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Annotation of OpenXM_contrib/PHC/Ada/Main/black_box_root_counting.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:
        !             5: procedure Black_Box_Root_Counting
        !             6:                ( file : in file_type;
        !             7:                  p : in out Poly_Sys; rc : out natural;
        !             8:                  q : out Poly_Sys; qsols : out Solution_List;
        !             9:                  rocotime,hocotime : out duration );
        !            10:
        !            11: -- DESCRIPTION :
        !            12: --   Calculates four different root counts: total degree, m-homogeneous
        !            13: --   Bezout number, generalized Bezout number based on set structure,
        !            14: --   and mixed volume.  Heuristics are used for the Bezout numbers.
        !            15: --   Returns the start system with lowest root count and least amount
        !            16: --   of work, which means that linear-product start systems are prefered,
        !            17: --   when Bezout numbers equal the mixed volume.
        !            18:
        !            19: -- ON ENTRY :
        !            20: --   file        must be opened for output;
        !            21: --   p           a polynomial system.
        !            22:
        !            23: -- ON RETURN :
        !            24: --   p           may have been permuted for semi-mixed inputs;
        !            25: --   rc          root count, Bezout number or mixed volume;
        !            26: --   q           start system;
        !            27: --   qsols       solutions of q, Length_Of(qsols) = rc;
        !            28: --   rocotime    elapsed user cpu time for computation of the root counts;
        !            29: --   hocotime    elapsed user cpu time for construction of start system.