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D.15.2.45 derivationLie
Procedure from library difform.lib (see difform_lib).
- Usage:
- diff(phi,df); phi derivation, df difform
- Return:
- the image of df under the Lie-derivative L_phi
- Remarks:
- The map L_phi is the anticommutator of the contraction map i_phi
and the differential d:
(i_phi o d) + (d o i_phi)
Example:
| LIB "difform.lib";
ring R = 0,(x,y,z),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
forms dDx, dDy, dDz, dx, dy, dz are available.
/////////////////////////////////
// Construction of derivations //
/////////////////////////////////
list L; L[1] = list(dx,dy,dz); L[2] = list(x2,y2,z2);
derivation phi = L; phi;
==> Omega_R^1 --> R
==> dx |--> x2
==> dy |--> y2
==> dz |--> z2
==>
==>
derivation phi_poly = x-y;
///////////////////////////////////
// Lie-derivative of derivations //
///////////////////////////////////
diff(phi,dx);
==> 2x*dx
==>
diff(phi,dx*dy);
==> (-2x+2y)*dx*dy
==>
diff(phi,dx*dy*dz);
==> (2x-2y+2z)*dx*dy*dz
==>
diff(phi,dx*dy + dy*dx);
==> 0
==>
diff(phi,dx*dy - dy*dx);
==> (-4x+4y)*dx*dy
==>
diff(phi_poly,dx);
==> dx+(-1)*dy
==>
diff(phi_poly,dx-dy);
==> 0
==>
diff(phi_poly,dx+dy);
==> 2*dx+(-2)*dy
==>
diff(phi_poly,dx*(x2-y4) + 1);
==> (3x2-4xy3-2xy+3y4)*dx+(-x2-8xy3+9y4)*dy
==>
kill Omega_R,dx,dy,dz,L,phi,phi_poly;
| See also:
derivationContraction;
difformDiff.
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