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7.5.1.0. center
Procedure from library center.lib (see center_lib).
- Usage:
- center(MaxDeg[, N]); int MaxDeg, int N
- Return:
- ideal, generated by elements of degree at most MaxDeg
- Purpose:
- computes a minimal set of central elements up to degree MaxDeg.
- Note:
- In general, one cannot predict the number or the heighest degree of
central elements. Hence, one has to specify a termination condition via arguments MaxDeg and/or N.
If MaxDeg is positive, the computation stops after all central elements of degree at most MaxDeg has been found.
If MaxDeg is negative, the termination is determined by N only.
If N is given, the computation stops if at least N central elements has been found.
Warning: if N is given and bigger than the real number of generators, the procedure may not terminate.
Example:
| LIB "center.lib";
ring A = 0,(x,y,z,t),dp;
matrix D[4][4]=0;
D[1,2]=-z; D[1,3]=2*x; D[2,3]=-2*y;
ncalgebra(1,D); // this algebra is U(sl_2) tensored with K[t]
ideal Z = center(3); // find all central elements of degree <= 3
Z;
==> Z[1]=t
==> Z[2]=4xy+z2-2z
inCenter(Z);
==> 1
ideal ZZ = center(-1, 1); // find one central element of the lowest degree
ZZ;
==> ZZ[1]=t
inCenter(ZZ);
==> 1
| centralizer, inCenter
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