WORKSHOP: An Introduction to Automatic Theorem Proving in Geometry and Automatic Search of Geometric Loci with DERIVE 5

There are two methods of Automatic Theorem Proving in Geometry: the Gröbner bases method and Wu’s pseudo-remainder method. The idea in the behind both methods is this: some hypotheses and a thesis are given. Instead of working with a geometric drawing of the configuration and reasoning “mathematically”, the hypotheses and the thesis are, respectively, translated into a set of polynomials and (usually just) a polynomial by using co-ordinates. Then the thesis will follow from the hypotheses if and only if the (polynomial) thesis is an algebraic combination of the (polynomial) hypotheses. In algebraic terminology: if and only if the (polynomial) thesis belongs to the ideal generated by the (polynomial) hypotheses.