LIB "tst.lib"; tst_init();
  ring r=0,(x,y,Dx,Dy),dp;
  matrix M[4][4]; M[1,3]=1;M[2,4]=1;
  def R = nc_algebra(1,M); // 2nd Weyl algebra
  setring R;
  dim(std(0)); // the GK dimension of the ring itself
  ideal I=x*Dy^2-2*y*Dy^2+2*Dy, Dx^3+3*Dy^2;
  dim(std(I)); // the GK dimension of the module R/I
  module T = (x*Dx -2)*gen(1), Dx^3*gen(1), (y*Dy +3)*gen(2);
  dim(std(T)); // the GK dimension of the module  R^2/T
tst_status(1);$