Simplification of Quantifier-Free Formulae over Ordered Fields

Good simpliication strategies are essential for implementing any kind of eeective real quantiier elimination. Given a quantiier-free rst-order formula over the theory of ordered elds, the aim is to nd an equivalent rst-order formula that is simpler. The notion of a formula being simpler will be speciied. An overview is given over various methods, which we have implemented in reduce. Our methods have been developed for simplifying intermediate and nal results of automatic quantiier elimination using elimination set ideas (Weispfenning, 1988, Loos and Weispfenning, 1993). They are, however, applicable to other elimination methods. y The second author was supported by the dfg (Schwerpunktprogramm: \Algorithmische Zahlen-theorie und Algebra"). 2 A. Dolzmann and T. Sturm