Solution of Algebraic Equations by Puiseux Series
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.