Generalized Constraint Solving over Differential Algebras

We describe an algorithm for quantifier elimination over differentially closed fields and its implementation within the computer logic package redlog of the computer algebra system reduce. We give various application examples, which on the one hand demonstrate the applicability of our software to non-trivial problems, and on the other hand give a good impression of the possible range of applications of our work. Essentially, our elimination technique dates back to Seidenberg. It has been made much more explicit on the basis of the common axioms for differentially closed fields in lectures on differential algebra by Weispfenning. In this explicit form, which we use and describe here, it had remained unpublished so far.