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D.15.3.37 derivationSub
Procedure from library difform.lib (see difform_lib).
- Usage:
- phi-psi; phi,psi derivation
- Return:
- the difference of the given derivations
- Remarks:
- The difference is computed componentwise - this works since the
structure lists of derivations are sorted the same way.
- Note:
- one can also subtract polynomials from derivations
Example:
| LIB "difform.lib";
ring R = 0,(x,y),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
forms dDx, dDy, dx, dy are available.
list L_1; L_1[1] = list(dx,dy); L_1[2] = list(x+y,1);
list L_2; L_2[1] = list(dy,dx); L_2[2] = list(x,y2);
/////////////////
// Derivations //
/////////////////
derivation phi_1 = L_1; phi_1;
==> Omega_R^1 --> R
==> dx |--> x+y
==> dy |--> 1
==>
==>
derivation phi_2 = L_2; phi_2;
==> Omega_R^1 --> R
==> dx |--> y2
==> dy |--> x
==>
==>
///////////////////////////////
// Difference of derivations //
///////////////////////////////
phi_1-phi_2;
==> Omega_R^1 --> R
==> dx |--> x-y2+y
==> dy |--> -x+1
==>
==>
phi_1-phi_2-phi_1;
==> Omega_R^1 --> R
==> dx |--> -y2
==> dy |--> -x
==>
==>
phi_1 - (x+y);
==> Omega_R^1 --> R
==> dx |--> 0
==> dy |--> -x-y+1
==>
==>
kill Omega_R,dx,dy,L_1,L_2,phi_1,phi_2;
| See also:
derivationAdd;
derivationNeg.
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