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