Singular Manual: difformDiv

D.15.4.18 difformDiv

Procedure from library difform.lib (see difform_lib).

Usage:: df/dg; df,dg difform
Return:: the quotient df/dg as differential form

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.
/////////////////////////////////
// Divisions without remainder //
/////////////////////////////////
dx / dx;
==> 1
==> 
dx*dy*dz / dz;
==> dx*dy
==> 
(dx*x2 - yx2) / x2;
==> -y+dx
==> 
//////////////////////////////
// Divisions with reaminder //
//////////////////////////////
(dx + dx*dy + 1) / dx;
==> 1+(-1)*dy
==> 
(x2*dx - x*dy) / (dx-dy);
==> x2
==> 
kill Omega_R,dx,dy,dz;