Singular

LIB "difform.lib";
ring R = 0,(x,y,z),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dx, dy, dz are available.
//////////////////////////////////////////
// Multiplication of differential forms //
//////////////////////////////////////////
difform df = 13*dx*dy - 7*dy*dz - 6*dx*dy*dz;
difform dg = dx - 8x;
df*dg;
==> (-104x)*dx*dy+56x*dy*dz+(-7+48x)*dx*dy*dz
==> 
/////////////////////////////////////////////////////////
// Multiplication of polynomials and differential forms //
/////////////////////////////////////////////////////////
df*(y2-x);
==> (-13x+13y2)*dx*dy+(7x-7y2)*dy*dz+(6x-6y2)*dx*dy*dz
==> 
12*dg;
==> -96x+12*dx
==> 
kill Omega_R,df,dg,dx,dy,dz;