M.units() will give a set of units which are a Z-basis for the units modulo roots of unity. There is no canonical basis, so there's no reason why (even if the unit ranks are the same) you should get the same generators.
For more functionality with units construct U=X.unit_group() and look at the member functions of U. John Cremona On Jul 21, 6:01 pm, mac8090 <[email protected]> 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? --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
