Singular

7.7.3.0. centerRed

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.

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