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Computation of Galois Groups Over Function Fields

Thomas Mattman and John McKay
Mathematics of Computation
Vol. 66, No. 218 (Apr., 1997), pp. 823-831
Stable URL: http://www.jstor.org/stable/2153898
Page Count: 9
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Computation of Galois Groups Over Function Fields
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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 Q(t1, t2,...,tm) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation groups of degree 8 as a Galois group over the rationals is included.

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