Singular

LIB "difform.lib";
ring R = 0,(a,b,t),ls;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms da, db, dt are available.
list L_1; L_1[1] = list(da,dt,db); L_1[2] = list(2a,2t-b,2t);
list L_2; L_2[1] = list(dt,db,da); L_2[2] = list(-a,-b,-t);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        da |--> 2a
==>        db |--> 2t
==>        dt |--> 2t-b
==> 
==> 
derivation phi_2 = L_2; phi_2;
==>  Omega_R^1 --> R
==>        da |--> -t
==>        db |--> -b
==>        dt |--> -a
==> 
==> 
///////////////////////////////////
// Multiplication of derivations //
///////////////////////////////////
phi_1*phi_2;
==>  Omega_R^1 --> R
==>        da |--> -2at
==>        db |--> -2bt
==>        dt |--> -2at+ab
==> 
==> 
phi_1*phi_2*phi_2;
==>  Omega_R^1 --> R
==>        da |--> 2at2
==>        db |--> 2b2t
==>        dt |--> 2a2t-a2b
==> 
==> 
phi_2*(3a2-bt);
==>  Omega_R^1 --> R
==>        da |--> bt2-3a2t
==>        db |--> b2t-3a2b
==>        dt |--> abt-3a3
==> 
==> 
kill Omega_R,da,db,dt,L_1,L_2,phi_1,phi_2;