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7.5.3.0. centerVS
Procedure from library central.lib (see central_lib).
- Usage:
- centerVS( D ); D int
- Return:
- ideal, generated by computed elements
- Purpose:
- computes a vector space basis of the center up to degree D
- Note:
- D must be non-negative
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)
// find a basis of the vector space of all
// central elements of degree <= 4:
ideal Z = centerVS(4);
Z;
==> Z[1]=4xy+z2-2z
==> Z[2]=16x2y2+8xyz2+z4-32xyz-4z3-4z2+16z
// note that the second element is the square of the first
// plus a multiple of the first:
Z[2] - Z[1]^2 + 8*Z[1];
==> 0
inCenter(Z); // check the result
==> 1
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See also:
center;
centralizerVS;
inCenter.
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