Skip to main content
SpringerLink
Log in

QE Software Based on Comprehensive Gröbner Systems

  • Conference paper
Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

Included in the following conference series:

Abstract

We introduce two quantifier elimination softwares, one is in the domain of an algebraically closed field and another is of a real closed field. Both softwares are based on the computations of comprehensive Gröbner systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Risa/Asir, http://www.math.kobe-u.ac.jp/Asir/asir.html

  2. Kalkbrener, M.: On the Stability of Gröbner Bases Under Specializations. J. Symbolic Computation 24(1), 51–58 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kapur, D., Sun, Y., Wang, D.: A New Algorithm for Computing Comprehensive Gröbner Systems. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 29–36. ACM-Press (2010)

    Google Scholar 

  4. Kurata, Y.: Improving Suzuki-Sato’s CGS Algorithm by Using Stability of Gröbner Bases and Basic Manipulations for Efficient Implementation. Communications of JSSAC 1, 39–66 (2011)

    Google Scholar 

  5. Montes, A.: A new algorithm for discussing Gröbner bases with parameters. Journal of Symbolic Computation 33(2), 183–208 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Manubens, M., Montes, A.: Improving DISPGB algorithm using the discriminant ideal. Journal of Symbolic Computation 41, 1245–1263 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Manubens, M., Montes, A.: Minimal Canonical Comprehensive Gröbner System. Journal of Symbolic Computation 44, 463–478 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Montes, A., Wibmer, M.: Gröbner Bases for Polynomial Systems with parameters. Journal of Symbolic Computation 45, 1391–1425 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Nabeshima, K.: A Speed-Up of the Algorithm for Computing Comprehensive Gröbner Systems. In: Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 299–306. ACM-Press (2007)

    Google Scholar 

  10. Nabeshima, K.: Stability Conditions of Monomial Bases and Comprehensive Gröbner Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2012. LNCS, vol. 7442, pp. 248–259. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Pedersen, P., Roy, M.F., Szpirglas, A.: F., and Szpirglas,A.: Counting real zeroes in the multivariate case. In: Eysette, F., Galigo, A. (eds.) Proceedings of the MEGA 92. Computational Algebraic Geometry. Progress in Mathematics, vol. 109, pp. 203–224. Birkhäuser, Boston (1993)

    Chapter  Google Scholar 

  12. Suzuki, A., Sato, Y.: A Simple Algorithm to Compute Comprehensive Gröbner Bases Using Gröbner Bases. In: International Symposium on Symbolic and Algebraic Computation, pp. 326–331. ACM-Press (2006)

    Google Scholar 

  13. Weispfenning, V.: Comprehensive Gröbner Bases. Journal of Symbolic Computation 14(1), 1–29 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  14. 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. Texts and monographs in symbolic computation, pp. 376–392. Springer (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Science, Tokyo University of Science, Japan

    Ryoya Fukasaku

Authors
  1. Ryoya Fukasaku
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fukasaku, R. (2014). QE Software Based on Comprehensive Gröbner Systems. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44199-2_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation