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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/reduction_of_polynomial_systems.ads, Revision 1.1.1.1

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;