Galois Theory, 5th Edition

Chapter 22Calculating Galois Groups

DOI: 10.1201/9781003213949-22

In order to apply Galois theory to specific polynomials, it is necessary to compute the corresponding Galois group. This was the weak point in the memoir that Galois submitted to the French Academy of Sciences, as Poisson and Lacroix pointed out in their referees’ report.

However, the computation is possible—at least in principle. It becomes practical only with modern computers. It is neither simple nor straightforward, and until now we have emulated Galois and strenuously avoided it. Instead we have either studied special equations whose Galois group is relatively easy to find, resorted to special tricks, or obtained results that require only partial knowledge of the Galois ...