Advertisement

Development of SyNRAC—Formula Description and New Functions

  • Hitoshi Yanami
  • Hirokazu Anai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)

Abstract

In this paper we present newly developed functions in Maple-package SyNRAC, for solving real algebraic constraints derived from various engineering problems. The current version of SyNRAC provides quantifier elimination (QE) for the quadratic case and an environment dealing with first-order formulas over the reals (including new simplifiers of formulas) on Maple.

Keywords

Symbolic Computation Atomic Formula Disjunctive Normal Form Quadratic Case Existential Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Anai, H., Yanami, H.: SyNRAC: A Maple-package for solving real algebraic constraints. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 828–837. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Dolzmann, A., Sturm, T., Weispfenning, V.: Real quantifier elimination in practice. In: Matzat, B.H., Greuel, G.M., Hiss, G. (eds.) Algorithmic Algebra and Number Theory, pp. 221–247. Springer, Berlin (1998)Google Scholar
  3. 3.
    Sakabe, K., Yanami, H., Anai, H., Hara, S.: A MATLAB toolbox for parametric robust control system design based on symbolic computation. In: Bulletin (Kokyuroku) of RIMS (Research Institute for Mathematical Sciences, Kyoto Univ.) Workshop on Computer Algebra—Algorithms, Implementations and Applications 2003, December 15-18 (2003) (to appear)Google Scholar
  4. 4.
    Anai, H., Hara, S.: Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination. In: Proceedings of American Control Conference 2000, pp. 1312–1316 (2000)Google Scholar
  5. 5.
    Anai, H., Hara, S.: Linear programming approach to robust controller design by a quantifier elimination. In: Proceedings of SICE Annual Conference 2002, Osaka, Japan, pp. 863–869 (2002)Google Scholar
  6. 6.
    Anai, H., Hara, S.: A parameter space approach for fixed-order robust controller synthesis by symbolic computation. In: Proceedings of IFAC World Congress on Automatic Control b (2002)Google Scholar
  7. 7.
    Anai, H., Yanami, H., Hara, S.: SyNRAC: a maple-package for solving real algebraic constraints toward a robust parametric control toolbox. In: Proceedings of SICE Annual Conference 2003, Fukui, Japan, pp. 1716–1721 (2003)Google Scholar
  8. 8.
    Weispfenning, V.: Quantifier elimination for real algebra—the quadratic case and beyond. Applicable Algebra in Engineering Communication and Computing 8, 85–101 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Loos, R., Weispfenning, V.: Applying linear quantifier elimination. The Computer Journal 36, 450–462 (1993) Special issue on computational quantifier eliminationzbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dolzmann, A., Sturm, T.: Simplification of quantifier-free formulae over ordered fields. Journal of Symbolic Computation 24, 209–231 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Collins, G.E.: Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. 2nd GI Conference, Gesellschaft für Informatik. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)Google Scholar
  12. 12.
    Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation 12, 299–328 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    González-Vega, L.: A combinatorial algorithm solving some quantifier elimination problems. In: Caviness, B., Johnson, J. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and monographs in symbolic computation, pp. 365–375. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hitoshi Yanami
    • 1
    • 2
  • Hirokazu Anai
    • 1
    • 2
  1. 1.Information Technology Core LaboratoriesFujitsu Laboratories Ltd.KawasakiJapan
  2. 2.CRESTJapan Science and Technology AgencyKawaguchiJapan

Personalised recommendations