7.7.3.0. centralizerRed

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.

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