Singular Manual: difformCoef

D.15.2.8 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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