Abstract
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.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Heintz, J.: Definability Bounds of First Order Theories of Algebraically Closed Fields (Abstract). Proc. Fundamentals of Computation Theory FCT'79 (1979), p. 160–166.
": " (1977) (unpublished).
": Towards a Decision Procedure for Prime Ideals in Polynomial Rings. Report on the 1979 Oberwolfach Conference on Complexity Theory, (1979).
", Schnorr, C.P.: Testing Polynomials which are Easy to Compute. 12 th Annual Symp. ACM on Computing, (1980), p. 262–272.
", Wüthrich, R.: An Efficient Quantifier Elimination Algorithm for Algebraically Closed Fields of Any Characteristic. SIGSAM Bull. Vol. 9, No 4, (1975), p. 11.
Herrmann, G.: Die Frage der endlich vielen Schritten in der Theorie der Polynomideale. Math. Ann. 95 (1926), p. 736–788.
Kendig, K.: Elementary Algebraic Geometry. New York, Springer Verlag, (1970).
Lang, S.: Introduction to Algebraic Geometry. New York, Interscience, (1964).
Šafarevič, I.R.: Osnovy Algebraičeskoj Geometrii. Moskva, Nauka, (1972). English Translation: Basic Algebraic Geometry. Springer Verlag, (1974).
Seidenberg, A.: Constructions in Algebra. Trans. AMS, Vol. 194, (1974), p. 273–313.
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heintz, J., Sieveking, M. (1981). Absolute primality of polynomials is decidable in random polynomial time in the number of variables. In: Even, S., Kariv, O. (eds) Automata, Languages and Programming. ICALP 1981. Lecture Notes in Computer Science, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10843-2_2
Download citation
DOI: https://doi.org/10.1007/3-540-10843-2_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10843-6
Online ISBN: 978-3-540-38745-9
eBook Packages: Springer Book Archive