manuscripta mathematica

, Volume 43, Issue 2–3, pp 289–307

On the computation of resolvents and Galois groups

  • Kurt Girstmair
Article

Abstract

A large class of algorithms for computing resolvents of algebraic equations — so called rational transformations — is investigated and characterized group theoretically. The concept of rational transformations implies a program how to develop good methods to determine the Galois group of an equation. It is shown that some known methods are special cases of rational transformations, and a new procedure to find the group of a sextic equation is given. Moreover, all cases in which Galois resolvents can be found by means of rational transformations are classified.

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Kurt Girstmair
    • 1
  1. 1.Institut für Mathematik der Universität InnsbruckInnsbruckAustria

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