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B.7.0.4 RootOfUnity
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- RootOfUnity(n); n an integer
- Return:
- number, the n-th primitive root of unity (for use as minpoly)
- Note:
- works only in field extensions by one element
Example:
| LIB "nctools.lib";
ring r8 = (0,q),(x,y,z),dp;
minpoly = RootOfUnity(8);
r8;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : (q4+1)
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
ring r7 = (0,q),(x,y,z),dp;
minpoly = RootOfUnity(7);
r7;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : (q6+q5+q4+q3+q2+q+1)
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
ring r6 = (0,q),(x,y,z),dp;
minpoly = RootOfUnity(6);
r6;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : (q2-q+1)
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
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