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7.5.3.0. centralizerVS
Procedure from library central.lib (see central_lib).
- Usage:
- centralizerVS( F, D ); F ideal, D int
- Return:
- ideal, generated by computed elements
- Purpose:
- computes a vector space basis of centralizer(F) 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)
ideal F = x, y;
// find generators of the vector space of elements
// of degree <= 4 commuting with x and y:
ideal C = centralizerVS(F, 4);
C;
==> C[1]=4xy+z2-2z
==> C[2]=16x2y2+8xyz2+z4-32xyz-4z3-4z2+16z
inCentralizer(C, F); // check the result
==> 1
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See also:
centerVS;
centralizer;
inCentralizer.
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