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Mathematics of Computation

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On invariant polynomials and their application in field theory

Author: Kurt Girstmair
Journal: Math. Comp. 48 (1987), 781-797
MSC: Primary 12-04; Secondary 12F10, 20B99
MathSciNet review: 878706
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Abstract: Certain polynomials invariant under a permutation group G (so called G-polynomials) play an important role in several computational methods of Galois theory. Since their practical value depends on the degree, it is important to know G-polynomials of smallest possible degree. A reasonable technique to find such G-polynomials is presented, and for certain classes of groups an explicit description is obtained. The list of G-polynomials given by Stauduhar in vol. 27 of this journal is thereby enlarged and improved. As an application of G-polynomials, three important resolvents of quintic and sextic algebraic equations are computed and a parametric family of sextic equations with given Galois group is exhibited.

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Article copyright: © Copyright 1987 American Mathematical Society