Improving a CGS-QE Algorithm

  • Ryoya Fukasaku
  • Hidenao Iwane
  • Yosuke SatoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


A real quantifier elimination algorithm based on computation of comprehensive Gröbner systems introduced by Weispfenning and recently improved by us has a weak point that it cannot handle a formula with many inequalities. In this paper, we further improve the algorithm so that we can handle more inequalities.


QE Comprehensive Gröbner system Descartes’ rule 


  1. 1.
    Becker, E., Wörmann, T.: On the trace formula for quadratic forms. Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991), pp. 271–291, Contemp. Math., 155, Amer. Math. Soc., Providence, RI (1994)Google Scholar
  2. 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 (2015)Google Scholar
  3. 3.
    Iwane, H., Higuchi, H., Anai, H.: An effective implementation of a special quantifier elimination for a sign definite condition by logical formula simplification. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 194–208. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Pedersen, P., Roy, M.-F., Szpirglas, A.: Counting real zeroes in the multivariate case. In: Proceedings of the Effective Methods in Algebraic Geometry, pp. 203–224. Springer (1993)Google Scholar
  5. 5.
    Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Caviness, B.F., Johnson, J.R. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 376–392. Springer, Vienna (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Tokyo University of ScienceShinjuku-kuJapan
  2. 2.Fujitsu Laboratories LtdNational Institute of InformaticsChiyoda-kuJapan

Personalised recommendations