2008/4/14 Nick Alexander <[EMAIL PROTECTED]>:
>
> This has been discussed at length; the relevant words are Conway
> polynomials and the relevant paper is "Lattices of compatibly
> embedded finite fields" (http://portal.acm.org/citation.cfm?id=268929).
>
> If you implement this I will be forever in your debt.
Very tempting!
Perhaps you should mention that the authors of that paper are the
Magma trio Bosma, Cannon and Steele. I have just printed it and will
take a look.
John
>
> Nick
>
>
>
> On 14-Apr-08, at 8:38 AM, Willem Jan Palenstijn wrote:
>
> >
> > On Mon, Apr 14, 2008 at 02:40:14PM +0100, John Cremona wrote:
> >> Does anyone know how Magma handles this?
> >
> > From what I can tell, magma seems to choose 'default' finite fields
> > of a
> > given size at run-time, and presumably also injections between them.
> >
> > Which fields become default can depend on the order in which they are
> > created. For example,
> >
> > K := FiniteField(3^100);
> > L := FiniteField(3^500);
> >
> > gives a different field ('measured' by MinimalPolynomial(K.1) ) than
> >
> > L := FiniteField(3^500);
> > K := FiniteField(3^100);
> >
> > while "IsDefault(K);" returns true in both cases.
> >
> > In the first case, MinimalPolynomial(K.1) is a sparse polynomial,
> > in the
> > second case we have L.1^( (3^500-1) div (3^100-1) ) eq L!K.1 .
> > In the first case, L!K.1 can change between two magma runs, so the
> > chosen injection appears to be chosen randomly at run-time.
> >
> >
> > Note that this behaviour may of course be different for smaller or
> > larger finite fields.
> >
> > -Willem Jan
> >
> > >
>
>
> >
>
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