Estimating the number of solutions equation of N-point gravitational
  lens algebraic geometry methods
  One of the main problems in the study of system of equations of the
gravitational lens, is the computation of coordinates from the known position
of the source. In the process of computing finds the solution of equations with
two unknowns. The difficulty lies in the fact that, in general, is not known
constructive or analytical algorithm for solving systems of polynomial
equations In this connection, use numerical methods like the method of tracing.
For the N-point gravitational lenses have a system of polynomial equations.
Systems Research is advisable to start with an assessment of the number of
solutions. This can be done by methods of algebraic geometry.
