Singular Manual: centralizerRed

| ##### 7.5.3.0. centralizerRed Procedure from library `central.lib` (see central_lib). Usage: centralizerRed( F, D[, N] ); F ideal, D int, N optional int Return: ideal, generated by computed elements Purpose: computes subalgebra generators of centralizer(F) up to degree D. Note: In general, one cannot compute the whole centralizer(F). Hence, one has to specify a termination condition via arguments D and/or N. If D is positive, only centralizing elements up to degree D are computed. 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;  D[1,3]=2*x;  D[2,3]=-2*y;
    def A = nc_algebra(1,D); setring A; // this algebra is U(sl_2)
    ideal F = x, y;
    // find subalgebra generators of degree <= 4 of the subalgebra of
    // all elements commuting with x and y:
    ideal C = centralizerRed(F, 4);
    C;
    ==> C[1]=4xy+z2-2z
    inCentralizer(C, F); // check the result
    ==> 1
See also: centerRed; centralizer; centralizerVS; inCentralizer.

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