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.
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