Package edu.jas.gbufd
Class SyzygyAbstract<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.gbufd.SyzygyAbstract<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
Syzygy<C>
,Serializable
- Direct Known Subclasses:
SyzygySeq
SyzygyAbstract class. Implements Syzygy computations and tests.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected BasicLinAlg
<GenPolynomial<C>> Linear algebra engine.private static final boolean
private static final org.apache.logging.log4j.Logger
Reduction engine. -
Constructor Summary
Constructors -
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.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.Syzygy module from arbitrary module base.List
<List<GenPolynomial<C>>> Syzygy module from arbitrary base.Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface edu.jas.gbufd.Syzygy
resolution, resolution, resolutionArbitrary, resolutionArbitrary, zeroRelationsArbitrary
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug -
red
Reduction engine. -
blas
Linear algebra engine.
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Constructor Details
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SyzygyAbstract
public SyzygyAbstract()Constructor.
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Method Details
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zeroRelations
Syzygy module from Groebner base. F must be a Groebner base.- Specified by:
zeroRelations
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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.- Specified by:
zeroRelations
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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.- Specified by:
zeroRelations
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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.- Specified by:
zeroRelations
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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.- Specified by:
isZeroRelation
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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.- Specified by:
isZeroRelation
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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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zeroRelationsArbitrary
Syzygy module from arbitrary base.- Specified by:
zeroRelationsArbitrary
in interfaceSyzygy<C extends GcdRingElem<C>>
- 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 module base.- Specified by:
zeroRelationsArbitrary
in interfaceSyzygy<C extends GcdRingElem<C>>
- Parameters:
M
- an arbitrary module base.- Returns:
- syz(M), a basis for the module of syzygies for M.
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