#8373: finite fields constructed with non-primitive defining polynomial
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Reporter: rkirov | Owner: AlexGhitza
Type: defect | Status: new
Priority: minor | Milestone:
Component: basic arithmetic | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by rkirov):
I guess you are right, it is a generator as an algebra. Somehow I assumed
F.<a> gives you 'a' as a multiplicative generator. So it is really a
renaming of 'x'(poly var)->'a'. I didn't see the convenient function
F.multiplicative_generator.
I checked that Magma has similar behavior.
{{{
> F2 := GF(2);
> FP<x> := PolynomialRing(F2);
> F<z> := ext< F2 | x^4+x^3+x^2+x+1 >;
}}}
It also seems to have different algorithm for primitive element,
{{{
> PrimitiveElement(F);
z^3 + z + 1
}}}
In any case I am leaving this open so someone can work on the bug you
found.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8373#comment:2>
Sage <http://www.sagemath.org>
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