On Thu, Dec 12, 2013 at 03:06:46PM +0200, Georgi Guninski wrote:
> On Thu, Dec 12, 2013 at 12:21:14PM +0000, John Cremona wrote:
> > On 12 December 2013 12:12, Georgi Guninski <[email protected]> wrote:
> > > Suppose I work in QQ[sqrt(a),sqrt(b)]
> > > where a and b are integer non-squares.
> > >
> > > Can I change it to something isomorphic to QQ[\alpha]
> > > where \alpha is algebraic, i.e., work with a conventional
> > > NumberField with a single defining polynomial
> > > without extending the NumberField?
> > >
> > 
> > Is this what you want?
> > 
> > sage: K = QQ[sqrt(2),sqrt(3)]
> > sage: K.absolute_field('a')
> > Number Field in a with defining polynomial x^4 - 10*x^2 + 1
> >
> 
> Thanks, exactly this.
> 
> How to get maps between the two fields, coercion
> doesn't appear to work.
> 
>

Nevermind, I found it.

Call K2.structure() for the maps.

Thank you!

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