Singular

LIB "difform.lib";
ring R = 0,(x,y,z,t),dp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dDt, dx, dy, dz, dt are available.
list L_1; L_1[1] = list(dy,dx,dt,dz); L_1[2] = list(x2-y,23y+t,tz4,z-y);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        dx |--> 23y+t
==>        dy |--> x2-y
==>        dz |--> -y+z
==>        dt |--> z4t
==> 
==> 
derivation phi_poly = 3xyz; phi_poly;
==>  Omega_R^1 --> R
==>        dx |--> 3xyz
==>        dy |--> 3xyz
==>        dz |--> 3xyz
==>        dt |--> 3xyz
==> 
==> 
/////////////////////////////
// Negation of derivations //
/////////////////////////////
-phi_1;
==>  Omega_R^1 --> R
==>        dx |--> -23y-t
==>        dy |--> -x2+y
==>        dz |--> y-z
==>        dt |--> -z4t
==> 
==> 
-(-phi_1);
==>  Omega_R^1 --> R
==>        dx |--> 23y+t
==>        dy |--> x2-y
==>        dz |--> -y+z
==>        dt |--> z4t
==> 
==> 
-(phi_poly);
==>  Omega_R^1 --> R
==>        dx |--> -3xyz
==>        dy |--> -3xyz
==>        dz |--> -3xyz
==>        dt |--> -3xyz
==> 
==> 
kill Omega_R,dx,dy,dz,dt,L_1,phi_1,phi_poly;