5-body woes

I've been working for the last few weeks with Anders Jensen, Eduardo Leandro, Gareth Roberts, John Little, Manuele Santoprete, and Alain Albouy on some celestial mechanics problems. While I was in Goettingen, Anders and I tried hard to get some results on central configurations in the five-body problem. Unfortunately, we hit one very, very nasty special case in our finiteness proof, which has me musing over a couple of big polynomials that start out looking like this:




Ouch!