Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight. Victor Sent from my iPhone On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
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
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