31 factorial is really large; it could be a very long night... :-)
My CPU runs at 2.4 GHz. time-consuming) FullSimplify. How do you try to avoid getting false
positives and false negatives?
My philosophy is don't worry, be happy. Every additional vertex introduces an error of at most 2^-51 or something like that, so I check the final area against 0 with an epsilon of about 1e-8, and then print the computed final area with the solution. If it's on the order of 1e-15, I'm not certain it's zero, but close enough to report. I'll let Bill and his posse do the hard bits of proving the result. (Or I'll throw multiprecision arithmetic at it. Anyone want to write a Mathematica procedure that takes a permutation, applies it to the roots of unity and computes the area, using high-precision math?) If multiprecision math says the area is < 1e-10000, I'm inclined to view it as zero, at least provisionally. -tom -- -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] --