Singular Manual: derivationFromList

| #### D.15.4.30 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;
See also: derivationCheckList; derivationConstructor; derivationFromPoly.

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