 ring r=0,(x,y,z),dp;
matrix d[3][3];
d[1,2]=z; d[1,3]=2x; d[2,3]=2y;
def R=nc_algebra(1,d); // this algebra is U(sl_2)
setring R;
ideal i=x2,y2,z21;
i=std(i);
print(matrix(i)); // print a compact presentation of i
==> z21,yzy,xz+x,y2,2xyz1,x2
kbase(i);
==> _[1]=z
==> _[2]=y
==> _[3]=x
==> _[4]=1
vdim(i);
==> 4
ideal j=x,z1;
j=std(j);
kbase(j,3);
==> _[1]=y3
