code: def test_PowerBasisElement_polys():
      T = Poly(cyclotomic_poly(5, x))
      A = PowerBasis(T)
      e = A(to_col([1, 15, 8, 0]), denom=2)
      assert e.numerator(x=zeta) == Poly(
          8 * zeta**2 + 15 * zeta + 1, domain=ZZ
      )
      assert e.poly(x=zeta) == Poly(
          4 * zeta**2 + QQ(15, 2) * zeta + QQ(1, 2), domain=QQ
      )
  
imports: from sympy.abc import x, zeta
  from sympy.polys import Poly, cyclotomic_poly
  from sympy.polys.domains import FF, QQ, ZZ
  from sympy.polys.matrices import DomainMatrix, DM
  from sympy.polys.numberfields.exceptions import ClosureFailure, MissingUnityError, StructureError
  from sympy.polys.numberfields.modules import Module, ModuleElement, ModuleEndomorphism, PowerBasis, PowerBasisElement, find_min_poly, is_sq_maxrank_HNF, make_mod_elt, to_col
  from sympy.polys.numberfields.utilities import is_int
  from sympy.polys.polyerrors import UnificationFailed
  from sympy.testing.pytest import raises
label_desc: Use image node_id 48 for calling a global function with example usage: test_PowerBasisElement_polys() without return types