
School of Mathematics and Statistics
JeanCharles Faugere
Université Pierre et Marie Currie  Paris 6
Solving polynomial systems.
Friday 27th March, 121pm, Carslaw 273.
The main purpose of this talk is to present the current state of
research in this domain. There is one question that must be answered
before we can describe the algorithms: what does it mean "solving" an
algebraic system ? The representation of the solution is not the same
if we want to compute the number of real roots or floating point
approximations of the solutions or a primary decomposition of an
ideal. The various meanings of polynomial solving are illustrated by
several real application problems ranging from pure mathematics (XVI
Hilbert Problem) to multimedia applications (image compression by
wavelet transforms). The computation of Groebner bases is however a
common intermediate step in all cases. With today's technology, all
the previous examples are too difficult to compute so we present new
efficient algorithms for the computation of Groebner bases.
