#13379: Add a splitting field function for polynomials over a finite field
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Reporter: abrochard | Owner: davidloeffler
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: number fields | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by robharron):
No, for F,,q,, the calling of Hom works:
{{{
sage: F = GF(3^4, 'z')
sage: K = GF(3^12, 'zz')
sage: F.Hom(K)
Set of field embeddings from Finite Field in z of size 3^4 to Finite Field
in zz of size 3^12
sage: F.Hom(K)[0]
Ring morphism:
From: Finite Field in z of size 3^4
To: Finite Field in zz of size 3^12
Defn: z |--> 2*zz^10 + zz^8 + 2*zz^7 + zz^6 + 2*zz^5 + zz^4 + 2*zz^3 +
2*zz^2 + zz + 2
}}}
The problem over F,,q,, is elsewhere: some coercion problem when calling
poly.change_ring().
Replying to [comment:8 mmasdeu]:
> Yes, I agree that for polynomials defined over F,,p,, the function
should be simplified. As for F,,q,, one definitely needs to fix the code,
since that calling of Hom won't work...
>
> Replying to [comment:7 robharron]:
> > But have you looked at the code? It doesn't do anything special with
regards to the embedding. (Do you see something I don't?) In the end it
simply says F.Hom(K)[0] (for instance, I think the code only runs when the
polynomial is defined over a prime field, in which case the embedding
returned is simply the canonical one sending 1 to 1). I just quickly wrote
a function that does what I suggested and it works just fine and is quite
quick.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13379#comment:9>
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