code: def interpolate(data, x):
      """
      Construct an interpolating polynomial for the data points
      evaluated at point x (which can be symbolic or numeric).
  
      Examples
      ========
  
      >>> from sympy.polys.polyfuncs import interpolate
      >>> from sympy.abc import a, b, x
  
      A list is interpreted as though it were paired with a range starting
      from 1:
  
      >>> interpolate([1, 4, 9, 16], x)
      x**2
  
      This can be made explicit by giving a list of coordinates:
  
      >>> interpolate([(1, 1), (2, 4), (3, 9)], x)
      x**2
  
      The (x, y) coordinates can also be given as keys and values of a
      dictionary (and the points need not be equispaced):
  
      >>> interpolate([(-1, 2), (1, 2), (2, 5)], x)
      x**2 + 1
      >>> interpolate({-1: 2, 1: 2, 2: 5}, x)
      x**2 + 1
  
      If the interpolation is going to be used only once then the
      value of interest can be passed instead of passing a symbol:
  
      >>> interpolate([1, 4, 9], 5)
      25
  
      Symbolic coordinates are also supported:
  
      >>> [(i,interpolate((a, b), i)) for i in range(1, 4)]
      [(1, a), (2, b), (3, -a + 2*b)]
      """
      n = len(data)
  
      if isinstance(data, dict):
          if x in data:
              return S(data[x])
          X, Y = list(zip(*data.items()))
      else:
          if isinstance(data[0], tuple):
              X, Y = list(zip(*data))
              if x in X:
                  return S(Y[X.index(x)])
          else:
              if x in range(1, n + 1):
                  return S(data[x - 1])
              Y = list(data)
              X = list(range(1, n + 1))
  
      try:
          return interpolating_poly(n, x, X, Y).expand()
      except ValueError:
          d = Dummy()
          return interpolating_poly(n, d, X, Y).expand().subs(d, x)
  
file_path: sympy/sympy/polys/polyfuncs.py
imports: from sympy.core import S, Basic, symbols, Dummy
  from sympy.polys.polyerrors import PolificationFailed, ComputationFailed, MultivariatePolynomialError, OptionError
  from sympy.polys.polyoptions import allowed_flags, build_options
  from sympy.polys.polytools import poly_from_expr, Poly
  from sympy.polys.specialpolys import symmetric_poly, interpolating_poly
  from sympy.polys.rings import sring
  from sympy.utilities import numbered_symbols, take, public
label_desc: Use image node_id 3 for calling a global function with example usage: interpolate(data, x) and returns: interpolating_poly, S, interpolating_poly, S, S