Package edu.jas.gbufd

Class SyzygyAbstract<C extends GcdRingElem<C>>

  • 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.
    See Also:
    Serialized Form
    • Constructor Detail

      • SyzygyAbstract

        public SyzygyAbstract()
        Constructor.
    • Method Detail

      • 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 interface Syzygy<C extends GcdRingElem<C>>
        Parameters:
        F - a Groebner base.
        Returns:
        syz(F), a basis for the module of syzygies for F.
      • 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 interface Syzygy<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.
      • 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 interface Syzygy<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.
      • 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 interface Syzygy<C extends GcdRingElem<C>>
        Parameters:
        M - a module Groebner base.
        Returns:
        syz(M), a basis for the module of syzygies for M.
      • 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 interface Syzygy<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.
      • isZeroRelation

        public boolean isZeroRelation​(ModuleList<C> Z,
                                      ModuleList<C> F)
        Test if sysygy of modules.
        Specified by:
        isZeroRelation in interface Syzygy<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.
      • 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 interface Syzygy<C extends GcdRingElem<C>>
        Parameters:
        F - a polynomial list.
        Returns:
        syz(F), a basis for the module of syzygies for F.
      • zeroRelationsArbitrary

        public ModuleList<C> zeroRelationsArbitrary​(ModuleList<C> M)
        Syzygy module from arbitrary module base.
        Specified by:
        zeroRelationsArbitrary in interface Syzygy<C extends GcdRingElem<C>>
        Parameters:
        M - an arbitrary module base.
        Returns:
        syz(M), a basis for the module of syzygies for M.