text: try:
      import mpmath as mp
  except ImportError:
      pass
  
  try:
      from sympy.abc import x  # type: ignore[import]
  except ImportError:
      pass
  
  
  def lagrange_inversion(a):
      """Given a series
  
      f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),
  
      use the Lagrange inversion formula to compute a series
  
      g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)
  
      so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
      necessarily b[0] = 0 too.
  
      The algorithm is naive and could be improved, but speed isn't an
      issue here and it's easy to read.
  
      """
      n = len(a)
      f = sum(a[i]*x**i for i in range(len(a)))
      h = (x/f).series(x, 0, n).removeO()
      hpower = [h**0]
      for k in range(n):
          hpower.append((hpower[-1]*h).expand())
      b = [mp.mpf(0)]
      for k in range(1, n):
          b.append(hpower[k].coeff(x, k - 1)/k)
      b = [mp.mpf(x) for x in b]
      return b
  