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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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


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:
  • MathSciNet review: 878706