In the project "Algorithmic Algebraic Geometry" the development of
the program system CASA for exact symbolic computations in algebraic
geometry has been started. The goal of SGC is to increase the
computational power of CASA. In order to reach this goal it will also
be necessary to continue research in mathematical foundations of
computer algebra and geometric computation. Computer algebra, which
deals with polynomial rings, differential fields, algebraic extension
fields, etc., is a prerequisite for symbolic computations in geometry,
which deals with algebraic curves and surfaces or solutions of
algebraic equations in general. Computations on such geometric objects
include determination of singularities, dimension, decomposition,
expansion into power series, finding rational points, absolute
factorization of polynomials.
