Checking whether points in space are concyclic

See Section 26.15.3 for checking for concyclicity in 2D geometry.

The is_concyclic command determines whether or not points are lying on the same circle.

is_concyclic takes L, a list or sequence of points.
is_concyclic(L) returns 1 if the points in L all lie on the same circle, and 0 otherwise.

is_concyclic([2,0,0],[0,2,0],[sqrt(2),sqrt(2),0], [0,0,2],[2/sqrt(3),2/sqrt(3),2/sqrt(3)])

is_concyclic([2,0,0],[0,2,0],[1,1,0],[0,0,2],[1,1,1])