This method is based on the mathematical concept of characteristic set introduced in the late 1940s by J.F.
[1][2] Wu's method is powerful for mechanical theorem proving in elementary geometry, and provides a complete decision process for certain classes of problem.
The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective.
[3][4] Wu's method has been applied in various scientific fields, like biology, computer vision, robot kinematics and especially automatic proofs in geometry.
More specifically, for an ideal I in the ring k[x1, ..., xn] over a field k, a (Ritt) characteristic set C of I is composed of a set of polynomials in I, which is in triangular shape: polynomials in C have distinct main variables (see the formal definition below).
This triangular set satisfies certain minimal condition with respect to the Ritt ordering, and it preserves many interesting geometrical properties of the ideal.
Let T = { t1, ..., tu} and S = { s1, ..., sv} be two triangular sets such that polynomials in T and S are sorted increasingly according to their main variables.