On Real Roots Counting for Non-radical Parametric Ideals
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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 Hermitian quadratic forms. It enables us to improve our algorithm so that we can get a simple formula without any radical computation.
KeywordsHermitian quadratic form Comprehensive Gröbner system Quantifier elimination
- 2.Fukasaku, R., Iwane, H., Sato, Y: Real quantifier elimination by computation of comprehensive Gröbner systems. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 173–180, ACM-Press (2015)Google Scholar