Dynamic computations inside the algebraic closure of a valued field
Franz‐Viktor Kuhlmann, Henri Lombardi, Hervé Perdry · 2003
We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the Newton Polygon Algorithm. 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.