Singular Manual: center

| ##### 7.5.3.0. center Procedure from library `central.lib` (see central_lib). Usage: center(D[, N]); D int, N optional int Return: ideal, generated by computed elements Purpose: computes subalgebra generators of the center up to degree D Note: In general, one cannot compute the whole center. Hence, one has to specify a termination condition via arguments D and/or N. If D is positive, only central elements up to degree D will be found. If D is negative, the termination is determined by N only. If N is given, the computation stops if at least N elements have been found. Warning: if N is given and bigger than the actual number of generators, the procedure may not terminate. Current ordering must be a degree compatible well-ordering. Example:
    LIB "central.lib";
    ring AA = 0,(x,y,z,t),dp;
    matrix D[4][4]=0;
    D[1,2]=-z;  D[1,3]=2*x;  D[2,3]=-2*y;
    def A = nc_algebra(1,D); setring A; // this algebra is U(sl_2) tensored with K[t]
    // find generators of the center of degree <= 3:
    ideal Z = center(3);
    Z;
    ==> Z[1]=t
    ==> Z[2]=4xy+z2-2z
    inCenter(Z); // check the result
    ==> 1
    // find at least one generator of the center:
    ideal Z2 = center(-1, 1);
    Z2;
    ==> Z2[1]=t
    inCenter(Z2); // check the result
    ==> 1
See also: centralizer; inCenter.

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