Singular

LIB "central.lib";
ring AA = 0,(e,f,h),dp;
matrix D[3][3]=0;
D[1,2]=-h;  D[1,3]=2*e;  D[2,3]=-2*f;
def A = nc_algebra(1,D); // this algebra is U(sl_2)
setring A;
// At most 1st degree in e, h and at most 2nd degree in f, unit is omitted:
PBW_maxMonom( e*(f^2)* h );
==> _[1]=e
==> _[2]=f
==> _[3]=ef
==> _[4]=f2
==> _[5]=ef2
==> _[6]=h
==> _[7]=eh
==> _[8]=fh
==> _[9]=efh
==> _[10]=f2h
==> _[11]=ef2h