Package edu.jas.gbufd

Interface SolvableSyzygy<C extends RingElem<C>>

  • Type Parameters:
    C - coefficient type
    All Superinterfaces:
    java.io.Serializable
    All Known Implementing Classes:
    SolvableSyzygyAbstract, SolvableSyzygySeq

    public interface SolvableSyzygy<C extends RingElem<C>>
    extends java.io.Serializable
    Syzygy interface for solvable polynomials. Defines syzygy computations and tests.
    • Method Detail

      • leftZeroRelations

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations​(java.util.List<GenSolvablePolynomial<C>> F)
        Left syzygy for left Groebner base.
        Parameters:
        F - a Groebner base.
        Returns:
        leftSyz(F), a basis for the left module of syzygies for F.
      • leftZeroRelations

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations​(int modv,
                                                                                   java.util.List<GenSolvablePolynomial<C>> F)
        Left syzygy for left Groebner base.
        Parameters:
        modv - number of module variables.
        F - a Groebner base.
        Returns:
        leftSyz(F), a basis for the left module of syzygies for F.
      • leftZeroRelations

        ModuleList<C> leftZeroRelations​(ModuleList<C> M)
        Left syzygy for left module Groebner base.
        Parameters:
        M - a Groebner base.
        Returns:
        leftSyz(M), a basis for the left module of syzygies for M.
      • isLeftZeroRelation

        boolean isLeftZeroRelation​(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
                                   java.util.List<GenSolvablePolynomial<C>> F)
        Test if left syzygy.
        Parameters:
        Z - list of sysygies.
        F - a polynomial list.
        Returns:
        true, if Z is a list of left syzygies for F, else false.
      • isRightZeroRelation

        boolean isRightZeroRelation​(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
                                    java.util.List<GenSolvablePolynomial<C>> F)
        Test if right syzygy.
        Parameters:
        Z - list of sysygies.
        F - a polynomial list.
        Returns:
        true, if Z is a list of right syzygies for F, else false.
      • isLeftZeroRelation

        boolean isLeftZeroRelation​(ModuleList<C> Z,
                                   ModuleList<C> F)
        Test if left sysygy of modules
        Parameters:
        Z - list of sysygies.
        F - a module list.
        Returns:
        true, if Z is a list of left syzygies for F, else false.
      • isRightZeroRelation

        boolean isRightZeroRelation​(ModuleList<C> Z,
                                    ModuleList<C> F)
        Test if right sysygy of modules
        Parameters:
        Z - list of sysygies.
        F - a module list.
        Returns:
        true, if Z is a list of right syzygies for F, else false.
      • resolution

        java.util.List<SolvResPart<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<SolvResPart<C>> resolutionArbitrary​(ModuleList<C> M)
        Resolution of a module.
        Parameters:
        M - a module list of an arbitrary basis.
        Returns:
        a resolution of M.
      • 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.
      • leftZeroRelationsArbitrary

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary​(java.util.List<GenSolvablePolynomial<C>> F)
        Left syzygy module from arbitrary base.
        Parameters:
        F - a solvable polynomial list.
        Returns:
        syz(F), a basis for the module of left syzygies for F.
      • leftZeroRelationsArbitrary

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary​(int modv,
                                                                                            java.util.List<GenSolvablePolynomial<C>> F)
        Left syzygy module from arbitrary base.
        Parameters:
        modv - number of module variables.
        F - a solvable polynomial list.
        Returns:
        syz(F), a basis for the module of left syzygies for F.
      • leftZeroRelationsArbitrary

        ModuleList<C> leftZeroRelationsArbitrary​(ModuleList<C> M)
        Left syzygy for arbitrary left module base.
        Parameters:
        M - an arbitrary base.
        Returns:
        leftSyz(M), a basis for the left module of syzygies for M.
      • rightZeroRelationsArbitrary

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary​(java.util.List<GenSolvablePolynomial<C>> F)
        Right syzygy module from arbitrary base.
        Parameters:
        F - a solvable polynomial list.
        Returns:
        syz(F), a basis for the module of right syzygies for F.
      • rightZeroRelationsArbitrary

        java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary​(int modv,
                                                                                             java.util.List<GenSolvablePolynomial<C>> F)
        Right syzygy module from arbitrary base.
        Parameters:
        modv - number of module variables.
        F - a solvable polynomial list.
        Returns:
        syz(F), a basis for the module of right syzygies for F.