On Real Roots Counting for Non-radical Parametric Ideals

摘要

An algorithm we have introduced has a great effect on quantifier elimination of a first order formula containing many equalities. When the parametric ideal generated by the underlying equalities is not radical, however, our algorithm tends to produce an unnecessarily complicated formula. In this short paper, we show a result concerning Her-mitian quadratic forms. It enables us to improve our algorithm so that we can get a simple formula without any radical computation.