On 20 Sep, 06:39, Robert Bradshaw <[EMAIL PROTECTED]>
wrote:
> > To define an abstract number field, something like K =
> > number_field(QQ, x^3-3*x^2+1) could work. Eventually one will want to
> > be able to do adjoin(K, y^5+7*y-1), compositum(L, M), etc.
>
> Would/could these functions return lists too, if, say, the
> intersection of L and M was not Q?
Yeah, thinking about it some more, I think these functions really only
make sense if everything is embedded in another field. In particular
they should make sense if everything is embedded in an algebraic
closure of Q.
But one might need to specify the field they are embedded in, since
ideally number fields should be allowed to be specified with more than
one embedding.
I suppose that one could limit the number of embeddings of K to 1 and
then just clone K and give the clone a different embedding. But
whatever means is used to clone K it should be able to specify an
isomorphism between the two copies so that one can easily go from the
elements of one embedding field to the other. For example it would be
nice to embed K into its Galois closure and then think of this as
being identified with a subfield of Q bar. This would require K to be
simultaneously embedded in Q bar and in the Galois closure of K.
Of course one's wish list always grows longer than one's lifespan and
ability to implement.
Bill.
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
