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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On invariant polynomials and their application in field theory
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by Kurt Girstmair PDF
Math. Comp. 48 (1987), 781-797 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 781-797
  • MSC: Primary 12-04; Secondary 12F10, 20B99
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0878706-1
  • MathSciNet review: 878706