14.13.7  Checking if points in space are concyclic: is_concyclic

See Section 13.16.3 for checking for concyclicity in two-dimensional geometry.

The is_concyclic command determines whether or not points are cyclic.

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

Examples.

• Input:

  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)])

  Output:

  1

• Input:
  is_concyclic([2,0,0],[0,2,0],[1,1,0],[0,0,2],[1,1,1])
  Output:

  0