# A geometrical decision algorithm based on the gröbner bases algorithm

## Abstract

Gröbner bases have been used in various ways for dealing with the problem of geometry theorem proving as posed by Wu. Kutzler and Stifter have proposed a procedure centered around the computation of a basis for the module of syzygies of the geometrical hypotheses. We elaborate this approach and extend it to a complete decision procedure. Also, in geometry theorem proving the problem of constructing subsidiary (or degeneracy) conditions arises. Such subsidiary conditions usually are not uniquely determined and obviously one wants to keep them as simple as possible. This problem, however, has not received enough attention in the geometry theorem proving literature. Our algorithm is able to construct the simplest subsidiary conditions with respect to certain predefined criteria, such as lowest degree or dependence on a given set of variables.

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