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D.15.2.30 derivationFromList
Procedure from library difform.lib (see difform_lib).
- Usage:
- derivation phi = derivationFromList(L); L list
- Return:
- the derivation defined by the list L
- Remarks:
- The structure of L is checked and L is sorted,
then it is set as structure list of phi
- Note:
- the structure of L must follow the rules:
- L[1] is a list of all degree-1 generators: all dx_i must occur 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
Example:
| | LIB "difform.lib";
ring R = 11,(u,v,w,x),lp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
forms dDu, dDv, dDw, dDx, 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;
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See also:
derivationCheckList;
derivationConstructor;
derivationFromPoly.
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