23 Aug
2011
23 Aug
'11
11:29 a.m.
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations: {1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0} Here's what I already know: There exist solutions where all the variables are 6th roots of 1. There exist solutions where all the variables are 7th roots of 1. Numerically I can find solutions different from either of the above to very many digits. When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions? Veit