Package edu.jas.gbufd

Interface Syzygy<C extends RingElem<C>>

  • 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

    • Method Detail

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.

      • 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.