Let's think about what users actually want when they call for the Galois Group of a (possibly non-Galois) number field K. First of all, they might want to know whether or not K is Galois itself; then they may want the Galois group of the closure and the closure itself; about the group, they may only want to know something about it such as its order, or its isomorphism type; and finally they may want to use the elements of the group as automorphisms, i.e. as maps from the Galois closure to itself. If there is a quicker way to get the group order and/or structure without the rest, that should be available.
John On 28 April 2014 09:42, Dima Pasechnik <[email protected]> wrote: > On 2014-04-28, Rob Beezer <[email protected]> wrote: > > The groups are isomorphic: > > > > sage: K.<a> = NumberField(x^4 - 2) > > sage: G1 = K.galois_group(names='bbb') > > sage: G2 = K.galois_group(type="gap",names='bbb').group() > > sage: G1.is_isomorphic(G2) > > True > > > > but > > > > sage: K.galois_closure(names="ccc") > > Number Field in ccc with defining polynomial x^8 + 28*x^4 + 2500 > > > > So "bug" sounds overly harsh to me. Is GAP cleaning up it's version, by > > replacing it with an isomorphic version? > In case of G2, no attempt to work out the Galois closure is made. > Sage basically returns the result of the following computation: > > sage: R.<x>=QQ[] > sage: p = x^4 - 2 > sage: p.galois_group() > Transitive group number 3 of degree 4 > > This still sounds like a documentation bug to me, no? > > > > > Pedagogically, I prefer G1, which uses 8 points, rather than the 4 used > by > > G2. > > computationally, G1 is often infeasible in cases where G2 is still > quick to find, as Nils pointed out, too. > > Dima > > > > Rob > > > > On Sunday, April 27, 2014 3:32:46 PM UTC-7, Dima Pasechnik wrote: > > > >> Is this a bug? > >> I ran into this while working on #16243. > >> > > > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > 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-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
