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: Parameters
  ==========
  
  gens : list
      A list of generators on which polycyclic subgroup
      is to be defined.
  
  Examples
  ========
  
  >>> from sympy.combinatorics.named_groups import SymmetricGroup
  >>> S = SymmetricGroup(8)
  >>> G = S.sylow_subgroup(2)
  >>> PcGroup = G.polycyclic_group()
  >>> collector = PcGroup.collector
  >>> gens = [G[0], G[1]]
  >>> ipcgs = collector.induced_pcgs(gens)
  >>> [gen.order() for gen in ipcgs]
  [2, 2, 2]
  >>> G = S.sylow_subgroup(3)
  >>> PcGroup = G.polycyclic_group()
  >>> collector = PcGroup.collector
  >>> gens = [G[0], G[1]]
  >>> ipcgs = collector.induced_pcgs(gens)
  >>> [gen.order() for gen in ipcgs]
  [3]
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code: def induced_pcgs(self, gens):
      """
  
      Parameters
      ==========
  
      gens : list
          A list of generators on which polycyclic subgroup
          is to be defined.
  
      Examples
      ========
  
      >>> from sympy.combinatorics.named_groups import SymmetricGroup
      >>> S = SymmetricGroup(8)
      >>> G = S.sylow_subgroup(2)
      >>> PcGroup = G.polycyclic_group()
      >>> collector = PcGroup.collector
      >>> gens = [G[0], G[1]]
      >>> ipcgs = collector.induced_pcgs(gens)
      >>> [gen.order() for gen in ipcgs]
      [2, 2, 2]
      >>> G = S.sylow_subgroup(3)
      >>> PcGroup = G.polycyclic_group()
      >>> collector = PcGroup.collector
      >>> gens = [G[0], G[1]]
      >>> ipcgs = collector.induced_pcgs(gens)
      >>> [gen.order() for gen in ipcgs]
      [3]
  
      """
      z = [1] * len(self.pcgs)
      G = gens
      while G:
          g = G.pop(0)
          h = self._sift(z, g)
          d = self.depth(h)
          if d < len(self.pcgs):
              for gen in z:
                  if gen != 1:
                      G.append(h**-1 * gen**-1 * h * gen)
              z[d - 1] = h
      z = [gen for gen in z if gen != 1]
      return z
  
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 12 for calling the Collector obj's underlying member method code with example usage: obj.induced_pcgs(gens) and returns: z