  This paper presents a method for investigating, through an automatic
procedure, the (lack of) identifiability of parametrized dynamical models. This
method takes into account constraints on parameters and returns parameters
whose estimations make the model identifiable. It is based on i) an equivalence
between an extension of the notion of identifiability and the existence of
solutions of algebraic systems, ii) the use of symbolic computations for
testing their existence.
  This method is described in details and is applied to two examples, of which
the last one involves 12 parameters.
