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D.15.2.36 derivationAdd
Procedure from library difform.lib (see difform_lib).
- Usage:
- phi+psi; phi,psi derivation
- Return:
- the sum of the given derivations
- Remark:
- The sum is computed componentwise - this works since the structure lists
of derivations are sorted the same way.
- Note:
- once can also add polynomials and derivations
Example:
| LIB "difform.lib";
ring R = 0,(x,y,z),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
forms dDx, dDy, dDz, dx, dy, dz are available.
list L_1; L_1[1] = list(dx,dy,dz); L_1[2] = list(2x,2y,2z);
list L_2; L_2[1] = list(dx,dy,dz); L_2[2] = list(y2-x,z4+x+y,y2);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==> Omega_R^1 --> R
==> dx |--> 2x
==> dy |--> 2y
==> dz |--> 2z
==>
==>
derivation phi_2 = L_2; phi_2;
==> Omega_R^1 --> R
==> dx |--> -x+y2
==> dy |--> x+y+z4
==> dz |--> y2
==>
==>
////////////////////////
// Sum of derivations //
////////////////////////
phi_1 + phi_2;
==> Omega_R^1 --> R
==> dx |--> x+y2
==> dy |--> x+3y+z4
==> dz |--> 2z+y2
==>
==>
phi_1 + phi_2 + phi_2;
==> Omega_R^1 --> R
==> dx |--> 2y2
==> dy |--> 2x+4y+2z4
==> dz |--> 2z+2y2
==>
==>
phi_1 + phi_2 + 3x2;
==> Omega_R^1 --> R
==> dx |--> x+3x2+y2
==> dy |--> x+3y+3x2+z4
==> dz |--> 2z+3x2+y2
==>
==>
kill Omega_R,dx,dy,dz,L_1,L_2,phi_1,phi_2;
| See also:
derivationSub.
|