Absolute primality of polynomials is decidable in random polynomial time in the number of variables

  • Joos Heintz
  • Malte Sieveking
Session 1: A. Paz, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)


Let F be a n-variate polynomial with deg F = d over an infinite field k0. Absolute primality of F can be decided randomly in time polynomial in n and exponential in d5 and determinalistically in time exponential in d6 + n2 d3.


Prime Ideal Arithmetical Operation Polynomial Ring Zero Divisor Quantifier Elimination 


  1. [1]
    Heintz, J.: Definability Bounds of First Order Theories of Algebraically Closed Fields (Abstract). Proc. Fundamentals of Computation Theory FCT'79 (1979), p. 160–166.Google Scholar
  2. [2]
    ": " (1977) (unpublished).Google Scholar
  3. [3]
    ": Towards a Decision Procedure for Prime Ideals in Polynomial Rings. Report on the 1979 Oberwolfach Conference on Complexity Theory, (1979).Google Scholar
  4. [4]
    ", Schnorr, C.P.: Testing Polynomials which are Easy to Compute. 12 th Annual Symp. ACM on Computing, (1980), p. 262–272.Google Scholar
  5. [5]
    ", Wüthrich, R.: An Efficient Quantifier Elimination Algorithm for Algebraically Closed Fields of Any Characteristic. SIGSAM Bull. Vol. 9, No 4, (1975), p. 11.Google Scholar
  6. [6]
    Herrmann, G.: Die Frage der endlich vielen Schritten in der Theorie der Polynomideale. Math. Ann. 95 (1926), p. 736–788.Google Scholar
  7. [7]
    Kendig, K.: Elementary Algebraic Geometry. New York, Springer Verlag, (1970).Google Scholar
  8. [8]
    Lang, S.: Introduction to Algebraic Geometry. New York, Interscience, (1964).Google Scholar
  9. [9]
    Šafarevič, I.R.: Osnovy Algebraičeskoj Geometrii. Moskva, Nauka, (1972). English Translation: Basic Algebraic Geometry. Springer Verlag, (1974).Google Scholar
  10. [10]
    Seidenberg, A.: Constructions in Algebra. Trans. AMS, Vol. 194, (1974), p. 273–313.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Joos Heintz
  • Malte Sieveking

There are no affiliations available

Personalised recommendations