Singular

LIB "difform.lib";
ring R = 0,(x,y,z),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dx, dy, dz are available.
list L_1; L_1[1] = list(dx,dy,dz); L_1[2] = list(2x,2y,2z);
list L_2; L_2[1] = list(dx,dy,dz); L_2[2] = list(y2-x,z4+x+y,y2);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        dx |--> 2x
==>        dy |--> 2y
==>        dz |--> 2z
==> 
==> 
derivation phi_2 = L_2; phi_2;
==>  Omega_R^1 --> R
==>        dx |--> -x+y2
==>        dy |--> x+y+z4
==>        dz |--> y2
==> 
==> 
////////////////////////
// Sum of derivations //
////////////////////////
phi_1 + phi_2;
==>  Omega_R^1 --> R
==>        dx |--> x+y2
==>        dy |--> x+3y+z4
==>        dz |--> 2z+y2
==> 
==> 
phi_1 + phi_2 + phi_2;
==>  Omega_R^1 --> R
==>        dx |--> 2y2
==>        dy |--> 2x+4y+2z4
==>        dz |--> 2z+2y2
==> 
==> 
phi_1 + phi_2 + 3x2;
==>  Omega_R^1 --> R
==>        dx |--> x+3x2+y2
==>        dy |--> x+3y+3x2+z4
==>        dz |--> 2z+3x2+y2
==> 
==> 
kill Omega_R,dx,dy,dz,L_1,L_2,phi_1,phi_2;