  We explain how to compute in the algebraic closure of a valued field. These
computations heavily rely on the \NPAz. They are made in the same spirit as the
dynamic algebraic closure of a field. They give a concrete content to the
theorem saying that a valued field does have an algebraically closed valued
extension. The algorithms created for that purpose can be used to perform an
effective quantifier elimination for algebraically closed valued fields, which
relies on a very natural geometric idea.
