#### D.15.4.8 difformCoef

Procedure from library `difform.lib` (see difform_lib).

Usage:
  difformCoef(df); df difform

Return:
  list of lists of differential forms and polynomials:
  - the first entry is a generator of the differential algebra which appears in df - the second entry is the corresponding coefficient

Remarks:
  Via the procedure coef, the coefficients are found - therefore the ring has to be changed to the differential algebra. After that, the coefficients have to be mapped back to the original ring.

Note:
  the returned list can be sorted with the procedure difformListSort and the optional string 'Llist'

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.
    difform df = 3*x25*dx - y*dx*dy + 12*dx*dy*dz - dz*dy + 3 + 12*x*dx + 24*(y4-y5) + dx*dy*x3*dz + dz - dy*dx + dz*x2 + z5*y*dy;
    ///////////////////////////////
    // Unsorted Coefficient List //
    ///////////////////////////////
    list L_1 = difformCoef(df);
    L_1;
    ==> [1]:
    ==>    [1]:
    ==>       dx*dy*dz
    ==>
    ==>    [2]:
    ==>       x3+12
    ==> [2]:
    ==>    [1]:
    ==>       dx*dy
    ==>
    ==>    [2]:
    ==>       -y+1
    ==> [3]:
    ==>    [1]:
    ==>       dy*dz
    ==>
    ==>    [2]:
    ==>       1
    ==> [4]:
    ==>    [1]:
    ==>       dx
    ==>
    ==>    [2]:
    ==>       3x25+12x
    ==> [5]:
    ==>    [1]:
    ==>       dy
    ==>
    ==>    [2]:
    ==>       yz5
    ==> [6]:
    ==>    [1]:
    ==>       dz
    ==>
    ==>    [2]:
    ==>       x2+1
    ==> [7]:
    ==>    [1]:
    ==>       1
    ==>
    ==>    [2]:
    ==>       -24y5+24y4+3
    /////////////////////////////
    // Sorted Coefficient List //
    /////////////////////////////
    L_1 = difformListSort(L_1,"Llist","gen","ds");
    L_1;
    ==> [1]:
    ==>    [1]:
    ==>       dx*dy*dz
    ==>
    ==>    [2]:
    ==>       x3+12
    ==> [2]:
    ==>    [1]:
    ==>       dy*dz
    ==>
    ==>    [2]:
    ==>       1
    ==> [3]:
    ==>    [1]:
    ==>       dx*dy
    ==>
    ==>    [2]:
    ==>       -y+1
    ==> [4]:
    ==>    [1]:
    ==>       dz
    ==>
    ==>    [2]:
    ==>       x2+1
    ==> [5]:
    ==>    [1]:
    ==>       dy
    ==>
    ==>    [2]:
    ==>       yz5
    ==> [6]:
    ==>    [1]:
    ==>       dx
    ==>
    ==>    [2]:
    ==>       3x25+12x
    ==> [7]:
    ==>    [1]:
    ==>       1
    ==>
    ==>    [2]:
    ==>       -24y5+24y4+3
    kill Omega_R,df,dx,dy,dz,L_1;

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