Singular

LIB "difform.lib";
ring R = 0,(x,y,z),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dx, dy, dz are available.
/////////////////////////////////
// Construction of derivations //
/////////////////////////////////
list L; L[1] = list(dx,dy,dz); L[2] = list(x2,y2,z2);
derivation phi = L; phi;
==>  Omega_R^1 --> R
==>        dx |--> x2
==>        dy |--> y2
==>        dz |--> z2
==> 
==> 
derivation phi_poly = x-y;
///////////////////////////////////
// Lie-derivative of derivations //
///////////////////////////////////
diff(phi,dx);
==> 2x*dx
==> 
diff(phi,dx*dy);
==> (-2x+2y)*dx*dy
==> 
diff(phi,dx*dy*dz);
==> (2x-2y+2z)*dx*dy*dz
==> 
diff(phi,dx*dy + dy*dx);
==> 0
==> 
diff(phi,dx*dy - dy*dx);
==> (-4x+4y)*dx*dy
==> 
diff(phi_poly,dx);
==> dx+(-1)*dy
==> 
diff(phi_poly,dx-dy);
==> 0
==> 
diff(phi_poly,dx+dy);
==> 2*dx+(-2)*dy
==> 
diff(phi_poly,dx*(x2-y4) + 1);
==> (3x2-4xy3-2xy+3y4)*dx+(-x2-8xy3+9y4)*dy
==> 
kill Omega_R,dx,dy,dz,L,phi,phi_poly;