On Jun 24, 4:35 am, David Joyner <[email protected]> wrote:
...
> At first I thought it should be 0 in this case because I
> confused "trivial character" with "identically equal to 1".
That makes it surprising that T.jacobi_sum(T) was correctly defined to
be p-2
(instead of p) for the trivial character T mod p.
> I don't understand why
>
> sage: parent(Z.jacobi_sum(Z))
> Cyclotomic Field of order 20 and degree 8
>
> is incorrect though.
EVERY Jacobi sum over GF(5) lies in a much smaller cyclotomic field,
namely the field of Gaussian integers. That's because each term of the
defining sum is a Gaussian integer. For example:
sage: parent(Z(3))
Cyclotomic Field of order 4 and degree 2
rje
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
