code: def test_booleans():
      """test basic unions and intersections"""
      half = S.Half
  
      p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)])
      p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)])
      l1 = Line(Point(0, 0), Point(1, 1))
      l2 = Line(Point(half, half), Point(5, 5))
      l3 = Line(p2, p3)
      l4 = Line(p3, p4)
      poly1 = Polygon(p1, p2, p3, p4)
      poly2 = Polygon(p5, p6, p7)
      poly3 = Polygon(p1, p2, p5)
      assert Union(l1, l2).equals(l1)
      assert Intersection(l1, l2).equals(l1)
      assert Intersection(l1, l4) == FiniteSet(Point(1, 1))
      assert Intersection(Union(l1, l4), l3) == FiniteSet(
          Point(Rational(-1, 3), Rational(-1, 3)), Point(5, 1)
      )
      assert Intersection(l1, FiniteSet(Point(7, -7))) == EmptySet
      assert Intersection(
          Circle(Point(0, 0), 3), Line(p1, p2)
      ) == FiniteSet(Point(-3, 0), Point(3, 0))
      assert Intersection(l1, FiniteSet(p1)) == FiniteSet(p1)
      assert Union(l1, FiniteSet(p1)) == l1
  
      fs = FiniteSet(
          Point(Rational(1, 3), 1),
          Point(Rational(2, 3), 0),
          Point(Rational(9, 5), Rational(1, 5)),
          Point(Rational(7, 3), 1),
      )
      # test the intersection of polygons
      assert Intersection(poly1, poly2) == fs
      # make sure if we union polygons with subsets, the subsets go away
      assert Union(poly1, poly2, fs) == Union(poly1, poly2)
      # make sure that if we union with a FiniteSet that isn't a subset,
      # that the points in the intersection stop being listed
      assert Union(poly1, FiniteSet(Point(0, 0), Point(3, 5))) == Union(
          poly1, FiniteSet(Point(3, 5))
      )
      # intersect two polygons that share an edge
      assert Intersection(poly1, poly3) == Union(
          FiniteSet(Point(Rational(3, 2), 1), Point(2, 1)),
          Segment(Point(0, 0), Point(1, 0)),
      )
  
imports: from sympy.core.numbers import Rational
  from sympy.core.singleton import S
  from sympy.geometry import Circle, Line, Point, Polygon, Segment
  from sympy.sets import FiniteSet, Union, Intersection, EmptySet
label_desc: Use image node_id 1 for calling a global function with example usage: test_booleans() without return types