A polynomial system with as many equations as unknowns is expected to have only isolated solutions. In the exceptional case of a solution curve we propose to develop the solution curve starting at infinity. A tropism defines the leading powers of this Puiseux series development of a solution curve. Computing these tropisms along with the coefficients of the Puiseux series leads to a polyhedral method for solution curves of polynomial systems.
AMS Special Session on AMS Session on Algebra and Number Theory with Polyhedra. San Francisco State University, San Francisco, 25-26 April 2009.