On Jul 21, 6:01 pm, mac8090 <bonzerpot...@hotmail.com> wrote: > For a field extension over Q of 2 values, for example M=QQ(i, sqrt > (2)), it is possible to find an absolute field X by the following > > L.<b>=NumberField(x^2-2) > R.<t>=L[] > M.<c>=L.extension(t^2+1) > > (this gets M) > > X.<d>=M.absolute_field() > > so far so good. A field in terms of b and c has now become a field in > terms of just one value, d. Also, the absolute_field command also > gives functions between M and X, namely definable as: > > from_X, to_X = X.structure() > > The units of M, X respectively can be found by > > X.units() > M.units() > > However, would it now make sense if the units of M corresponded to the > units of X? Or is that wrong? > > If so, the following statement > > [to_X(g) for g in M.units()]==X.units() > > would return True. But it does not. Nor are the values of X.units() a > rearrangement of the values in the set on the left hand side. Why > doesn't this work?
I find it curious that the example doesn't work for you, because for me it does work; in fact, if you look at the code of the units() command, you'll see that for a relative field like M, it's internally calculating the units in the corresponding absolute field (using Pari) and mapping them over to the relative field, exactly as you're doing "by hand" in your example. Which version of Sage are you using? Some of this code has been changed relatively recently -- Francis Clarke fixed a number of bugs in the relative number fields code in patch #5842, which was included in Sage 4.0.2 (released about a month back). David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
