#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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Consider the following code:
{{{
sage: R.<x> = PolynomialRing(GF(2))
sage: K.<a> = GF(16, modulus=x^4+x^3+x^2+x+1)
sage: a^5
1
}}}
This is all fine mathematically, as long as the user is clear what a is
and isn't (it isn't a generator for the multiplicative group of the finite
field). So the options as I see them (in increasing difficulty for
implementation):
1)GF already checks modulus for irreducibility, just add check for
modulus.is_primitive().
2)Rewrite the help for the GF function to indicate that the function does
not return a generator necessarily (like in this specific case).
3)Find an actual generator (that might not be the polynomial x) and return
that.
Opinions?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8373>
Sage <http://www.sagemath.org>
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