
7.7.3.0. 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 wellordering.
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+z22z
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.
