class_docstr: References
  ==========
  
  .. [1] Holt, D., Eick, B., O'Brien, E.
         "Handbook of Computational Group Theory"
         Section 8.1.3
class_docstr_tok: ["References","==========","..","[","1","]","Holt",",","D.",",","Eick",",","B.",",","O'Brien",",","E.","``","Handbook","of","Computational","Group","Theory","''","Section","8.1.3"]
docstr: Separates the given relators of pc presentation in power and
  conjugate relations.
  
  Returns
  =======
  
  (power_rel, conj_rel)
      Separates pc presentation into power and conjugate relations.
  
  Examples
  ========
  
  >>> from sympy.combinatorics.named_groups import SymmetricGroup
  >>> G = SymmetricGroup(3)
  >>> PcGroup = G.polycyclic_group()
  >>> collector = PcGroup.collector
  >>> power_rel, conj_rel = collector.relations()
  >>> power_rel
  {x0**2: (), x1**3: ()}
  >>> conj_rel
  {x0**-1*x1*x0: x1**2}
  
  See Also
  ========
  
  pc_relators
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code: def relations(self):
      """
      Separates the given relators of pc presentation in power and
      conjugate relations.
  
      Returns
      =======
  
      (power_rel, conj_rel)
          Separates pc presentation into power and conjugate relations.
  
      Examples
      ========
  
      >>> from sympy.combinatorics.named_groups import SymmetricGroup
      >>> G = SymmetricGroup(3)
      >>> PcGroup = G.polycyclic_group()
      >>> collector = PcGroup.collector
      >>> power_rel, conj_rel = collector.relations()
      >>> power_rel
      {x0**2: (), x1**3: ()}
      >>> conj_rel
      {x0**-1*x1*x0: x1**2}
  
      See Also
      ========
  
      pc_relators
  
      """
      power_relators = {}
      conjugate_relators = {}
      for key, value in self.pc_presentation.items():
          if len(key.array_form) == 1:
              power_relators[key] = value
          else:
              conjugate_relators[key] = value
      return power_relators, conjugate_relators
  
imports: from sympy.ntheory.primetest import isprime
  from sympy.combinatorics.perm_groups import PermutationGroup
  from sympy.printing.defaults import DefaultPrinting
  from sympy.combinatorics.free_groups import free_group
label_desc: Use image node_id 3 for calling the Collector obj's underlying member method code with example usage: obj.relations() and returns: power_relators,  conjugate_relators