old_contents: """
  
  Hilbert projective metric
  =========================
  
  - boundary of Ω
  - order of the points p,x, q, y
  - || || norm
  
                ||py|| ||xq||         
  d(x,y) = ln( ---------------- )
                ||px|| ||yq||
  
  """
  
  from sympy import symbols
  from sympy import log
  
  x, y = symbols('x, y')
  p, q = symbols('p, q')
  
  def Norm():
    pass
  
  def d(x, y):
    pass 
                
  
new_contents: """
  
  Hilbert projective metric
  =========================
  
  - boundary of Ω
  - order of the points p,x, q, y
  - || || Real norm
  
                ||py|| ||xq||         
  d(x,y) = ln( ---------------- )
                ||px|| ||yq||
  
  """
  
  from sympy import symbols
  from sympy import log
  
  x, y = symbols('x, y')
  p, q = symbols('p, q')
  
  def d(x, y):
    pass 
                
  
subject: Update hilbert.py