code: def test_approximants():
      x, t = symbols("x,t")
      g = [lucas(k) for k in range(16)]
      assert list(approximants(g)) == (
          [
              2,
              -4 / (x - 2),
              (5 * x - 2) / (3 * x - 1),
              (x - 2) / (x**2 + x - 1),
          ]
      )
      g = [lucas(k) + fibonacci(k + 2) for k in range(16)]
      assert list(approximants(g)) == (
          [
              3,
              -3 / (x - 1),
              (3 * x - 3) / (2 * x - 1),
              -3 / (x**2 + x - 1),
          ]
      )
      g = [lucas(k) ** 2 for k in range(16)]
      assert list(approximants(g)) == (
          [
              4,
              -16 / (x - 4),
              (35 * x - 4) / (9 * x - 1),
              (37 * x - 28) / (13 * x**2 + 11 * x - 7),
              (50 * x**2 + 63 * x - 52) / (37 * x**2 + 19 * x - 13),
              (-(x**2) - 7 * x + 4)
              / (x**3 - 2 * x**2 - 2 * x + 1),
          ]
      )
      p = [
          sum(binomial(k, i) * x**i for i in range(k + 1))
          for k in range(16)
      ]
      y = approximants(p, t, simplify=True)
      assert next(y) == 1
      assert next(y) == -1 / (t * (x + 1) - 1)
  
imports: from sympy.series import approximants
  from sympy.core.symbol import symbols
  from sympy.functions.combinatorial.factorials import binomial
  from sympy.functions.combinatorial.numbers import fibonacci, lucas
label_desc: Use image node_id 1 for calling a global function with example usage: test_approximants() without return types