Hi,

I'm trying to find the minimal polynomial of the 12th primitive root of unity over

Is there a best way of going about this?

Thanks,

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- May 18th 2013, 02:33 PMAntMin polynomial
Hi,

I'm trying to find the minimal polynomial of the 12th primitive root of unity over

Is there a best way of going about this?

Thanks, - May 18th 2013, 04:30 PMHallsofIvyRe: Min polynomial
I would start by

**finding**the primitive roots then constructing the minimal polynomial from that.

The twelfth roots of unity, of course, satisfy the equation . They are of the form with n from 0 to 11: 1, , , , , , , , , , , and .

A**primitive**root is one that does NOT satisfy for any smaller value of n which removes 1, -1, i, and -i. What about cube roots?

It might help to note that is equivalent to

. - May 18th 2013, 04:56 PMAntRe: Min polynomial
Perhaps my terminology isn't quite right, by the "12th primitive root of unity" I meant:

So I am trying to find

As is a root of we have that the min poly divides .

I think perhaps the factorisation is off by power 2?

Hence, the min polynomial is one of the above bracketed terms:

Hence is the min poly.

Thanks! - May 18th 2013, 05:01 PMShakarriRe: Min polynomial