code: def find_simple_recurrence_vector(l):
      """
      This function is used internally by other functions from the
      sympy.concrete.guess module. While most users may want to rather use the
      function find_simple_recurrence when looking for recurrence relations
      among rational numbers, the current function may still be useful when
      some post-processing has to be done.
  
      Explanation
      ===========
  
      The function returns a vector of length n when a recurrence relation of
      order n is detected in the sequence of rational numbers v.
  
      If the returned vector has a length 1, then the returned value is always
      the list [0], which means that no relation has been found.
  
      While the functions is intended to be used with rational numbers, it should
      work for other kinds of real numbers except for some cases involving
      quadratic numbers; for that reason it should be used with some caution when
      the argument is not a list of rational numbers.
  
      Examples
      ========
  
      >>> from sympy.concrete.guess import find_simple_recurrence_vector
      >>> from sympy import fibonacci
      >>> find_simple_recurrence_vector([fibonacci(k) for k in range(12)])
      [1, -1, -1]
  
      See Also
      ========
  
      See the function sympy.concrete.guess.find_simple_recurrence which is more
      user-friendly.
  
      """
      q1 = [0]
      q2 = [1]
      b, z = 0, len(l) >> 1
      while len(q2) <= z:
          while l[b] == 0:
              b += 1
              if b == len(l):
                  c = 1
                  for x in q2:
                      c = lcm(c, denom(x))
                  if q2[0] * c < 0:
                      c = -c
                  for k in range(len(q2)):
                      q2[k] = int(q2[k] * c)
                  return q2
          a = S.One / l[b]
          m = [a]
          for k in range(b + 1, len(l)):
              m.append(
                  -sum(l[j + 1] * m[b - j - 1] for j in range(b, k)) * a
              )
          l, m = m, [0] * max(len(q2), b + len(q1))
          for k, q in enumerate(q2):
              m[k] = a * q
          for k, q in enumerate(q1):
              m[k + b] += q
          while m[-1] == 0:
              m.pop()  # because trailing zeros can occur
          q1, q2, b = q2, m, 1
      return [0]
  
file_path: sympy/sympy/concrete/guess.py
imports: from sympy.concrete.products import Product, product
  from sympy.core import Function, S
  from sympy.core.add import Add
  from sympy.core.numbers import Integer, Rational
  from sympy.core.symbol import Symbol, symbols
  from sympy.core.sympify import sympify
  from sympy.functions.elementary.exponential import exp
  from sympy.functions.elementary.integers import floor
  from sympy.integrals.integrals import integrate
  from sympy.polys.polyfuncs import rational_interpolate
  from sympy.polys.polytools import lcm
  from sympy.simplify.radsimp import denom
  from sympy.utilities import public
label_desc: Use image node_id 1 for calling a global function with example usage: find_simple_recurrence_vector(l) and returns: list, q2