|
7.5.1.0. 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 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;
nc_algebra(1,D); // this algebra is U(sl_2)
==> // characteristic : 0
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
==> // noncommutative relations: ...
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]=x
==> C[2]=y
==> C[3]=z
==> C[4]=z2
==> C[5]=yz
==> C[6]=y2
==> C[7]=xz
==> C[8]=xy
==> C[9]=x2
==> C[10]=z3
==> C[11]=yz2
==> C[12]=y2z
==> C[13]=y3
==> C[14]=xz2
==> C[15]=xyz
==> C[16]=xy2
==> C[17]=x2z
==> C[18]=x2y
==> C[19]=x3
==> C[20]=z4
==> C[21]=yz3
==> C[22]=y2z2
==> C[23]=y3z
==> C[24]=y4
==> C[25]=xz3
==> C[26]=xyz2
==> C[27]=xy2z
==> C[28]=xy3
==> C[29]=x2z2
==> C[30]=x2yz
==> C[31]=x2y2
==> C[32]=x3z
==> C[33]=x3y
==> C[34]=x4
inCentralizer(C, F); // check the result
==> 1
| centerVS, centralizer, inCentralizer
|