code: def _two_elt_rep(gens, ZK, p, f=None, Np=None):
      r"""
      Given a set of *ZK*-generators of a prime ideal, compute a set of just two
      *ZK*-generators for the same ideal, one of which is *p* itself.
  
      Parameters
      ==========
  
      gens : list of :py:class:`PowerBasisElement`
          Generators for the prime ideal over *ZK*, the ring of integers of the
          field $K$.
  
      ZK : :py:class:`~.Submodule`
          The maximal order in $K$.
  
      p : int
          The rational prime divided by the prime ideal.
  
      f : int, optional
          The inertia degree of the prime ideal, if known.
  
      Np : int, optional
          The norm $p^f$ of the prime ideal, if known.
          NOTE: There is no reason to supply both *f* and *Np*. Either one will
          save us from having to compute the norm *Np* ourselves. If both are known,
          *Np* is preferred since it saves one exponentiation.
  
      Returns
      =======
  
      :py:class:`~.PowerBasisElement` representing a single algebraic integer
      alpha such that the prime ideal is equal to ``p*ZK + alpha*ZK``.
  
      References
      ==========
  
      .. [1] Cohen, H. *A Course in Computational Algebraic Number Theory.*
      (See Algorithm 4.7.10.)
  
      """
      _check_formal_conditions_for_maximal_order(ZK)
      pb = ZK.parent
      T = pb.T
      # Detect the special cases in which either (a) all generators are multiples
      # of p, or (b) there are no generators (so `all` is vacuously true):
      if all((g % p).equiv(0) for g in gens):
          return pb.zero()
  
      if Np is None:
          if f is not None:
              Np = p**f
          else:
              Np = abs(pb.submodule_from_gens(gens).matrix.det())
  
      omega = ZK.basis_element_pullbacks()
      beta = [p * om for om in omega[1:]]  # note: we omit omega[0] == 1
      beta += gens
      search = coeff_search(len(beta), 1)
      for c in search:
          alpha = sum(ci * betai for ci, betai in zip(c, beta))
          # Note: It may be tempting to reduce alpha mod p here, to try to work
          # with smaller numbers, but must not do that, as it can result in an
          # infinite loop! E.g. try factoring 2 in Q(sqrt(-7)).
          n = alpha.norm(T) // Np
          if n % p != 0:
              # Now can reduce alpha mod p.
              return alpha % p
  
imports: from sympy.polys.polytools import Poly
  from sympy.polys.domains.finitefield import FF
  from sympy.polys.domains.rationalfield import QQ
  from sympy.polys.domains.integerring import ZZ
  from sympy.polys.matrices.domainmatrix import DomainMatrix
  from sympy.polys.polyerrors import CoercionFailed
  from sympy.polys.polyutils import IntegerPowerable
  from sympy.utilities.decorator import public
  from .basis import round_two, nilradical_mod_p
  from .exceptions import StructureError
  from .modules import ModuleEndomorphism, find_min_poly
  from .utilities import coeff_search, supplement_a_subspace
label_desc: Use image node_id 4 for calling a global function with example usage: _two_elt_rep(gens, ZK, p, f, Np) and returns: pb, unknown