On 2014-04-22 23:11, Dima Pasechnik wrote:
On 2014-04-22, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote:
On 2014-04-21 10:10, Dima Pasechnik wrote:
this is not a normal extension, and apparently neither Pari nor GAP
can deal with it.
Pathetic...
Is it really so hard to implement, having the library of permutation
groups at hand (from GAP)?
The hard part is the number theory, not the group theory. If the
splitting field is very large (that seems to be the case here), then how
would you represent elements of the Galois group?
I am pretty ignorant about the way(s) these elements become available
in this setting.
The most economic way I know offhand involves generators and relations
(either in the classical combinatorial group theory sense, or in the
sense of "vector enumeration" - when the action is defined "locally"
on a module).
Matrices or permutations aren't often too bad either - depends upon
the sparsity.
Yes, but you're thinking again in terms of group theory and, like I
said, that's the easy part. What I'm trying to say is that there is no
easy way to compute *any* representation of the Galois group.
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