Singular Manual: centerRed

| ##### 7.5.3.0. centerRed Procedure from library `central.lib` (see central_lib). Usage: centerRed( 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),dp;
    matrix D[3][3]=0;
    D[1,2]=z;
    def A = nc_algebra(1,D); setring A; // it is a Heisenberg algebra
    // find a basis of the vector space of
    // central elements of degree <= 3:
    ideal VSZ = centerVS(3);
    // There should be 3 degrees of z.
    VSZ;
    ==> VSZ[1]=z
    ==> VSZ[2]=z2
    ==> VSZ[3]=z3
    inCenter(VSZ); // check the result
    ==> 1
    // find "minimal" central elements of degree <= 3
    ideal SAZ = centerRed(3);
    // Only 'z' must be computed
    SAZ;
    ==> SAZ[1]=z
    inCenter(SAZ); // check the result
    ==> 1
See also: center; centerVS; centralizerRed; inCenter.

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