code: def test_SDM_lu():
      A = SDM(
          {0: {0: QQ(1), 1: QQ(2)}, 1: {0: QQ(3), 1: QQ(4)}}, (2, 2), QQ
      )
      L = SDM({0: {0: QQ(1)}, 1: {0: QQ(3), 1: QQ(1)}}, (2, 2), QQ)
      # U = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(-2)}}, (2, 2), QQ)
      # swaps = []
      # This doesn't quite work. U has some nonzero elements in the lower part.
      # assert A.lu() == (L, U, swaps)
      assert A.lu()[0] == L
  
imports: from itertools import product
  from sympy.core.singleton import S
  from sympy.external.gmpy import GROUND_TYPES
  from sympy.testing.pytest import raises
  from sympy.polys.domains import QQ, ZZ, EXRAW
  from sympy.polys.matrices.sdm import SDM
  from sympy.polys.matrices.ddm import DDM
  from sympy.polys.matrices.exceptions import DMBadInputError, DMDomainError, DMShapeError
label_desc: Use image node_id 34 for calling a global function with example usage: test_SDM_lu() without return types