Computation of Galois groups over function fields

Mattman, Thomas; McKay, John

doi:10.1090/S0025-5718-97-00831-4

Computation of Galois groups over function fields
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by Thomas Mattman and John McKay PDF

Math. Comp. 66 (1997), 823-831 Request permission

Abstract:

Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over $\mathbb {Q}(t_1,t_2,\ldots ,t_m)$ in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.

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