code: def is_degenerate(identity_set, gate_identity):
      """Checks if a gate identity is a permutation of another identity.
  
      Parameters
      ==========
  
      identity_set : set
          A Python set with GateIdentity objects.
      gate_identity : GateIdentity
          The GateIdentity to check for existence in the set.
  
      Examples
      ========
  
      Check if the identity is a permutation of another identity:
  
      >>> from sympy.physics.quantum.identitysearch import (
      ...     GateIdentity, is_degenerate)
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> an_identity = GateIdentity(x, y, z)
      >>> id_set = {an_identity}
      >>> another_id = (y, z, x)
      >>> is_degenerate(id_set, another_id)
      True
  
      >>> another_id = (x, x)
      >>> is_degenerate(id_set, another_id)
      False
      """
  
      # For now, just iteratively go through the set and check if the current
      # gate_identity is a permutation of an identity in the set
      for an_id in identity_set:
          if gate_identity in an_id.equivalent_ids:
              return True
      return False
  
imports: from collections import deque
  from sympy.core.random import randint
  from sympy.external import import_module
  from sympy.core.basic import Basic
  from sympy.core.mul import Mul
  from sympy.core.numbers import Number, equal_valued
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.physics.quantum.represent import represent
  from sympy.physics.quantum.dagger import Dagger
label_desc: Use image node_id 10 for calling a global function with example usage: is_degenerate(identity_set, gate_identity) and returns: False, True