Singular

LIB "difform.lib";
ring R = 0,(x,y),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dx, dy are available.
list L_1; L_1[1] = list(dx,dy); L_1[2] = list(x+y,1);
list L_2; L_2[1] = list(dy,dx); L_2[2] = list(x,y2);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        dx |--> x+y
==>        dy |--> 1
==> 
==> 
derivation phi_2 = L_2; phi_2;
==>  Omega_R^1 --> R
==>        dx |--> y2
==>        dy |--> x
==> 
==> 
///////////////////////////////
// Difference of derivations //
///////////////////////////////
phi_1-phi_2;
==>  Omega_R^1 --> R
==>        dx |--> x-y2+y
==>        dy |--> -x+1
==> 
==> 
phi_1-phi_2-phi_1;
==>  Omega_R^1 --> R
==>        dx |--> -y2
==>        dy |--> -x
==> 
==> 
phi_1 - (x+y);
==>  Omega_R^1 --> R
==>        dx |--> 0
==>        dy |--> -x-y+1
==> 
==> 
kill Omega_R,dx,dy,L_1,L_2,phi_1,phi_2;