The aim of this paper is to present how the dynamic evaluation method can be used to deal with the real closure of an ordered field. Two kinds of questions, or tests, may be asked in an ordered field: equality tests (a = b?) and sign tests (a b?). Equality tests are handled through splittings,...

In the neighbourhood of irregular singularities the formal power series solutions of complex analytic ordinary differential equations are generally divergent. The resummation theory developed by J. Ecalle and J.P. Ramis enables us to sum these series by multisummation effective algorithms. In...