Singular

D.15.12.40 derivationNeg

Procedure from library `difform.lib` (see difform_lib).

Usage:
-phi; phi derivation

Return:
the negation of a given derivation

Example:
 ```LIB "difform.lib"; ring R = 0,(x,y,z,t),dp; diffAlgebra(); ==> // The differential algebra Omega_R was constructed and the differential \ forms 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; ```