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Seminar on Algebraic Geometry

Thursday, 24.11. at 10:15
Seminar room Altenbergerstrasse 50

Christiaan van de Woestijne
Deterministic equation solving over finite fields.

Taking of roots in finite fields and, more generally, factoring polynomials over them is usually only efficient if one uses probabilistic algorithms, like the Tonelli-Shanks square root algorithm. In my talk, I'll explain the reason for this, and also I'll give some results from my PhD project, which show that in some cases efficient deterministic algorithms do exist. This is notably the case for quadrics, for diagonal varieties whose degree is less than their dimension, and for elliptic curves.