The virtues of laziness: Complexity of the Tangent Cone Algorithm

  • Abdallah Assi
  • Teo Mora


The Tangent Cone Algorithm is a variant of Buchberger Algorithm, to compute standard bases with respect to orderings which are not well-orderings, which is useful in computational local algebra. We show here that its complexity is the same as the one of Buchberger Algorithm.


Computational algebra Tangent cone Standard bases Algebraic complexity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gräbe, H.: The tangent cone algorithm and homogeneization, PreprintGoogle Scholar
  2. 2.
    Lazard, D.: Gröbner bases, Gaussian elimination and resolution of systems of polynomial equations, Proc. EUROCAL 83, Lect. Notes. Comp. Sci.162, 146–156 (1983)Google Scholar
  3. 3.
    Mora, T.: La queste del Saint Gra(AL): a computational approach to local algebra, Disc. Appl. Math.33, 161–190 (1991)Google Scholar
  4. 4.
    Mora, T., Pfister, G., Traverso, C: An introduction to the tangent cone algorithm. In: C. M. Hoffmann (ed.) Issues in robotics and non-linear geometry, JAI Press (1992)Google Scholar
  5. 5.
    Moreno, G.: An Ackermannian polynomial ideal, Proc. AAECC 9, Lect. Notes Comp. Sci.539, 269–280(1991)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Abdallah Assi
    • 1
  • Teo Mora
    • 2
  1. 1.Department MathématiqueUniversité de NiceGermany
  2. 2.Dipartimento InformaticaUniversità di GenovaGermany

Personalised recommendations