A Singular web service for geometric computations

  • 158 Accesses

  • 6 Citations


Outsourcing algebraic computations in dynamic geometry tools is a possible strategy used when software distribution constraints apply. If the target user machine has hardware limitations, or if the computer algebra system cannot be easily (or legally) packaged inside the geometric software, this approach can solve current shortcomings in dynamic environments.We report the design and implementation of a web service using Singular, a program specialized in ideal theory and commutative algebra. Besides its canonical address, a virtual appliance and a port to a low-cost ARM based computer are also provided. Any interactive geometric environment can then outsource computations where Singular is used, and incorporate their results into the system. In particular, we illustrate the capabilities of the web service by extending current abilities of GeoGebra to deal with algebraic loci and envelopes by means of a recent algorithm for studying parametric polynomial systems.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.


  1. 1.

    Sutherland, I.E.: Sketchpad: A man-machine graphical communication system, Tech. Rep. 574, Computer Laboratory, University of Cambridge (2003)

  2. 2.

    Gao, X.S., Lin, Q.: MMP/Geometer - A software package for automated geometric reasoning. Lect. Notes Artif. Int. 3763, 44–66 (2006)

  3. 3.

    Gao, X.S., Zhang, J.Z., Chou, S.C.: Geometry Expert. Nine Chapters, Taiwan (1998)

  4. 4.

    Recio, T., Vélez, M.P.: Automatic discovery of theorems in elementary geometry. J. Autom. Reason. 23, 63–82 (1999)

  5. 5.

    Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Comput. Educ. 38, 21–35 (2002)

  6. 6.

    Janičić, P.: Geometry constructions language. J. Autom. Reason. 44, 3–24 (2010)

  7. 7.

    Decker, W., Greuel, G.M., Pfister, G., Schönemann, H.: Singular - A computer algebra system for polynomial computations. (2013). Accessed 27 December 2013

  8. 8.

    Montes, A., Wibmer, M.: Gröbner bases for polynomial systems with parameters. J. Symb. Comput. 45, 1391–1425 (2010)

  9. 9.

    Oracle Corporation: Java Native Interface (2013)

  10. 10.

    Ancsin, G., Hohenwarter, M., Kovács, Z.: GeoGebra Goes Web. Electron. J. Math. Technol. 7(6) 412–418 (2013)

  11. 11.

    Botana, F., Kovács Z., Weitzhofer, S.: Implementing theorem proving in GeoGebra by using a Singular webservice. In: Sendra, J.R., Villarino, C. (eds.) Proceedings EACA 2012, pp. 67–70. Universidad de Alcalá , Alcalá de Henares (2012)

  12. 12.

    Kovács, Z., Parisse, B.: Giac and GeoGebra — improved Gröbner basis computations, Special Semester on Applications of Algebra and Number Theory, Workshop 3 on Computer Algebra and Polynomials. (2013). Accessed 27 December 2013

  13. 13.

    Kovács, Z.: Singular WebService. VirtualBox ISO Image. (2014). Accessed 7 January 2014

  14. 14.

    Kovács, Z.: Singular WebService in GeoGebra. (2012). Accessed 27 December 2013

  15. 15.

    Kovács, Z.: Singular WebService documentation and source code. (2012). Accessed 27 December 2013

  16. 16.

    Freundt, S., Horn, P., Konovalov, A., Linton, S., Roozemond, D.: Symbolic Computation Software Composability Protocol (SCSCP) specification, Version 1.3. ( (2009)

  17. 17.

    Chen, X., Wang, D.: Management of geometric knowledge in textbooks. Data Knowl. Eng. 73, 43–57 (2012)

  18. 18.

    Botana, F., Abánades, M.A.: Automatic deduction in (dynamic) geometry: Loci computation. Comp. Geom-Theor. Appl. 47, 75–89 (2014)

  19. 19.

    Abánades, M.A., Botana, F.: A dynamic symbolic geometry environment based on the GröbnerCover algorithm for the computation of geometric loci and envelopes. Lect. Notes Comput. Sc. 7961, 349–353 (2013)

  20. 20.

    Botana, F.: Interactive versus symbolic approaches to plane loci generation in dynamic geometry environments. Lect. Notes Comput. Sc. 2330, 211–218 (2002)

  21. 21.

    Bruce, J.W., Giblin, P.J.: Curves and Singularities. Cambridge University Press, Cambridge (1984)

  22. 22.

    Botana, F.: A parametric approach to 3D dynamic geometry. Math. Comput. Simulat. 104, 3–20 (2014)

Download references

Author information

Correspondence to Francisco Botana.

Additional information

First author partially supported by the Spanish “Ministerio de Economía y Competitividad” and by the European Regional Development Fund (ERDF), under the Project MTM2011–25816–C02–02.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(MPG 9.48 MB)

(MPG 25.2 MB)

(MPG 9.48 MB)

(ZIP 34.1 KB)

(MPG 25.2 MB)

(ZIP 32.1 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Botana, F., Kovács, Z. A Singular web service for geometric computations. Ann Math Artif Intell 74, 359–370 (2015) doi:10.1007/s10472-014-9438-2

Download citation


  • Web services
  • Dynamic geometry
  • Parametric polynomial systems
  • Geometric loci
  • Envelopes

Mathematics Subject Classification (2010)

  • MSC2010 68W30
  • MSC2010 68T35