def test_point(): p1 = Point(x1, x2) p2 = Point(y1, y2) p3 = Point(0, 0) p4 = Point(1, 1) p5 = Point(0, 1) assert p1.origin == p3 assert p1.ambient_dimension == 2 assert p1 in p1 assert p1 not in p2 assert p2.y == y2 assert (p3 + p4) == p4 assert (p2 - p1) == Point(y1 - x1, y2 - x2) assert p4*5 == Point(5, 5) assert -p2 == Point(-y1, -y2) pytest.raises(ValueError, lambda: Point(3, I)) pytest.raises(ValueError, lambda: Point(2*I, I)) pytest.raises(ValueError, lambda: Point(3 + I, I)) assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3)) assert Point.midpoint(p3, p4) == Point(half, half) assert Point.midpoint(p1, p4) == Point(half + half*x1, half + half*x2) assert Point.midpoint(p2, p2) == p2 assert p2.midpoint(p2) == p2 assert Point.distance(p3, p4) == sqrt(2) assert Point.distance(p1, p1) == 0 assert Point.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2) p1_1 = Point(x1, x1) p1_2 = Point(y2, y2) p1_3 = Point(x1 + 1, x1) assert Point.is_collinear(p3) assert Point.is_collinear(p3, p4) assert Point.is_collinear(p3, p4, p1_1, p1_2) assert Point.is_collinear(p3, p4, p1_1, p1_3) is False assert Point.is_collinear(p3, p3, p4, p5) is False line = Line(Point(1, 0), slope=1) pytest.raises(TypeError, lambda: Point.is_collinear(line)) pytest.raises(TypeError, lambda: p1_1.is_collinear(line)) assert p3.intersection(Point(0, 0)) == [p3] assert p3.intersection(p4) == [] x_pos = Symbol('x', real=True, positive=True) p2_1 = Point(x_pos, 0) p2_2 = Point(0, x_pos) p2_3 = Point(-x_pos, 0) p2_4 = Point(0, -x_pos) p2_5 = Point(x_pos, 5) assert Point.is_concyclic(p2_1) assert Point.is_concyclic(p2_1, p2_2) assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_4) assert Point.is_concyclic(p2_1, p2_2, p2_3, p2_5) is False assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False assert p4.scale(2, 3) == Point(2, 3) assert p3.scale(2, 3) == p3 assert p4.rotate(pi, Point(0.5, 0.5)) == p3 assert p1.__radd__(p2) == p1.midpoint(p2).scale(2, 2) assert (-p3).__rsub__(p4) == p3.midpoint(p4).scale(2, 2) assert p4 * 5 == Point(5, 5) assert p4 / 5 == Point(0.2, 0.2) pytest.raises(ValueError, lambda: Point(0, 0) + 10) # Point differences should be simplified assert Point(x*(x - 1), y) - Point(x**2 - x, y + 1) == Point(0, -1) a, b = Rational(1, 2), Rational(1, 3) assert Point(a, b).evalf(2) == \ Point(a.n(2), b.n(2)) pytest.raises(ValueError, lambda: Point(1, 2) + 1) # test transformations p = Point(1, 0) assert p.rotate(pi/2) == Point(0, 1) assert p.rotate(pi/2, p) == p p = Point(1, 1) assert p.scale(2, 3) == Point(2, 3) assert p.translate(1, 2) == Point(2, 3) assert p.translate(1) == Point(2, 1) assert p.translate(y=1) == Point(1, 2) assert p.translate(*p.args) == Point(2, 2) # Check invalid input for transform pytest.raises(ValueError, lambda: p3.transform(p3)) pytest.raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
def test_point3D(): p1 = Point3D(x1, x2, x3) p2 = Point3D(y1, y2, y3) p3 = Point3D(0, 0, 0) p4 = Point3D(1, 1, 1) p5 = Point3D(0, 1, 2) assert p1 in p1 assert p1 not in p2 assert p2.y == y2 assert (p3 + p4) == p4 assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3) assert p4*5 == Point3D(5, 5, 5) assert -p2 == Point3D(-y1, -y2, -y3) assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3)) assert Point3D.midpoint(p3, p4) == Point3D(half, half, half) assert Point3D.midpoint(p1, p4) == Point3D(half + half*x1, half + half*x2, half + half*x3) assert Point3D.midpoint(p2, p2) == p2 assert p2.midpoint(p2) == p2 assert Point3D.distance(p3, p4) == sqrt(3) assert Point3D.distance(p1, p1) == 0 assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2) p1_1 = Point3D(x1, x1, x1) p1_2 = Point3D(y2, y2, y2) p1_3 = Point3D(x1 + 1, x1, x1) # according to the description in the docs, points are collinear # if they like on a single line. Thus a single point should always # be collinear assert Point3D.are_collinear(p3) assert Point3D.are_collinear(p3, p4) assert Point3D.are_collinear(p3, p4, p1_1, p1_2) assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False assert Point3D.are_collinear(p3, p3, p4, p5) is False assert p3.intersection(Point3D(0, 0, 0)) == [p3] assert p3.intersection(p4) == [] assert p4 * 5 == Point3D(5, 5, 5) assert p4 / 5 == Point3D(0.2, 0.2, 0.2) pytest.raises(ValueError, lambda: Point3D(0, 0, 0) + 10) # Point differences should be simplified assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \ Point3D(0, -1, 1) a, b = Rational(1, 2), Rational(1, 3) assert Point(a, b).evalf(2) == \ Point(a.n(2), b.n(2)) pytest.raises(ValueError, lambda: Point(1, 2) + 1) # test transformations p = Point3D(1, 1, 1) assert p.scale(2, 3) == Point3D(2, 3, 1) assert p.translate(1, 2) == Point3D(2, 3, 1) assert p.translate(1) == Point3D(2, 1, 1) assert p.translate(z=1) == Point3D(1, 1, 2) assert p.translate(*p.args) == Point3D(2, 2, 2) # Test __new__ assert Point3D(Point3D(1, 2, 3), 4, 5, evaluate=False) == Point3D(1, 2, 3) # Test length property returns correctly assert p.length == 0 assert p1_1.length == 0 assert p1_2.length == 0 # Test are_colinear type error pytest.raises(TypeError, lambda: Point3D.are_collinear(p, x)) # Test are_coplanar planar2 = Point3D(1, -1, 1) planar3 = Point3D(-1, 1, 1) assert Point3D.are_coplanar(p, planar2, planar3) is True assert Point3D.are_coplanar(p, planar2, planar3, p3) is False pytest.raises(ValueError, lambda: Point3D.are_coplanar(p, planar2)) planar2 = Point3D(1, 1, 2) planar3 = Point3D(1, 1, 3) pytest.raises(ValueError, lambda: Point3D.are_coplanar(p, planar2, planar3)) # Test Intersection assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)] # Test Scale assert planar2.scale(1, 1, 1) == planar2 assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1) assert planar2.scale(1, 1, 1, p3) == planar2 # Test Transform identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) assert p.transform(identity) == p trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]]) assert p.transform(trans) == Point3D(2, 2, 2) pytest.raises(ValueError, lambda: p.transform(p)) pytest.raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]]))) # Test Equals assert p.equals(x1) is False # Test __sub__ p_2d = Point(0, 0) pytest.raises(ValueError, lambda: (p - p_2d))
def test_sympyissue_8245(): a = Rational(6506833320952669167898688709329, 5070602400912917605986812821504) q = a.n(10) assert (a == q) is True assert (a != q) is False assert (a > q) is S.false assert (a < q) is S.false assert (a >= q) is S.true assert (a <= q) is S.true a = sqrt(2) r = Rational(str(a.n(30))) assert (r == a) is False assert (r != a) is True assert (r > a) is S.true assert (r < a) is S.false assert (r >= a) is S.true assert (r <= a) is S.false a = sqrt(2) r = Rational(str(a.n(29))) assert (r == a) is False assert (r != a) is True assert (r > a) is S.false assert (r < a) is S.true assert (r >= a) is S.false assert (r <= a) is S.true