Thank you all,
I hope that I didn't seem annoyed by the current way of doing things.
I have been charged with translating some examples for an
undergraduate algebra course which use Magma where this is a valid
construction.
The whole goal of the example was to have the students do the
extension over the non-prime field, but since this isn't possible, and
may be very difficult to do in general, I will find a way around this.
Thank you for all of the help!
Regards,
David M. Monarres
<dmmonar...@gmail.com>
P.S. If anybody has any literature which outlines the algorithms
required to implement the more general construction it would be great.
I have time over the summer and would love to contribute what I can.
On Thu, Jun 2, 2011 at 11:44 AM, Nils Bruin <nbr...@sfu.ca> wrote:
> On May 25, 12:26 pm, "D. Monarres" <dmmonar...@gmail.com> wrote:
>> Then I construct F_{5^2}
>>
>> sage: F25.<a> = F5.extension( PR[0], 'a')
>>
>> and everything works great. The problem arises when I want to extend
>> this field. When I try to construct my polynomial over F25 I get an
>> error that F25 does not allow for iteration.
>
> You are hitting a generic implementation here. The same code would get
> called for other base rings as well. If you want a finite field, you
> can use the "modulus=" keyword with GF. See "GF?" for more
> information.
>
>> Do you think that
>> PolynomialQuotientRing_field can be extended to support iteration as
>> long as it is finite?
>
> It could, but it might be the wrong place to do it. The fact that the
> result was going to be finite was already known when F5.extension got
> called, so the obvious place to effect a changed behaviour would be by
> specializing the "extension" method on finite fields. If the modulus
> is irreducible (and even the generic code seems to check for that), it
> could specialize to the required GF(...,modulus=,,,) call.
>
> One might want to check that all the generic methods available on the
> result of F5.extension are also available on the result of GF,
> otherwise the change would break code that depends on the current
> behaviour (if any).
>
> The reason why F5.extension doesn't produce a "finite field" is
> probably because there is another way of doing that and the original
> authors didn't bother specializing F5.extension to it (the very
> existence of F5.extension might postdate the GF(...modulus=...) call
> and only appear on finite fields due to inheritance).
>
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