Singular Manual: derivationEqu

D.15.2.40 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 dDu, dDv, du, dv are available.
list L_1; L_1[1] = list(dv,du); L_1[2] = 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;