The geometrically enhanced ER model (GERM) addresses conceptual geometric modelling on two levels. On the surface level GERM is an extended ER model, in which attributes are associated with types with sets of values as domains. On the internal level some of the types, the geometric types, are further associated with geometric domains, which define point sets by means of algebraic curves. For query handling the operations on geometric types give rise to operations on point sets, which can be realized by a small set of operations on algebraic curves. The core problem is then to obtain a surface representation as the result. We show that symbolic computation is essential for solving this problem.