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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/reduction_of_polynomial_systems.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
        !             2: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             3:
        !             4: package Reduction_of_Polynomial_Systems is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   Linear and nonlinear reduction to reduce the total degree.
        !             8:
        !             9:   function Total_Degree ( p : Poly_Sys ) return natural;
        !            10:
        !            11:   -- DESCRIPTION :
        !            12:   --   Returns the total degree of the polynomial system,
        !            13:   --   i.e. the product of the degrees of the polynomials.
        !            14:
        !            15:   procedure Reduce ( p : in out Poly_Sys;
        !            16:                      diagonal,inconsistent,infinite : in out boolean );
        !            17:
        !            18:   -- DESCRIPTION :
        !            19:   --   This procedure tries to lower the total degree of p by means
        !            20:   --   of linear reduction.
        !            21:
        !            22:   -- ON ENTRY :
        !            23:   --   p             a polynomial system.
        !            24:
        !            25:   -- ON RETURN :
        !            26:   --   p             a polynomial system with a possible lower total degree;
        !            27:   --   diagonal      true if all leading terms in p are different;
        !            28:   --   inconsistent  is true if the reduced system has equations `4=0';
        !            29:   --   infinite      is true if some equations of the original system
        !            30:   --                 disappeared during the reduction process.
        !            31:
        !            32:   procedure Sparse_Reduce ( p : in out Poly_Sys;
        !            33:                             inconsistent,infinite : in out boolean );
        !            34:
        !            35:   -- DESCRIPTION :
        !            36:   --   This procedure makes the coefficient matrix of p as sparse as
        !            37:   --   possible.
        !            38:
        !            39:   procedure Reduce ( p : in Poly_Sys; res : in out Poly_Sys;
        !            40:                      cnt_eq : in out natural; max_eq : in natural;
        !            41:                      cnt_sp : in out natural; max_sp : in natural;
        !            42:                      cnt_rp : in out natural; max_rp : in natural );
        !            43:
        !            44:   -- DESCRIPTION :
        !            45:   --   This procedure tries to lower the total degree of the system p
        !            46:   --   by means of nonlinear reduction.
        !            47:
        !            48:   -- REQUIRED : the counters must equal 0, on entry.
        !            49:
        !            50:   -- ON ENTRY :
        !            51:   --   p              a polynomial system;
        !            52:   --   cnt_eq         counts the number of equal degree substitutions;
        !            53:   --   max_eq         limit on the number of equal degree substitutions;
        !            54:   --   cnt_sp         counts the number of S-polynomial computations;
        !            55:   --   max_sp         limit on the number of S-polynomial computations.
        !            56:   --   cnt_rp         counts the number of R-polynomial computations;
        !            57:   --   max_rp         limit on the number of R-polynomial computations.
        !            58:
        !            59:   -- ON RETURN :
        !            60:   --   res            the reduced system;
        !            61:   --   cnt_eq         the number of equal degree substitutions;
        !            62:   --   cnt_sp         the number of computed S-polynomials;
        !            63:   --   cnt_rp         the number of computed R-polynomials.
        !            64:
        !            65:   procedure Sparse_Reduce ( p : in Poly_Sys; res : in out Poly_Sys;
        !            66:                             cnt_eq : in out natural; max_eq : in natural );
        !            67:
        !            68:   -- DESCRIPTION :
        !            69:   --   the polynomial system is reduced by computing S-polynomials.
        !            70:   --   After each replacement, the coefficient matrix is made as sparse
        !            71:   --   as possible.
        !            72:
        !            73: end Reduction_of_Polynomial_Systems;