On the width of full rank linear differential systems with power series coefficients

par Sergei A. Abramov (Computing Centre of the Russian Academy of Sciences)

jeudi 6 déc. 2012, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

If a(x)=a_0+a_1x+a_2x^2+... is a formal power series, k is a non-negaitive integer then the polynomial a_0+a_1x+a_2x^2+...+a_kx^k is the k-truncation of a(x). If S is an arbitrary-order linear differential system with formal power series coefficients then the k-truncation of S is the system whose coefficients are the k-truncations of corresponding coefficients of S. The following problem is discussed in the talk: given a full rank system S with formal power series coefficients, compute the width of S, i.e. the smallest non-negative integer w such that any k-truncation of S with k \geq w is a full rank system. We suppose that the series coefficients of systems are represented algorithmically; thus we are not able, in general, to recognize whether a given series is equal to zero or not. (Joint work with M.Barkatou and D.Khmelnov.)