# Singular          Procedure from library `difform.lib` (see difform_lib).

Usage:
phi+psi; phi,psi derivation

Return:
the sum of the given derivations

Remark:
The sum is computed componentwise - this works since the structure lists of derivations are sorted the same way.

Note:
once can also add polynomials and derivations

Example:
 ```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 = list(dx,dy,dz); L_1 = list(2x,2y,2z); list L_2; L_2 = list(dx,dy,dz); L_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; ``` 