Also, I am not sure whether there is a practical algorithm to compute the Galois group when the extension is not normal (for splitting fields, there is one due to Susan Landau; however there are mod p techniques too)! On Apr 23, 2014, at 2:41 AM, Dima Pasechnik <dimp...@gmail.com> 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. > > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
