I have a degree 5 polynomial whose Galois group is large (S_5): sage: x = polygen(QQ) sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1
I can compute its splitting field easily, thanks to code written by Jeroen Demeyer I believe: sage: %time L = f.splitting_field(names='b') CPU times: user 1min 1s, sys: 272 ms, total: 1min 2s Wall time: 1min 2s Note that the result is a number field of degree 120. However, if I form the degree 5 field by adjoining one root of f first, and then ask for its Galois closure, it takes very much longer: sage: K.<a> = NumberField(f) sage: %time L = K.galois_closure(names='b') CPU times: user 15min 24s, sys: 36 ms, total: 15min 24s Wall time: 15min 25s Any idea why? Essentailly the only difference I can see is that in the second case the polynomial f is first base-changed to K and then the method splitting_field is applied to that, but it is not clear to me why that should be slower since I think the first step of computing f.splitting_field() would do just that anyway? It would be very convenient for me to gain this speedup, by changing the method galois_closure() if necessary. I already plan to make the latter a @cached_method. John -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
