On Jul 22, 12:21 pm, davidloeffler <dave.loeff...@gmail.com> wrote:
> 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
Good point. Remember Rule 1: always say exactly which version of
Sage you are using (and preferably which platform, etc), and give the
exact input which causes the problem!
John
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