Algebra Seminar

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.