I looked at it, but will have to go into more detail, perhaps a good
starting point to revise the whole field staff after 28 years, but would
take its time. Right now I had worked
on a such kind of domains anyway, as for a project I need
TranscendentalExtensionField
and
FiniteTranscendentalExtensionField
etc. to be able to construct towers of field extensions, either
algrebraic or transcendental.
Am 07.11.19 um 17:52 schrieb Ralf Hemmecke:
> Hello Johannes,
>
> as one of the authors of the finite field implementation you might
> probably be able to tell me what is happening here, see attachment.
>
> The last
>
> coerce(c2)$F4
>
> takes nearly 18 seconds on my laptop (first time only, of course).
> That's probably due to the computation of the discrete logarithm table.
>
> Unfortunately, for p>10^6 that makes the finite field implementation
> impractical (at least for my purpose).
>
> Actually, I wonder why it takes so long. Is there really need to trigger
> the computation of the table. Doesn't this "coerce" (inclusion of F2
> into F4) just mean consider c2 as a constant polynomial in the
> representation (SAE) of F4?
>
> Maybe some background for my problem.
> In fact, I want to implement algebraic numbers via the following paper.
>
> @article{Steel:AlgebraicallyClosedFields:2010,
> author = {Allan K. Steel},
> title = {Computing with algebraically closed fields},
> journal = {Journal of Symbolic Compuation},
> volume = 45,
> number = 3,
> pages = {342--372},
> year = 2010,
> issn = {0747-7171},
> doi = {10.1016/j.jsc.2009.09.005},
> url =
> {http://www.sciencedirect.com/science/article/pii/S0747717109001497},
> keywords = {Algebraic closure, Algebraic number field, Algebraic
> function field, Field extension, Inseparability,
> Non-perfect field, Polynomial factorization, Root
> finding},
> }
>
> As far as I understand, this needs an "evaluation (finite) field" in
> which there are enough roots. So potentially, I'd need the algebraic
> closure of a prime field of a prime characteristic close to machine
> integer size.
>
> Any idea how such a field could be implemented in FriCAS?
>
> I thought, I could somehow use FiniteFieldExtension to dynamically grow
> this "evaluation field", but the above problem hinders me in thinking
> further in this direction.
>
> Ralf
>
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Johannes Grabmeier
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