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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/interpolating_homotopies.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Matrices;          use Standard_Integer_Matrices;
        !             2: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             3: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             4: with Partitions_of_Sets_of_Unknowns;     use Partitions_of_Sets_of_Unknowns;
        !             5:
        !             6: package Interpolating_Homotopies is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package contains facilities for constructing interpolating
        !            10: --   homotopies, based on a given m-homogeneous structure.
        !            11: --   The routines are given in the order in which they should be applied.
        !            12: --   Null polynomials are ignored, making scaled interpolation possible,
        !            13: --   the scaling equation, used for generating the interpolating vectors,
        !            14: --   can be added afterwards.  For linear scalers, the last unknown of the
        !            15: --   scaling equation should be ignored in those monomials that have degree
        !            16: --   one in that unknown, to avoid singular interpolation matrices.
        !            17:
        !            18:   function Dense_Representation
        !            19:               ( p : Poly_Sys; z : partition ) return Poly_Sys;
        !            20:   function Dense_Representation
        !            21:               ( p : Poly_Sys; z : partition; d : Matrix ) return Poly_Sys;
        !            22:
        !            23:   -- DESCRIPTION :
        !            24:   --   A dense representation of an m-homogeneous structure is returned.
        !            25:   --   The coefficients of the polynomials in the returned system are all one.
        !            26:
        !            27:   function Independent_Representation ( p : Poly_Sys ) return Poly_Sys;
        !            28:
        !            29:   -- DESCRIPTION :
        !            30:   --   An independent representation of a polynomial system is returned.
        !            31:   --   This means that the initial term of each polynomial does not occur
        !            32:   --   in every other polynomial.
        !            33:
        !            34:   function Independent_Roots ( p : Poly_Sys ) return natural;
        !            35:   function Independent_Roots ( p : Poly_Sys; i : natural ) return natural;
        !            36:
        !            37:   -- DESCRIPTION :
        !            38:   --   Returns the number of independent roots the system p can have.
        !            39:   --   When the ith unknown is given as parameter, the monomials that
        !            40:   --   have degree one in x_i are not counted.
        !            41:
        !            42:   -- IMPORTANT NOTE : p must be an independent representation of a polynomial
        !            43:   --                  system, otherwise the result might not be reliable.
        !            44:
        !            45:   function Interpolate ( p : Poly_Sys; b : natural; sols : Solution_List )
        !            46:                        return Poly_Sys;
        !            47:   function Interpolate ( p : Poly_Sys; i,b : natural; sols : Solution_List )
        !            48:                        return Poly_Sys;
        !            49:
        !            50:   -- DESCRIPTION :
        !            51:   --   This routine constructs a start system q with the same monomial
        !            52:   --   structure as the system p.
        !            53:
        !            54:   -- ON ENTRY :
        !            55:   --  p         a polynomial system;
        !            56:   --  i         monomials with degree one in x_i will be ignored;
        !            57:   --  b         must equal Independent_Roots(p);
        !            58:   --  sols      interpolation vectors, Length_Of(sols) = b.
        !            59:
        !            60:   -- ON RETURN :
        !            61:   --  q         system that has the given list sols as solutions.
        !            62:
        !            63: end Interpolating_Homotopies;