  A highly recurrent traditional bottleneck in applied mathematics, for which
the most popular codes (Mathematica and Matlab) do not offer a solution, is to
find all the real solutions of a system of N nonlinear equations in a certain
finite domain of the N-dimensional space of variables. We present an algorithm
of minimum length and computational weight to solve this problem, resembling a
graphical tool of edge detection in an image extended to N dimensions. Once the
hypersurfaces (edges) defined by each nonlinear equation have been identified
in a single, simultaneous step, the coincidence of the hypersurfaces in the
vicinity of all the hyperpoints that constitute the solutions makes the final
Newton-Raphson step rapidly convergent to all the solutions with the desired
degree of accuracy. As long as N remains smaller than about five, which is
often the case for physical systems that depend on fewer than five parameters,
this approach demonstrates excellent effectiveness.
