The solutions of a bivariate algebraic equation can be represented as
Puiseux series, i.e. power series in a parameter t. Such a
Puiseux series gives information on the branches of the curve and it
is a very valuable tool for investigating the geometry of curves in
the neighbourhood of singularities. In the period of the project, the
method of Puiseux series is generalized to algebraic equations in more
than two variables. Applications to symbolic integration and the
solution of linear differential equations is studied. The method is
implemented in the SCRATCHPAD-2 computer algebra system.
