We give a deterministic polynomial-time algorithm to check whether the Galois group Gal (f) of an input polynomial f(X) ∈ ℚ[X] is nilpotent: the running time is polynomial in size (f). Also, we generalize the Landau-Miller solvability test to an algorithm that tests if Gal (f) is in Τd: this algorithm runs in time polynomial in size (f) and n d and, moreover, if Gal (f) ∈ Τd it computes all the prime factors of #Gal (f). © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Arvind, V., & Kurur, P. P. (2006). A polynomial time nilpotence test for galois groups and related results. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4162 LNCS, pp. 134–145). Springer Verlag. https://doi.org/10.1007/11821069_12
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