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International Conference on Mathematical Aspects of Computer and Information Sciences

MACIS 2015: Mathematical Aspects of Computer and Information Sciences pp 231–235Cite as

Improving a CGS-QE Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

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.

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References

  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)

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  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)

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  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)

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  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)

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  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)

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Author information

Authors and Affiliations

  1. Tokyo University of Science, 1–3, Kagurazaka, Shinjuku-ku, Tokyo, Japan

    Ryoya Fukasaku & Yosuke Sato

  2. Fujitsu Laboratories Ltd, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan

    Hidenao Iwane

Authors
  1. Ryoya Fukasaku
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  2. Hidenao Iwane
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  3. Yosuke Sato
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Corresponding author

Correspondence to Yosuke Sato .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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© 2016 Springer International Publishing Switzerland

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Fukasaku, R., Iwane, H., Sato, Y. (2016). Improving a CGS-QE Algorithm. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_20

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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