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Needs
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Theoretical: | *
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simple facts from algebraic geometry, singularity theory,
finite fields;
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| * |
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):
# C
( Fp ) > p+1 - 2g*sqrt(p)
(> 0 if p>572);
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| * |
simple facts from the theory of standard bases;
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Computational: | * |
Gröbner basis computations without content
extractions;
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| * |
multivariate factorization;
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| * |
resolution of plane curve singularities;
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| * |
primary decomposition.
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