3
$\begingroup$

Does galois theory actually have some involvement in solving a solvable quintic, or does it just tell you whether it IS solvable or not?

  • 1
    @KannappanSampath, there are solvable pol$y$nomial equations of all degrees...2012-03-07

1 Answers 1

3

When the quintic is solvable, one can use the structure of the Galois group to explicitely construct the solutions. It is an immensely impractical task, though!

GAP has a package called RadiRoot which does precisely this.

  • 0
    If a rational $p$olynomial has all its roots rational, its Galois group is trivial and you are not going to get anything out of it (in fact, an extremely, utmostly silly way of checking that a rational polynomial has all its roots rational is to run an algorithm to compute its Galois group and seeing if the result is trivial or not!)2012-03-07