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B.1.0.1 center
Procedure from library center.lib (see center_lib).
- Usage:
- center(MaxDeg[, N]); int MaxDeg, int N
- Return:
- ideal generated by found elements
- Note:
- computes the 'minimal' set of central elements.
Since in general algorithms knows nothing about the number and degrees of
desired polynomials one have to specify any kind of termination condition:
1. MaxDeg - maximal degree of desired elements or/and
2. n - the minimal number of desired elements to find.
Example:
| LIB "center.lib";
ring a=0,(x,y,z),dp;
matrix D[3][3]=0;
D[1,2]=-z;
D[1,3]=2*x;
D[2,3]=-2*y;
ncalgebra(1,D); // this is U(sl_2)
ideal Z = center(2); // find all central elements of degree <= 2
Z;
==> Z[1]=4xy+z2-2z
inCenter(Z);
==> 1
ideal ZZ = center(-1, 1 ); // find the first non trivial central element
ZZ; "";
==> ZZ[1]=4xy+z2-2z
==>
inCenter(ZZ);
==> 1
| centralizer, inCenter
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