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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/set_structures_and_volumes.ads, Revision 1.1

1.1     ! maekawa     1: with text_io;                            use text_io;
        !             2: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             3: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             4: with Trees_of_Vectors;                   use Trees_of_Vectors;
        !             5:
        !             6: package Set_Structures_and_Volumes is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package contains routines for implementing the
        !            10: --   hybrid approach of working with set structures and
        !            11: --   computing mixed volumes.
        !            12:
        !            13:   procedure Build_RPS ( k,n : in natural; p : in Poly_Sys );
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   If the set structure is empty, then a set structure will
        !            17:   --   be constructed for the first k polynomials of p.
        !            18:   --   This allows the construction of random product polynomials.
        !            19:
        !            20:   -- ON ENTRY :
        !            21:   --   k        number of polynomials for which a random product structure
        !            22:   --            needs to be constructed, 0 < k <= n;
        !            23:   --   n        total number of polynomials in the system;
        !            24:   --   p        polynomial system.
        !            25:
        !            26:   -- ON RETURN :
        !            27:   --   The result of this operation can be found in
        !            28:   --   the data of the package Random_Product_System.
        !            29:
        !            30:   function Bezout_BKK ( k,n : natural; p : Poly_Sys ) return natural;
        !            31:
        !            32:   function Bezout_BKK ( k,n : natural; p : Poly_Sys; tv : Tree_of_Vectors )
        !            33:                      return natural;
        !            34:
        !            35:   procedure Bezout_BKK ( k,n : in natural; p : in Poly_Sys;
        !            36:                         tv : in out Tree_of_Vectors; bb : out natural );
        !            37:
        !            38:   -- DESCRIPTION :
        !            39:   --   If the set structure is empty, then a set structure will be
        !            40:   --   constructed for the first k equations.
        !            41:   --   This set structure will be used to eliminate k unknowns,
        !            42:   --   for the last equations of p, the BKK bound will be computed.
        !            43:
        !            44:   -- ON ENTRY :
        !            45:   --   k        number of polynomials for which a random product
        !            46:   --            structure needs to be constructed, 0 <= k <= n;
        !            47:
        !            48:   -- ON RETURN :
        !            49:   --   tv       tree of useful directions used to compute mixed volume,
        !            50:   --            once tv has been constructed, the mixed volume
        !            51:   --            can be computed more efficiently;
        !            52:   --   bb       if k = 0, then the BKK bound is returned,
        !            53:   --            if 0 < k < n, then for the first k polynomials a product
        !            54:   --            structure has been used to eliminate k unknowns,
        !            55:   --            if k = n, then the Bezout number based on the set structure
        !            56:   --            will be returned;
        !            57:
        !            58:   procedure Mixed_Solve
        !            59:                ( file : in file_type; k,n : in natural; p : in Poly_Sys;
        !            60:                  bb : out natural;
        !            61:                  g : in out Poly_Sys; sols : in out Solution_List );
        !            62:
        !            63:   procedure Mixed_Solve
        !            64:                ( file : in file_type; k,n : in natural; p : in Poly_Sys;
        !            65:                  tv : in Tree_of_Vectors;
        !            66:                  bb : out natural; g : in out Poly_Sys;
        !            67:                  sols : in out Solution_List );
        !            68:
        !            69:   -- DESCRIPTION :
        !            70:   --   Constructs a random product coefficient start system for p.
        !            71:
        !            72:   -- ON ENTRY :
        !            73:   --   file      needed to write intermediate results on;
        !            74:   --   k         a number between 0 and n;
        !            75:   --   n         the number of variables and equations;
        !            76:   --   p         a polynomial system;
        !            77:   --   tv        the tree of useful directions.
        !            78:
        !            79:   -- ON RETURN :
        !            80:   --   g         a random product coefficient start system;
        !            81:   --             if k = 0, then a random coefficient start system,
        !            82:   --             if k = n, then a random product start system;
        !            83:   --   bb        the Bezout BKK bound for the system p;
        !            84:   --             if k = 0, then bb = BKK bound,
        !            85:   --             if k = n, then bb = Bezout number based on set structure;
        !            86:   --   sols      the solutions of g.
        !            87:
        !            88: end Set_Structures_and_Volumes;