LIB "difform.lib";
ring R = 0,(x,y,z),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dx, dy, dz are available.
/////////////////////////////////
// Construction of derivations //
/////////////////////////////////
list L_1; L_1[1] = list(dx,dy,dz); L_1[2] = list(x,y,z);
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        dx |--> x
==>        dy |--> y
==>        dz |--> z
==> 
==> 
list L_2; L_2[1] = list(dx,dy,dz); L_2[2] = list(y-x,z-y,x-z);
derivation phi_2 = L_2; phi_2;
==>  Omega_R^1 --> R
==>        dx |--> -x+y
==>        dy |--> -y+z
==>        dz |--> x-z
==> 
==> 
/////////////////////////////////
// Contractions of derivations //
/////////////////////////////////
derivationContraction(phi_1,dx+dy+dz);
==> x+y+z
==> 
derivationContraction(phi_1,x2*y4-z);
==> 0
==> 
derivationContraction(phi_1,x2*dx*dy + dx*dy*dz);
==> (-x2y)*dx+(-x3)*dy+z*dx*dy+y*dx*dz+x*dy*dz
==> 
derivationContraction(phi_2,dx+dy+dz);
==> 0
==> 
derivationContraction(phi_2,dx*dy*dz - dx*dy + dx*dz);
==> (-x-y+2z)*dx+(-x+y)*dy+(x-y)*dz+(x-z)*dx*dy+(-y+z)*dx*dz+(-x+y)*dy*dz
==> 
kill Omega_R,dx,dy,dz,L_1,L_2,phi_1,phi_2;