z ← (a×d) - (b×c)
 

extern A qtimes(A,A);
extern A qminus(A,A);
A z;
z=qminus(qtimes(a,d),qtimes(b,c));
 

extern PP qtimes(PP,PP);
extern PP qminus(PP,PP);
LOCALP t0,t1; 
PP z;
regp(&t0); regp(&t1);
t0.p=qtimes(a,d);
t1.p=qtimes(b,c);
z=qminus(t0.p,t1.p);
cutp(&t0);