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

1.1       maekawa     1: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
                      2:
                      3: package Reduction_of_Nonsquare_Systems is
                      4:
                      5: -- DESCRIPTION :
                      6: --   This package provides two different approaches for reducing
                      7: --   a overconstrained system to a square system.
                      8:
                      9:   function Random_Square ( p : in Poly_Sys ) return Poly_Sys;
                     10:
                     11:   -- DESCRIPTION :
                     12:   --   The system q (q'range = 1..N) on return will be square, like
                     13:   --     q(i) = p(i) + l(i,N+1)*p(N+1) + .. + l(i,n)*p(n), for i=1,2,..,N.
                     14:   --   This type of reduction is recommended when the solution of any
                     15:   --   subsystem of p (p'range = 1,..,n) has a connected solution component.
                     16:
                     17:   function Reduced_Square ( p : in Poly_Sys ) return Poly_Sys;
                     18:
                     19:   -- DESCRIPTION :
                     20:   --   The system q (q'range = 1,..,N) on return will be square, like
                     21:   --     q(i) = Rpoly(..(Rpoly(p(i),p(N+1)), p(n)), for i=1,2,..,N,
                     22:   --   i.e.: the additional polynomial will be used for reducing the system.
                     23:   --   This type of reduction is recommended when the solution set of the
                     24:   --   first N equation of p consists of isolated points that do not all
                     25:   --   satisfy the remaining equations.
                     26:
                     27: end Reduction_of_Nonsquare_Systems;