All cyclic p-roots of index 3, found by symmetry-preserving calculations

Understand

When using a Groebner basis to solve the highly symmetric system of algebraic equations defining the cyclic p-roots, one has the feeling that much of the advantage of computerized symbolic algebra over hand calculation is lost through the fact that the symmetry is immediately ``thrown out'' by the calculations.

• In this paper, the problem of finding (for all relevant primes p) all cyclic p-roots of index 3 is treated with the symmetry preserved through the calculations.
• Once we had found the relevant formulas, using MAPLE and MATHEMATICA, the calculations could even be made by hand.
• On the other hand, with respect to a straightforward attack with Groebner basis, it is not even clear how this could be organized for a general p.