| Theoretical: | * | simple facts from algebraic geometry, singularity theory, finite fields; |
| * |
theorem of Hasse-Weil, estimating the number of
rational points on an absolutely irreducible
projective curve C defined over a finite field (g=arithmetic
genus=12,
d=degree=10):
# C
( Fp )> p+1 - 2g*sqrt(p) - d
(> 0 if p>593);
|
|
| * | simple facts from the theory of standard bases; |
| Computational: | * | standard operations, e.g., Gröbner bases, quotients and elimination, but: need powerful CAS |