phcpack, sage, and interact

I've been working on integrating Jan Verschelde's phcpack software with Sage. phcpack finds solutions to pretty nasty systems of multivariable polynomials by using polyhedral homotopy continuation. Sage can provide a nice frontend for this. Here's an interactive display of the complex solutions of the Albouy-Chenciner equations (from the paper "Le problème des n corps et les distances mutuelles", Inventiones Mathematicae 131 p.151-184, 1998) for the 4-vortex problem: