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D.2.12.15 rootofUnity
Procedure from library ring.lib (see ring_lib).
- Usage:
- rootofUnity(n); n an integer
- Return:
- number
- Purpose:
- compute the minimal polynomial for the n-th primitive root of unity
- Note:
- works only in field extensions by one element
Example:
| | LIB "ring.lib";
ring r = (0,q),(x,y,z),dp;
rootofUnity(6);
==> (q2-q+1)
rootofUnity(7);
==> (q6+q5+q4+q3+q2+q+1)
minpoly = rootofUnity(8);
r;
==> // coefficients: QQ[q]/(q4+1)
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
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