Varieties over finite fields Rational points 10 Effective elimination theory 4 Effective first Bertini theorem 4 Estimation 4 First Bertini theorem 4 Geometric solutions 4 Normal complete intersection 4 Probabilistic algorithms 4 Problem solving 4 Second Bertini theorem 4 Straight-line programs 4 Theorem proving 4 q-rational points 4 Bertini 2 Bertini smoothness theorem 2 Deligne estimate 2 Finite fields 2 Hooley-Katz estimate 2 Multihomogeneous Bézout theorem 2 Polar varieties 2 Singular locus 2