On Fri, May 24, 2013 at 10:38 AM, Karl-Dieter Crisman
> <kcris...@gmail.com> wrote:
> > Just pass this on to anyone who might know the answer (you? sage-nt?) -
> the
> > same person asked this twice:
> >
> >
> http://stackoverflow.com/questions/11850418/computing-maximal-orders-in-large-number-fields-with-sage
> >
> >
> http://ask.sagemath.org/question/1652/computing-maximal-orders-in-relative-extensions
> >
>


I tried to answer the question, but ran into trouble. And the worst part is
that Ctrl+C does not help me. Is a KeyboardInterrupt caught accidentally?
Or is a keyboard interrupt not properly passed on to another program? I'm
having trouble debugging this one. Perhaps I'm not knowledgeable or patient
enough to work with the "trace" command. Any ideas?

sage: Qa12.<kappa12> = NumberField(x^14 - 26*x^13 + 325*x^12 - 2548*x^11 +
13832*x^10 - 54340*x^9 + 157118*x^8 - 333580*x^7 + 509366*x^6 - 534820*x^5
+ 354536*x^4 - 124852*x^3 + 15145*x^2 - 33514*x + 13)
sage: y = polygen(Qa12)
sage: L.<c> = Qa12.extension(y^2-kappa12)
sage: L.<alpha> = L.absolute_field()
sage: OO = Qa12.maximal_order()
sage: bas = [L.structure()[1](b) for b in OO.basis()]
sage: subOrderK = L.order(bas + [b*alpha for b in bas])
^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C^C

And once we get Ctrl+C to work, there is more work to do:
In this case, Sage is having trouble with just one order, supplied by an
actual basis. All Sage needs to do is verify that the input spans a ring.
And the example is not too large. Indeed, Magma has no trouble even in
finding the maximal order:

sage: Om = magma(L).MaximalOrder()
(a functional answer in a few seconds)

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