Singular Manual: rootofUnity

| #### 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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