Return to m_homogeneous_bezout_numbers.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Product

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

1.1     ! maekawa     1: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             2: with Partitions_of_Sets_Of_Unknowns;     use Partitions_of_Sets_of_Unknowns;
        !             3:
        !             4: package m_Homogeneous_Bezout_Numbers is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package allows the computation of m-homogeneous Bezout numbers.
        !             8: --   It provides various enumeration strategies for computing a minimal
        !             9: --   m-homogeneous Bezout number.
        !            10:
        !            11:   function Total_Degree ( p : Poly_Sys ) return natural;
        !            12:
        !            13:   -- DESCRIPTION :
        !            14:   --   Returns the 1-homogeneous Bezout number of the system.
        !            15:
        !            16:   function Bezout_Number ( p : Poly_Sys; z : Partition ) return natural;
        !            17:   function Bezout_Number ( p : Poly_Sys; z : Partition; max : natural )
        !            18:                          return natural;
        !            19:
        !            20:   -- DESCRIPTION :
        !            21:   --   Returns the m-homogeneous Bezout number w.r.t. the given partition.
        !            22:   --   When max is given as parameter, the computation stops when the
        !            23:   --   result becomes larger than or equal to max.
        !            24:
        !            25:   function Bezout_Number ( p : Poly_Sys ) return natural;
        !            26:   function Bezout_Number ( max : natural; p : Poly_Sys ) return natural;
        !            27:   function Bezout_Number ( p : Poly_Sys; min : natural ) return natural;
        !            28:   function Bezout_Number ( max : natural; p : Poly_Sys; min : natural )
        !            29:                          return natural;
        !            30:   -- DESCRIPTION :
        !            31:   --   A minimal m-homogeneous Bezout number of the polynomial system
        !            32:   --   p is computed, by generating partitions of the sets of unknowns.
        !            33:
        !            34:   -- ON ENTRY :
        !            35:   --   p         a polynomial system;
        !            36:   --   max       a maximum number of partition to be evaluated,
        !            37:   --             if max=0, then the total degree is returned;
        !            38:   --   min       the procedure stops when the Bezout number becomes
        !            39:   --             smaller than min.
        !            40:
        !            41:   procedure Bezout_Number
        !            42:                ( p : in Poly_Sys; b,m : out natural; z : in out Partition );
        !            43:   procedure Bezout_Number
        !            44:                ( max : in natural; p : in Poly_Sys; b,m : out natural;
        !            45:                  z : in out Partition );
        !            46:   procedure Bezout_Number
        !            47:                ( p : in Poly_Sys; min : in natural; b,m : out natural;
        !            48:                  z : in out Partition );
        !            49:   procedure Bezout_Number
        !            50:                ( max : in natural; p : in Poly_Sys; min : in natural;
        !            51:                  b,m : out natural; z : in out Partition );
        !            52:
        !            53:   -- DESCRIPTION :
        !            54:   --   A minimal m-homogeneous Bezout number of the polynomial system
        !            55:   --   is computed.  The partition with the calculated Bezout number
        !            56:   --   is returned.
        !            57:
        !            58:   -- ON ENTRY :
        !            59:   --   p         a polynomial system;
        !            60:   --   max       a maximum number of partition to be evaluated,
        !            61:   --             if max=0, then the total degree is returned;
        !            62:   --   min       the procedure stops when the Bezout number becomes
        !            63:   --             smaller than min.
        !            64:
        !            65:   -- ON RETURN :
        !            66:   --   b         a minimal m-homogeneous Bezout number;
        !            67:   --   m         the number of sets in the partition z;
        !            68:   --   z         the partition with the computed Bezout number b.
        !            69:
        !            70:   procedure PB ( p : in Poly_Sys; b,m : out natural; z : in out Partition );
        !            71:
        !            72:   -- DESCRIPTION :
        !            73:   --   This is a fast heuristic for computing `the' Bezout number of p.
        !            74:   --   It is fast because it does not generate all partitions,
        !            75:   --   it is a heuristic because it does not always give then
        !            76:   --   minimal partition.
        !            77:
        !            78:   -- ON ENTRY :
        !            79:   --   p         a polynomial system.
        !            80:
        !            81:   -- ON RETURN :
        !            82:   --   b         an m-homogeneous Bezout number;
        !            83:   --   m         the number of sets in the partition z;
        !            84:   --   z         the partition corresponding to b.
        !            85:
        !            86: end m_Homogeneous_Bezout_Numbers;