Package edu.jas.gbufd
Class SyzygyAbstract<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.gbufd.SyzygyAbstract<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
Syzygy<C>
,java.io.Serializable
- Direct Known Subclasses:
SyzygySeq
public abstract class SyzygyAbstract<C extends GcdRingElem<C>> extends java.lang.Object implements Syzygy<C>
SyzygyAbstract class. Implements Syzygy computations and tests.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected BasicLinAlg<GenPolynomial<C>>
blas
Linear algebra engine.protected Reduction<C>
red
Reduction engine.
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Constructor Summary
Constructors Constructor Description SyzygyAbstract()
Constructor.
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Method Summary
All Methods Instance Methods Concrete 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<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.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.-
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface edu.jas.gbufd.Syzygy
resolution, resolution, resolutionArbitrary, resolutionArbitrary, zeroRelationsArbitrary
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Field Detail
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red
protected Reduction<C extends GcdRingElem<C>> red
Reduction engine.
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blas
protected BasicLinAlg<GenPolynomial<C extends GcdRingElem<C>>> blas
Linear algebra engine.
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Constructor Detail
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SyzygyAbstract
public SyzygyAbstract()
Constructor.
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Method Detail
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zeroRelations
public 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.- 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
public 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.- 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
public 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.- 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
public ModuleList<C> zeroRelations(ModuleList<C> M)
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
public boolean isZeroRelation(java.util.List<java.util.List<GenPolynomial<C>>> Z, java.util.List<GenPolynomial<C>> F)
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
public boolean isZeroRelation(ModuleList<C> Z, ModuleList<C> F)
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
public java.util.List<java.util.List<GenPolynomial<C>>> zeroRelationsArbitrary(java.util.List<GenPolynomial<C>> F)
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
public ModuleList<C> zeroRelationsArbitrary(ModuleList<C> M)
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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