial<C>> F)
Test if sysygy.java.util.List<edu.jas.gbufd.ResPart<C>>
resolution(ModuleList<C> M)
Resolution of a module.java.util.List
resolution(PolynomialList<C> F)
Resolution of a polynomial list.java.util.List<edu.jas.gbufd.ResPart<C>>
resolutionArbitrary(ModuleList<C> M)
Resolution of a module.java.util.List
resolutionArbitrary(PolynomialList<C> F)
Resolution of a polynomial list.java.util.List<java.util.List<GenPolynomial<C>>>
zeroRelations(int modv, GenVector<GenPolynomial<C>> v)
Syzygy module from Groebner base. v must be a Groebner base.java.util.List<java.util.List<GenPolynomial<C>>>
zeroRelations(int modv, java.util.List<GenPolynomial<C>> F)
Syzygy module from Groebner base.ModuleList<C>
zeroRelations(ModuleList<C> M)
Syzygy module from module Groebner base.java.util.List<java.util.List<GenPolynomial<C>>>
zeroRelations(java.util.List<GenPolynomial<C>> F)
Syzygy module from Groebner base.java.util.List<java.util.List<GenPolynomial<C>>>
zeroRelationsArbitrary(int modv, java.util.List<GenPolynomial<C>> F)
Syzygy module from arbitrary base.ModuleList<C>
zeroRelationsArbitrary(ModuleList<C> M)
Syzygy module from arbitrary module base.java.util.List<java.util.List<GenPolynomial<C>>>
zeroRelationsArbitrary(java.util.List<GenPolynomial<C>> F)
Syzygy module from arbitrary base.
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Method Detail
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zeroRelations
java.util.List<java.util.List<GenPolynomial<C>>> zeroRelations(java.util.List<GenPolynomial<C>> F)
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
java.util.List<java.util.List<GenPolynomial<C>>> zeroRelations(int modv, java.util.List<GenPolynomial<C>> F)
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
java.util.List<java.util.List<GenPolynomial<C>>> zeroRelations(int modv, GenVector<GenPolynomial<C>> v)
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
ModuleList<C> zeroRelations(ModuleList<C> M)
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
boolean isZeroRelation(java.util.List<java.util.List<GenPolynomial<C>>> Z, java.util.List<GenPolynomial<C>> F)
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
boolean isZeroRelation(ModuleList<C> Z, ModuleList<C> F)
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
java.util.List<edu.jas.gbufd.ResPart<C>> resolution(ModuleList<C> M)
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
java.util.List resolution(PolynomialList<C> F)
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
java.util.List resolutionArbitrary(PolynomialList<C> F)
Resolution of a polynomial list.- Parameters:
F
- a polynomial list of an arbitrary basis.- Returns:
- a resolution of F.
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resolutionArbitrary
java.util.List<edu.jas.gbufd.ResPart<C>> resolutionArbitrary(ModuleList<C> M)
Resolution of a module.- Parameters:
M
- a module list of an arbitrary basis.- Returns:
- a resolution of M.
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zeroRelationsArbitrary
java.util.List<java.util.List<GenPolynomial<C>>> zeroRelationsArbitrary(java.util.List<GenPolynomial<C>> F)
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
java.util.List<java.util.List<GenPolynomial<C>>> zeroRelationsArbitrary(int modv, java.util.List<GenPolynomial<C>> F)
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
ModuleList<C> zeroRelationsArbitrary(ModuleList<C> M)
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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