Singular

LIB "difform.lib";
ring R = 13,(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.
/////////////////////////////////
// Construction of derivations //
/////////////////////////////////
list L_1; L_1[1] = list(dx,dt,dz,dy); L_1[2] = list(x,y,z,t);
derivation phi_1 = L_1; phi_1;
==>  Omega_R^1 --> R
==>        dx |--> x
==>        dy |--> t
==>        dz |--> z
==>        dt |--> y
==> 
==> 
list L_2; L_2[1] = list(dx,dy,dz,dt); L_2[2] = list(y2x-zt,zt + y, t3-x, y4-y5);
derivation phi_2 = L_2; phi_2;
==>  Omega_R^1 --> R
==>        dx |--> xy2-zt
==>        dy |--> zt+y
==>        dz |--> t3-x
==>        dt |--> -y5+y4
==> 
==> 
list L_3; L_3[1] = list(dx,dy,dz,dt); L_3[2] = list(0,0,0,0);
derivation phi_3 = L_3; phi_3;
==>  Omega_R^1 --> R
==>        dx |--> 0
==>        dy |--> 0
==>        dz |--> 0
==>        dt |--> 0
==> 
==> 
///////////////////////////////
// Evaluation of derivations //
///////////////////////////////
phi_1(0);
==> 0
phi_1(dx+dy+dz+dt);
==> x+y+z+t
phi_1(3*dx - dt);
==> 3x-y
phi_2(dt);
==> -y5+y4
phi_2(dx+dt);
==> -y5+y4+xy2-zt
phi_2(dx - dy + (x3-y2)*dz + 12*dt);
==> x3t3+y5-y2t3-x4-y4+2xy2-2zt-y
phi_3(dx);
==> 0
phi_3(dy);
==> 0
phi_3(dx - 24*(dx + dz) - x4*dy);
==> 0
kill Omega_R,dx,dy,dz,dt,L_1,L_2,L_3,phi_1,phi_2,phi_3;