Polynomials with Galois groups and
over
Author:
Gunter Malle
Journal:
Math. Comp. 51 (1988), 761-768
MSC:
Primary 12F10; Secondary 12-04, 12E10, 65H10
DOI:
https://doi.org/10.1090/S0025-5718-1988-0958642-3
MathSciNet review:
958642
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Abstract: In this paper the construction of infinite families of polynomials with Galois groups ,
and
over
is achieved. The determination of these polynomials leads to a system of nonlinear algebraic equations in 22 unknowns. The solutions belonging to the Galois extensions with the desired Galois groups are computed with a p-modular version of the Buchberger algorithm. The application of this method, which is described in some detail, turns out to be feasible even for relatively large systems of nonlinear equations.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1988-0958642-3
Article copyright:
© Copyright 1988
American Mathematical Society