# Singular          #### D.15.12.39 derivationSub

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

Usage:
phi-psi; phi,psi derivation

Return:
the difference of the given derivations

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

Note:
one can also subtract polynomials from derivations

Example:
 ```LIB "difform.lib"; ring R = 0,(x,y),lp; diffAlgebra(); ==> // The differential algebra Omega_R was constructed and the differential \ forms dx, dy are available. list L_1; L_1 = list(dx,dy); L_1 = list(x+y,1); list L_2; L_2 = list(dy,dx); L_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; ``` 