Industrial Applications of Computer Algebra: Climbing Up a Mountain, Going Down a Hill

  • Laureano Gonzalez-Vega
  • Tomas Recio
Conference paper
Part of the Progress in Mathematics book series (PM, volume 202)


In this paper we present some personal experiences with Computer Algebra applications to industrial problems. In many cases the involved Computer Algebra problems seem as challenging as climbing up a difficult peak. Then one finds out that the trail leads up to a quite rugged hill… This point of view will be illustrated with “real” examples coming from robot kinematics and path planning, parametric CAD and shape design in automotive industry.


Computer Algebra Polynomial System Implicit Equation Quantifier Elimination Polynomial Parameterization 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Alami and J. P. Laumond, A geometrical approach to planning manipulation tasks in robotics, First Canadian Conference on Computational Geometry (Montreal, 1989).Google Scholar
  2. [2]
    B. Buchberger, G. Collins, M. Encarnación, H. Hong, J. Johnson, W. Krandick, R. Loos and A. Neubacher, A SACLIB Primer, Tech. Rep. 92–34, RISC-Linz, Johannes Kepler University (Linz, Austria), 1992. Google Scholar
  3. [3]
    J. F. Canny, The complexity of robot motion planning, ACM Doctoral Dissertation Series, MIT Press, Cambridge Mass., 1988. Google Scholar
  4. [4]
    G. E. Collins, Quantifier elimination for real closed fields by Cylindrical Algebraic Decomposition, Lecture Notes in Computer Science (Second GI Conference on Automata Theory and Formal Languages), 33 (1975), 134–183.CrossRefGoogle Scholar
  5. [5]
    I. J. Cox and G. T. Wilfong, Motion Planning, Autonomous Robot Vehicles (I. J. Cox and G. T. Wilfong eds), Springer-Verlag, 1990. CrossRefGoogle Scholar
  6. [6]
    J. H. Davenport and J. Heintz, Real Quantifier Elimination is Doubly Exponential, Journal of Symbolic Computation, 5 (1988), 29–36.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    D. Duval, Calcul symbolique: automatisation en cours, La Recherche, 291 (1996), 64–71.Google Scholar
  8. [8]
    J. Espinola, L. Gonzalez-Vega and I. Necula, Generic implicitation of low degree rational surfaces, Preprint available at (1999).Google Scholar
  9. [9]
    J. Espinola, L. Gonzalez-Vega and I. Necula, Algebraic approximation in CAGD, Preprint available at http:// (2000).Google Scholar
  10. [10]
    K. Geddes, S. R. Czapor and G. Labhan, Algorithms for computer algebra, Kluwer Academic Publishers, Boston, 1992. zbMATHCrossRefGoogle Scholar
  11. [11]
    L. Gonzalez-Vega, The Needs of Industry for Polynomial System Solving, The SAC Newsletter, 3 (1998), 21–46.Google Scholar
  12. [12]
    L. Gonzalez-Vega, FRISCO Software Overview, Preprint available at Scholar
  13. [13]
    P. Kovacs, Rechnergestiitzte Symbolische Roboterkinematik, Vieweg Verlag, 1993. Google Scholar
  14. [14]
    J. C. Latombe, Robot Motion Planning, The Kluwer International Series Series in Engineering and Computer Sceince, Kluwer Academic Publishers, 1991. Google Scholar
  15. [15]
    J. M. McCarthy, Kinematics of Robot Manipulators, International Journal of Robotics Research, 5(2) (1986).Google Scholar
  16. [16]
    R. P. Paul, Robot manipulators: Mathematics, Programming and Control, The MIT Press Series in Artificial Intelligence, 1981. Google Scholar
  17. [17]
    R. Pavelle, M. Rothstein and J. Fitch, Algebra por ordenador, Scientific American (Spanish edition), 1981. Google Scholar
  18. [18]
    L. SteenComputer calculus, Science News, 119 (1981), 250–251.MathSciNetCrossRefGoogle Scholar
  19. [19]
    N. Patrikalakis, Approximate Conversion of Rational B-spline Patches, Computer Aided Geometric Design, 6 (1989), 189–204.MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    M. Raghavan and B. RothKinematic analysis of the 6R manipulator of general geometry. Proceedings of the International Symposium on Robotics Research (Tokyo), 314–320 (1989).Google Scholar
  21. [21]
    J. T. Schwartz and M. SharirOn the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds, Advances in Applied Mathematics, 4(3) (1983), 298–351.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    Algebra Made Mechanical, Nature, 290 (1981), 198–200.Google Scholar
  23. [23]
    Liberating the prose of math from its grammar,New York Times, july 19 (1988), 21.Google Scholar

Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Laureano Gonzalez-Vega
    • 1
  • Tomas Recio
    • 1
  1. 1.Departamento de Matemàticas, Estadística y Computación, Facultad de CienciasUniversidad de CantabriaSantanderSpain

Personalised recommendations