March 2015
Intermediate to advanced
344 pages
10h 18m
English
Content preview from Galois Theory, 4th Edition
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Chapter 22
Calculating Galois Groups
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 (I did say ‘relatively’),
resorted to
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.