#10971: Finite Field elements in terms of powers of a generator
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Reporter: aly.deines | Owner: joyner
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: group theory | Resolution:
Keywords: GF, finite field | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old description:
> For large values of q, a prime power, GF(q) has elements represented as
> polynomials over a generator.
> sage: F.<a> = GF(2^8)
> sage: a^10
> a^6 + a^5 + a^4 + a^2
>
> If you further want to compute in a polynomial ring over F, then the
> polynomials aren't very pretty as they are polynomials with polynomial
> coefficients.
> sage: R.<x> = F[]
> sage: a^10*x+1
> (a^6 + a^5 + a^4 + a^2)*x + 1
>
> It would be nice to be able to be able to print and work with the
> elements as powers of the generator.
New description:
For large values of q, a prime power, GF(q) has elements represented as
polynomials over a generator.
{{{
sage: F.<a> = GF(2^8)
sage: a^10
a^6 + a^5 + a^4 + a^2
}}}
If you further want to compute in a polynomial ring over F, then the
polynomials aren't very pretty as they are polynomials with polynomial
coefficients.
{{{
sage: R.<x> = F[]
sage: a^10*x+1
(a^6 + a^5 + a^4 + a^2)*x + 1
}}}
It would be nice to be able to be able to print and work with the elements
as powers of the generator.
--
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Ticket URL: <http://trac.sagemath.org/ticket/10971#comment:6>
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