# Find the product of two points a and b.
# Note for the reader: 
#	"elt" means "is an element of" or "is a point in"
#	"meet" means "intersection"
#	"a-bis" means "angle bisector"
#	"perp" means "line on ... perpendicular to ... "
# Each of these corresponds to a Cabri action.

Input: points: 0, 1, a, b ;
Output: point: ab.

L1 = line (0, 1) ;
R1 = ray (0, 1) ;
L2 = perp (0, L1) ;
Ca = circle (0, a) ;
Cb = circle (0, b) ;
|b| = meet (R1, Cb) ;
z elt meet (L2, Ca) ;
L3 = parallel (|b|, seg (1, z) ) ;
y = meet (L2, L3) ;
Cab = circle (0, y) ;
L4 = a-bis (a, 0, 1) ;
x = refl (b, L1) ;
w = refl (x, L4) ;
R3 = ray (0, w) ;
ab = meet (Cab, R3) .