> For fields of characteristic p>0, I need to work in GF(p^a) for some a so
> I guess that my question really is: does anyone know how to construct the
> smallest extension of GF(p) which contains a primitive eth root of unity
> when gcd(e,p)=1?
>
Oops, when I phrase my question this way the
Thanks for the replies!
Over other fields it's no good just extending by a root of the n'th
> cyclotomic polynomial, since that need not be irreducible! The example you
> gave was particularly unfortunate since over GF(5) the 5th cyclotomic poly
> has only 1 root with multiplicity 4. So it's
As Volker said, over Q specifically the right thing to do is use
CyclotomicField():
sage: K. = CyclotomicField(5)
sage: z^5
1
sage: CC(z)
0.309016994374947 + 0.951056516295154*I
sage: CC(z) == CC(exp(2*pi*i/5))
True
Note that the latter is True because Sage constructs Cyclotomic fields with
a sp
In characteristic zero there is a dedicated CyclotomicField. Presumably
this is the most efficient implementation.
On Sunday, April 15, 2012 9:53:41 AM UTC-4, Andrew Mathas wrote:
>
> Hi,
>
> I was wondering if some one can tell me the most efficient way of doing
> calculations with roots of
