code: def test_singular_points_and_multiplicty():
      r1 = ImplicitRegion((x, y, z), Eq(x + y + z, 0))
      assert r1.singular_points() == EmptySet
      r2 = ImplicitRegion(
          (x, y, z), x * y * z + y**4 - x**2 * z**2
      )
      assert r2.singular_points() == FiniteSet((0, 0, z), (x, 0, 0))
      assert r2.multiplicity((0, 0, 0)) == 3
      assert r2.multiplicity((0, 0, 6)) == 2
      r3 = ImplicitRegion((x, y, z), z**2 - x**2 - y**2)
      assert r3.singular_points() == FiniteSet((0, 0, 0))
      assert r3.multiplicity((0, 0, 0)) == 2
      r4 = ImplicitRegion((x, y), x**2 + y**2 - 2 * x)
      assert r4.singular_points() == EmptySet
      assert r4.multiplicity(Point(1, 3)) == 0
  
file_path: sympy/sympy/vector/tests/test_implicitregion.py
imports: from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.abc import x, y, z, s, t
  from sympy.sets import FiniteSet, EmptySet
  from sympy.geometry import Point
  from sympy.vector import ImplicitRegion
  from sympy.testing.pytest import raises
label_desc: Use image node_id 3 for calling a global function with example usage: test_singular_points_and_multiplicty() without return types