Singular Manual: difformHomogDecomp

D.15.2.10 difformHomogDecomp

Procedure from library difform.lib (see difform_lib).

Usage:: difformHomogDecomp(df); df difform
Return:: list of differential forms: homogeneous decomposition
Note:: the output list always has as length the maximal possible degree plus one and the degree-0 part is the last element in the list

Example:

LIB "difform.lib";
ring R = 0,(x,y,z),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dx, dy, dz are available.
difform df = 3*dx*dz - x8*dx*dy + 12 + dy*dz + dz*dx - (y4-y5)*x12*dx*dy*dz - dx - dy + dz + x2*dx*dy;
///////////////////////////////
// Homogeneous decomposition //
///////////////////////////////
list L = difformHomogDecomp(df);
L;
==> [1]:
==>    (-1)*dx+(-1)*dy+dz
==> 
==> [2]:
==>    (x2-x8)*dx*dy+2*dx*dz+dy*dz
==> 
==> [3]:
==>    (-x12y4+x12y5)*dx*dy*dz
==> 
==> [4]:
==>    12
==> 
kill Omega_R,df,L,dx,dy,dz;