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D.15.12.32 derivationFromList

Procedure from library difform.lib (see difform_lib).

derivation phi = derivationFromList(L); L list

the derivation defined by the list L

The structure of L is checked and L is sorted,
then it is set as structure list of phi

the structure of L must follow the rules:
- L[1] is a list of all degree-1 generators: all dx_i must occure once and no other differential forms are allowed. The order of the list is not important - L[2] is the list of images of the dx_i: these must be polynomials Since the map is linear, it is enough to store the images of the dx_i

LIB "difform.lib";
ring R = 11,(u,v,w,x),lp;
==> // The differential algebra Omega_R was constructed and the differential \
   forms du, dv, dw, dx are available.
// Construction of structure lists //
list L_1;
L_1[1] = list(du,dv,dw,dx);
L_1[2] = list(u,v,w,x);
list L_2;
L_2[1] = list(dx,dw,du,dv);
L_2[2] = list(x2,w2,u2,v-wu);
// Construction of derivations //
derivation phi = derivationFromList(L_1); phi;
==>  Omega_R^1 --> R
==>        du |--> u
==>        dv |--> v
==>        dw |--> w
==>        dx |--> x
derivation psi = derivationFromList(L_2); psi;
==>  Omega_R^1 --> R
==>        du |--> u2
==>        dv |--> -uw+v
==>        dw |--> w2
==>        dx |--> x2
kill Omega_R,du,dv,dw,dx,phi,psi,L_1,L_2;
See also: derivationCheckList; derivationConstructor; derivationFromPoly.