Proceedings of the 10 th International Workshop on Automated Deduction in Geometry ( ADG 2014 ) 9 - 11 July 2014 University of Coimbra , Portugal

Tarski proved in the 1930s that the theory of real algebraic geometry admitted quantifier elimination. However, it was not until 1973 that Collins produced a remotely practical method. While inherently doubly-exponential in the number of alternations of quantifiers, it is nevertheless capable of deciding non-trivial questions, especially with the many practical improvements that have been made over the years. We will outline some of these recent improvements. We will also consider the question — “can such complicated algorithms provide proofs”? Proc. ADG 2014, 9-11 July 2014, University of Coimbra, Portugal CISUC/TR 2014-01 3 ADG 2014 Proc. ADG 2014, 9-11 July 2014, University of Coimbra, Portugal CISUC/TR 2014-01 4 ADG 2014 Teaching Tiles (Azulejos que Ensinam)