code: def shor(N):
      """This function implements Shor's factoring algorithm on the Integer N
  
      The algorithm starts by picking a random number (a) and seeing if it is
      coprime with N. If it is not, then the gcd of the two numbers is a factor
      and we are done. Otherwise, it begins the period_finding subroutine which
      finds the period of a in modulo N arithmetic. This period, if even, can
      be used to calculate factors by taking a**(r/2)-1 and a**(r/2)+1.
      These values are returned.
      """
      a = random.randrange(N - 2) + 2
      if igcd(N, a) != 1:
          return igcd(N, a)
      r = period_find(a, N)
      if r % 2 == 1:
          shor(N)
      answer = (igcd(a ** (r / 2) - 1, N), igcd(a ** (r / 2) + 1, N))
      return answer
  
imports: import math
  import random
  from sympy.core.mul import Mul
  from sympy.core.singleton import S
  from sympy.functions.elementary.exponential import log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.core.intfunc import igcd
  from sympy.ntheory import continued_fraction_periodic
  from sympy.utilities.iterables import variations
  from sympy.physics.quantum.gate import Gate
  from sympy.physics.quantum.qubit import Qubit, measure_partial_oneshot
  from sympy.physics.quantum.qapply import qapply
  from sympy.physics.quantum.qft import QFT
  from sympy.physics.quantum.qexpr import QuantumError
label_desc: Use image node_id 1 for calling a global function with example usage: shor(N) and returns: answer, igcd