electrons on sphere

E denoted by (theta, phi). rho is fixed as R. E in cartesian coord is R ( sin(theta) cos(phi), sin(theta) sin(phi), cos(theta) )

F on E[i] is SUM_(k!=i) X(E[i]-E[k])

----

class X3:

  x, y, z

  def __init__(self, x, y, z):

    self.x, self.y, self.z = x, y, z

  def plus(self, Y):

    return X3(self.x + Y.x, self.y + Y.y, self.z + Y.z)

  ...

----

class E :

  r = R

  th = 0

  ph = 0

  v = X3(0, 0, 0)

  def __init__(self, theta, phi):

    self.th, self.ph = theta, phi

    self.x, self.y, self.z = R*sin(self.th)*cos(self.ph), R*sin(self.th)*sin(self.ph), R*cos(self.th)

  def update(self, t):

    self = self + t * v

----

How to represent the N-gram in 2D.

Find outermost encloser of the points. 

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