code: def test_Submodule_represent():
      T = Poly(cyclotomic_poly(5, x))
      A = PowerBasis(T)
      B = A.submodule_from_matrix(2 * DomainMatrix.eye(4, ZZ))
      C = B.submodule_from_matrix(3 * DomainMatrix.eye(4, ZZ))
      a0 = A(to_col([6, 12, 18, 24]))
      a1 = A(to_col([2, 4, 6, 8]))
      a2 = A(to_col([1, 3, 5, 7]))
  
      b1 = B.represent(a1)
      assert b1.flat() == [1, 2, 3, 4]
  
      c0 = C.represent(a0)
      assert c0.flat() == [1, 2, 3, 4]
  
      Y = A.submodule_from_matrix(
          DomainMatrix(
              [
                  [1, 0, 0, 0],
                  [0, 1, 0, 0],
                  [0, 0, 1, 0],
              ],
              (3, 4),
              ZZ,
          ).transpose()
      )
  
      U = Poly(cyclotomic_poly(7, x))
      Z = PowerBasis(U)
      z0 = Z(to_col([1, 2, 3, 4, 5, 6]))
  
      raises(ClosureFailure, lambda: Y.represent(A(3)))
      raises(ClosureFailure, lambda: B.represent(a2))
      raises(ClosureFailure, lambda: B.represent(z0))
  
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 24 for calling a global function with example usage: test_Submodule_represent() without return types