, Volume 43, Issue 2-3, pp 289-307

On the computation of resolvents and Galois groups

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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.

This work was done while the author had a Humboldt research fellowship in the Universität Karlsruhe.