Singular

7.7.3.0. variablesSorted

Usage:

variablesSorted();

Return:

ideal, generated by sorted algebra variables

Purpose:

computes the set of algebra variables sorted so that
Cartan variables go first

Note:

This is a heuristics for the computation of the center:
it is better to compute centralizers of Cartan variables first since in this
case we can omit solving the system of equations.

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)
// There is only one Cartan variable - z in U(sl_2),
// it must go 1st:
variablesSorted();
==> _[1]=z
==> _[2]=y
==> _[3]=x