# Singular          #### D.15.12.42 derivationEqu

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

Usage:
phi == psi; phi,psi derivation

Return:
1, if phi and psi are equal - 0, otherwise

Remarks:
The images of the generators are compared compononentwise - this works since the structure lists of derivations are sorted the same way.

Note:
derivations can also be compared to polynomials

Example:
 ```LIB "difform.lib"; ring R = 0,(u,v),lp; diffAlgebra(); ==> // The differential algebra Omega_R was constructed and the differential \ forms du, dv are available. list L_1; L_1 = list(dv,du); L_1 = list(u,-v); ///////////////// // Derivations // ///////////////// derivation phi_1 = L_1; phi_1; ==> Omega_R^1 --> R ==> du |--> -v ==> dv |--> u ==> ==> derivation phi_poly = u*v; phi_poly; ==> Omega_R^1 --> R ==> du |--> uv ==> dv |--> uv ==> ==> /////////////////////////////// // Comparison of derivations // /////////////////////////////// phi_1 == phi_1; ==> 1 phi_1 == phi_poly; ==> 0 phi_poly == u*v; ==> 1 kill Omega_R,du,dv,phi_1,phi_poly; ``` 