def test_warns_match_non_matching(): with warnings.catch_warnings(record=True) as w: with raises(Failed): with warns(UserWarning, match='this is the warning message'): warnings.warn('this is not the expected warning message', UserWarning) assert len(w) == 0
def plot_implicit_tests(name): x = Symbol('x') y = Symbol('y') z = Symbol('z') #implicit plot tests plot_and_save(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2), name=name) plot_and_save(Eq(y**2, x**3 - x), (x, -5, 5), (y, -4, 4), name=name) plot_and_save(y > 1 / x, (x, -5, 5), (y, -2, 2), name=name) plot_and_save(y < 1 / tan(x), (x, -5, 5), (y, -2, 2), name=name) plot_and_save(y >= 2 * sin(x) * cos(x), (x, -5, 5), (y, -2, 2), name=name) plot_and_save(y <= x**2, (x, -3, 3), (y, -1, 5), name=name) #Test all input args for plot_implicit plot_and_save(Eq(y**2, x**3 - x)) plot_and_save(Eq(y**2, x**3 - x), adaptive=False) plot_and_save(Eq(y**2, x**3 - x), adaptive=False, points=500) plot_and_save(y > x, (x, -5, 5)) plot_and_save(And(y > exp(x), y > x + 2)) plot_and_save(Or(y > x, y > -x)) plot_and_save(x**2 - 1, (x, -5, 5)) plot_and_save(x**2 - 1) plot_and_save(y > x, depth=-5) plot_and_save(y > x, depth=5) plot_and_save(y > cos(x), adaptive=False) plot_and_save(y < cos(x), adaptive=False) plot_and_save(And(y > cos(x), Or(y > x, Eq(y, x)))) plot_and_save(y - cos(pi / x)) #Test plots which cannot be rendered using the adaptive algorithm with warns(UserWarning, match="Adaptive meshing could not be applied"): plot_and_save(Eq(y, re(cos(x) + I * sin(x))), name=name) plot_and_save(x**2 - 1, title='An implicit plot')
def test_rsa_public_key(): assert rsa_public_key(2, 3, 1) == (6, 1) assert rsa_public_key(5, 3, 3) == (15, 3) with warns(NonInvertibleCipherWarning): assert rsa_public_key(2, 2, 1) == (4, 1) assert rsa_public_key(8, 8, 8) is False
def test_warns_hides_other_warnings(): # This isn't ideal but it's what pytest's warns does: with warnings.catch_warnings(record=True) as w: with warns(UserWarning): warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) assert len(w) == 0
def test_warns_hides_other_warnings(): # This isn't ideal but it's what pytest's warns does: with warnings.catch_warnings(record=True) as w: with warns(UserWarning): warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) assert len(w) == 0
def test_rsa_private_key(): assert rsa_private_key(2, 3, 1) == (6, 1) assert rsa_private_key(5, 3, 3) == (15, 3) assert rsa_private_key(23, 29, 5) == (667, 493) with warns(NonInvertibleCipherWarning): assert rsa_private_key(2, 2, 1) == (4, 1) assert rsa_private_key(8, 8, 8) is False
def test_warns_continues_after_warning(): with warnings.catch_warnings(record=True) as w: finished = False with warns(UserWarning): warnings.warn('this is the warning message') finished = True assert finished assert len(w) == 0
def test_warns_continues_after_warning(): with warnings.catch_warnings(record=True) as w: finished = False with warns(UserWarning): warnings.warn('this is the warning message') finished = True assert finished assert len(w) == 0
def test_encipher_rsa(): puk = rsa_public_key(2, 3, 1) assert encipher_rsa(2, puk) == 2 puk = rsa_public_key(5, 3, 3) assert encipher_rsa(2, puk) == 8 with warns(NonInvertibleCipherWarning): puk = rsa_public_key(2, 2, 1) assert encipher_rsa(2, puk) == 2
def test_decipher_rsa(): prk = rsa_private_key(2, 3, 1) assert decipher_rsa(2, prk) == 2 prk = rsa_private_key(5, 3, 3) assert decipher_rsa(8, prk) == 2 with warns(NonInvertibleCipherWarning): prk = rsa_private_key(2, 2, 1) assert decipher_rsa(2, prk) == 2
def test_dispatcher(): f = Dispatcher('f') f.add((int, ), inc) f.add((float, ), dec) with warns(DeprecationWarning): assert f.resolve((int, )) == inc assert f.dispatch(int) is inc assert f(1) == 2 assert f(1.0) == 0.0
def test_issue_11463(): numpy = import_module('numpy') if not numpy: skip("numpy not installed.") x = Symbol('x') f = lambdify(x, real_root((log(x/(x-2))), 3), 'numpy') # numpy.select evaluates all options before considering conditions, # so it raises a warning about root of negative number which does # not affect the outcome. This warning is suppressed here with warns(RuntimeWarning): assert f(numpy.array(-1)) < -1
def test_issue_11463(): numpy = import_module('numpy') if not numpy: skip("numpy not installed.") x = Symbol('x') f = lambdify(x, real_root((log(x / (x - 2))), 3), 'numpy') # numpy.select evaluates all options before considering conditions, # so it raises a warning about root of negative number which does # not affect the outcome. This warning is suppressed here with warns(RuntimeWarning): assert f(numpy.array(-1)) < -1
def test_dispatcher(): f = Dispatcher('f') f.add((int,), inc) f.add((float,), dec) with warns(DeprecationWarning): assert f.resolve((int,)) == inc assert f.dispatch(int) is inc assert f(1) == 2 assert f(1.0) == 0.0
def test_contains(): p1 = Point(0, 0) r = Ray(p1, Point(4, 4)) r1 = Ray3D(p1, Point3D(0, 0, -1)) r2 = Ray3D(p1, Point3D(0, 1, 0)) r3 = Ray3D(p1, Point3D(0, 0, 1)) l = Line(Point(0, 1), Point(3, 4)) # Segment contains assert Point(0, (a + b) / 2) in Segment((0, a), (0, b)) assert Point((a + b) / 2, 0) in Segment((a, 0), (b, 0)) assert Point3D(0, 1, 0) in Segment3D((0, 1, 0), (0, 1, 0)) assert Point3D(1, 0, 0) in Segment3D((1, 0, 0), (1, 0, 0)) assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains([]) is True assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains( Segment3D(Point3D(2, 2, 2), Point3D(3, 2, 2))) is False # Line contains assert l.contains(Point(0, 1)) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False # Ray contains assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False assert r.contains(Segment((1, 1), (2, 2))) is True assert r.contains(Segment((1, 2), (2, 5))) is False assert r.contains(Ray((2, 2), (3, 3))) is True assert r.contains(Ray((2, 2), (3, 5))) is False assert r1.contains(Segment3D(p1, Point3D(0, 0, -10))) is True assert r1.contains(Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))) is False assert r2.contains(Point3D(0, 0, 0)) is True assert r3.contains(Point3D(0, 0, 0)) is True assert Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)).contains([]) is False assert Line3D((0, 0, 0), (x, y, z)).contains((2 * x, 2 * y, 2 * z)) with warns(UserWarning): assert Line3D(p1, Point3D(0, 1, 0)).contains(Point(1.0, 1.0)) is False with warns(UserWarning): assert r3.contains(Point(1.0, 1.0)) is False
def test_contains(): p1 = Point(0, 0) r = Ray(p1, Point(4, 4)) r1 = Ray3D(p1, Point3D(0, 0, -1)) r2 = Ray3D(p1, Point3D(0, 1, 0)) r3 = Ray3D(p1, Point3D(0, 0, 1)) l = Line(Point(0, 1), Point(3, 4)) # Segment contains assert Point(0, (a + b) / 2) in Segment((0, a), (0, b)) assert Point((a + b) / 2, 0) in Segment((a, 0), (b, 0)) assert Point3D(0, 1, 0) in Segment3D((0, 1, 0), (0, 1, 0)) assert Point3D(1, 0, 0) in Segment3D((1, 0, 0), (1, 0, 0)) assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains([]) is True assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains( Segment3D(Point3D(2, 2, 2), Point3D(3, 2, 2))) is False # Line contains assert l.contains(Point(0, 1)) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False # Ray contains assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False assert r.contains(Segment((1, 1), (2, 2))) is True assert r.contains(Segment((1, 2), (2, 5))) is False assert r.contains(Ray((2, 2), (3, 3))) is True assert r.contains(Ray((2, 2), (3, 5))) is False assert r1.contains(Segment3D(p1, Point3D(0, 0, -10))) is True assert r1.contains(Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))) is False assert r2.contains(Point3D(0, 0, 0)) is True assert r3.contains(Point3D(0, 0, 0)) is True assert Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)).contains([]) is False assert Line3D((0, 0, 0), (x, y, z)).contains((2 * x, 2 * y, 2 * z)) with warns(UserWarning): assert Line3D(p1, Point3D(0, 1, 0)).contains(Point(1.0, 1.0)) is False with warns(UserWarning): assert r3.contains(Point(1.0, 1.0)) is False
def test_warns_many_warnings(): # This isn't ideal but it's what pytest's warns does: with warnings.catch_warnings(record=True) as w: finished = False with warns(UserWarning): warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) warnings.warn('this is the other message', RuntimeWarning) finished = True assert finished assert len(w) == 0
def test_warns_many_warnings(): # This isn't ideal but it's what pytest's warns does: with warnings.catch_warnings(record=True) as w: finished = False with warns(UserWarning): warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) warnings.warn('this is the warning message', UserWarning) warnings.warn('this is the other message', RuntimeWarning) warnings.warn('this is the other message', RuntimeWarning) finished = True assert finished assert len(w) == 0
def test_competing_ambiguous(): test_namespace = dict() dispatch = partial(orig_dispatch, namespace=test_namespace) @dispatch(A, C) def f(x, y): return 2 with warns(AmbiguityWarning): @dispatch(C, A) def f(x, y): return 2 assert f(A(), C()) == f(C(), A()) == 2
def test_competing_ambiguous(): test_namespace = dict() dispatch = partial(orig_dispatch, namespace=test_namespace) @dispatch(A, C) def f(x, y): # noqa:F811 return 2 with warns(AmbiguityWarning): @dispatch(C, A) def f(x, y): # noqa:F811 return 2 assert f(A(), C()) == f(C(), A()) == 2
def plot_and_save_4(name): tmp_file = TmpFileManager.tmp_file x = Symbol('x') y = Symbol('y') ### # Examples from the 'advanced' notebook ### # XXX: This raises the warning "The evaluation of the expression is # problematic. We are trying a failback method that may still work. Please # report this as a bug." It has to use the fallback because using evalf() # is the only way to evaluate the integral. We should perhaps just remove # that warning. with warns(UserWarning, match="The evaluation of the expression is problematic"): i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y)) p = plot(i, (y, 1, 5)) p.save(tmp_file('%s_advanced_integral' % name)) p._backend.close()
def plot_implicit_tests(name): temp_dir = mkdtemp() TmpFileManager.tmp_folder(temp_dir) x = Symbol('x') y = Symbol('y') z = Symbol('z') #implicit plot tests plot_and_save(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2), name=name, dir=temp_dir) plot_and_save(Eq(y**2, x**3 - x), (x, -5, 5), (y, -4, 4), name=name, dir=temp_dir) plot_and_save(y > 1 / x, (x, -5, 5), (y, -2, 2), name=name, dir=temp_dir) plot_and_save(y < 1 / tan(x), (x, -5, 5), (y, -2, 2), name=name, dir=temp_dir) plot_and_save(y >= 2 * sin(x) * cos(x), (x, -5, 5), (y, -2, 2), name=name, dir=temp_dir) plot_and_save(y <= x**2, (x, -3, 3), (y, -1, 5), name=name, dir=temp_dir) #Test all input args for plot_implicit plot_and_save(Eq(y**2, x**3 - x), dir=temp_dir) plot_and_save(Eq(y**2, x**3 - x), adaptive=False, dir=temp_dir) plot_and_save(Eq(y**2, x**3 - x), adaptive=False, points=500, dir=temp_dir) plot_and_save(y > x, (x, -5, 5), dir=temp_dir) plot_and_save(And(y > exp(x), y > x + 2), dir=temp_dir) plot_and_save(Or(y > x, y > -x), dir=temp_dir) plot_and_save(x**2 - 1, (x, -5, 5), dir=temp_dir) plot_and_save(x**2 - 1, dir=temp_dir) plot_and_save(y > x, depth=-5, dir=temp_dir) plot_and_save(y > x, depth=5, dir=temp_dir) plot_and_save(y > cos(x), adaptive=False, dir=temp_dir) plot_and_save(y < cos(x), adaptive=False, dir=temp_dir) plot_and_save(And(y > cos(x), Or(y > x, Eq(y, x))), dir=temp_dir) plot_and_save(y - cos(pi / x), dir=temp_dir) #Test plots which cannot be rendered using the adaptive algorithm with warns(UserWarning, match="Adaptive meshing could not be applied"): plot_and_save(Eq(y, re(cos(x) + I*sin(x))), name=name, dir=temp_dir) plot_and_save(x**2 - 1, title='An implicit plot', dir=temp_dir)
def plot_and_save_4(name): tmp_file = TmpFileManager.tmp_file x = Symbol('x') y = Symbol('y') z = Symbol('z') ### # Examples from the 'advanced' notebook ### # XXX: This raises the warning "The evaluation of the expression is # problematic. We are trying a failback method that may still work. Please # report this as a bug." It has to use the fallback because using evalf() # is the only way to evaluate the integral. We should perhaps just remove # that warning. with warns(UserWarning, match="The evaluation of the expression is problematic"): i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y)) p = plot(i, (y, 1, 5)) p.save(tmp_file('%s_advanced_integral' % name)) p._backend.close()
def test_polygon(): x = Symbol('x', real=True) y = Symbol('y', real=True) q = Symbol('q', real=True) u = Symbol('u', real=True) v = Symbol('v', real=True) w = Symbol('w', real=True) x1 = Symbol('x1', real=True) half = Rational(1, 2) a, b, c = Point(0, 0), Point(2, 0), Point(3, 3) t = Triangle(a, b, c) assert Polygon(a, Point(1, 0), b, c) == t assert Polygon(Point(1, 0), b, c, a) == t assert Polygon(b, c, a, Point(1, 0)) == t # 2 "remove folded" tests assert Polygon(a, Point(3, 0), b, c) == t assert Polygon(a, b, Point(3, -1), b, c) == t # remove multiple collinear points assert Polygon(Point(-4, 15), Point(-11, 15), Point(-15, 15), Point(-15, 33/5), Point(-15, -87/10), Point(-15, -15), Point(-42/5, -15), Point(-2, -15), Point(7, -15), Point(15, -15), Point(15, -3), Point(15, 10), Point(15, 15)) == \ Polygon(Point(-15,-15), Point(15,-15), Point(15,15), Point(-15,15)) p1 = Polygon( Point(0, 0), Point(3, -1), Point(6, 0), Point(4, 5), Point(2, 3), Point(0, 3)) p2 = Polygon( Point(6, 0), Point(3, -1), Point(0, 0), Point(0, 3), Point(2, 3), Point(4, 5)) p3 = Polygon( Point(0, 0), Point(3, 0), Point(5, 2), Point(4, 4)) p4 = Polygon( Point(0, 0), Point(4, 4), Point(5, 2), Point(3, 0)) p5 = Polygon( Point(0, 0), Point(4, 4), Point(0, 4)) p6 = Polygon( Point(-11, 1), Point(-9, 6.6), Point(-4, -3), Point(-8.4, -8.7)) p7 = Polygon( Point(x, y), Point(q, u), Point(v, w)) p8 = Polygon( Point(x, y), Point(v, w), Point(q, u)) p9 = Polygon( Point(0, 0), Point(4, 4), Point(3, 0), Point(5, 2)) p10 = Polygon( Point(0, 2), Point(2, 2), Point(0, 0), Point(2, 0)) p11 = Polygon(Point(0, 0), 1, n=3) r = Ray(Point(-9,6.6), Point(-9,5.5)) # # General polygon # assert p1 == p2 assert len(p1.args) == 6 assert len(p1.sides) == 6 assert p1.perimeter == 5 + 2*sqrt(10) + sqrt(29) + sqrt(8) assert p1.area == 22 assert not p1.is_convex() assert Polygon((-1, 1), (2, -1), (2, 1), (-1, -1), (3, 0) ).is_convex() is False # ensure convex for both CW and CCW point specification assert p3.is_convex() assert p4.is_convex() dict5 = p5.angles assert dict5[Point(0, 0)] == pi / 4 assert dict5[Point(0, 4)] == pi / 2 assert p5.encloses_point(Point(x, y)) is None assert p5.encloses_point(Point(1, 3)) assert p5.encloses_point(Point(0, 0)) is False assert p5.encloses_point(Point(4, 0)) is False assert p1.encloses(Circle(Point(2.5,2.5),5)) is False assert p1.encloses(Ellipse(Point(2.5,2),5,6)) is False p5.plot_interval('x') == [x, 0, 1] assert p5.distance( Polygon(Point(10, 10), Point(14, 14), Point(10, 14))) == 6 * sqrt(2) assert p5.distance( Polygon(Point(1, 8), Point(5, 8), Point(8, 12), Point(1, 12))) == 4 with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance( Polygon(Point(0, 0), Point(0, 1), Point(1, 1))) assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4))) assert hash(p1) == hash(p2) assert hash(p7) == hash(p8) assert hash(p3) != hash(p9) assert p5 == Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) assert Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) in p5 assert p5 != Point(0, 4) assert Point(0, 1) in p5 assert p5.arbitrary_point('t').subs(Symbol('t', real=True), 0) == \ Point(0, 0) raises(ValueError, lambda: Polygon( Point(x, 0), Point(0, y), Point(x, y)).arbitrary_point('x')) assert p6.intersection(r) == [Point(-9, -S(84)/13), Point(-9, S(33)/5)] assert p10.area == 0 assert p11 == RegularPolygon(Point(0, 0), 1, 3, 0) assert p11.vertices[0] == Point(1, 0) assert p11.args[0] == Point(0, 0) p11.spin(pi/2) assert p11.vertices[0] == Point(0, 1) # # Regular polygon # p1 = RegularPolygon(Point(0, 0), 10, 5) p2 = RegularPolygon(Point(0, 0), 5, 5) raises(GeometryError, lambda: RegularPolygon(Point(0, 0), Point(0, 1), Point(1, 1))) raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2)) raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5)) assert p1 != p2 assert p1.interior_angle == 3*pi/5 assert p1.exterior_angle == 2*pi/5 assert p2.apothem == 5*cos(pi/5) assert p2.circumcenter == p1.circumcenter == Point(0, 0) assert p1.circumradius == p1.radius == 10 assert p2.circumcircle == Circle(Point(0, 0), 5) assert p2.incircle == Circle(Point(0, 0), p2.apothem) assert p2.inradius == p2.apothem == (5 * (1 + sqrt(5)) / 4) p2.spin(pi / 10) dict1 = p2.angles assert dict1[Point(0, 5)] == 3 * pi / 5 assert p1.is_convex() assert p1.rotation == 0 assert p1.encloses_point(Point(0, 0)) assert p1.encloses_point(Point(11, 0)) is False assert p2.encloses_point(Point(0, 4.9)) p1.spin(pi/3) assert p1.rotation == pi/3 assert p1.vertices[0] == Point(5, 5*sqrt(3)) for var in p1.args: if isinstance(var, Point): assert var == Point(0, 0) else: assert var == 5 or var == 10 or var == pi / 3 assert p1 != Point(0, 0) assert p1 != p5 # while spin works in place (notice that rotation is 2pi/3 below) # rotate returns a new object p1_old = p1 assert p1.rotate(pi/3) == RegularPolygon(Point(0, 0), 10, 5, 2*pi/3) assert p1 == p1_old assert p1.area == (-250*sqrt(5) + 1250)/(4*tan(pi/5)) assert p1.length == 20*sqrt(-sqrt(5)/8 + S(5)/8) assert p1.scale(2, 2) == \ RegularPolygon(p1.center, p1.radius*2, p1._n, p1.rotation) assert RegularPolygon((0, 0), 1, 4).scale(2, 3) == \ Polygon(Point(2, 0), Point(0, 3), Point(-2, 0), Point(0, -3)) assert repr(p1) == str(p1) # # Angles # angles = p4.angles assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) angles = p3.angles assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) # # Triangle # p1 = Point(0, 0) p2 = Point(5, 0) p3 = Point(0, 5) t1 = Triangle(p1, p2, p3) t2 = Triangle(p1, p2, Point(Rational(5, 2), sqrt(Rational(75, 4)))) t3 = Triangle(p1, Point(x1, 0), Point(0, x1)) s1 = t1.sides assert Triangle(p1, p2, p1) == Polygon(p1, p2, p1) == Segment(p1, p2) raises(GeometryError, lambda: Triangle(Point(0, 0))) # Basic stuff assert Triangle(p1, p1, p1) == p1 assert Triangle(p2, p2*2, p2*3) == Segment(p2, p2*3) assert t1.area == Rational(25, 2) assert t1.is_right() assert t2.is_right() is False assert t3.is_right() assert p1 in t1 assert t1.sides[0] in t1 assert Segment((0, 0), (1, 0)) in t1 assert Point(5, 5) not in t2 assert t1.is_convex() assert feq(t1.angles[p1].evalf(), pi.evalf()/2) assert t1.is_equilateral() is False assert t2.is_equilateral() assert t3.is_equilateral() is False assert are_similar(t1, t2) is False assert are_similar(t1, t3) assert are_similar(t2, t3) is False assert t1.is_similar(Point(0, 0)) is False assert t1.is_similar(t2) is False # Bisectors bisectors = t1.bisectors() assert bisectors[p1] == Segment( p1, Point(Rational(5, 2), Rational(5, 2))) assert t2.bisectors()[p2] == Segment( Point(5, 0), Point(Rational(5, 4), 5*sqrt(3)/4)) p4 = Point(0, x1) assert t3.bisectors()[p4] == Segment(p4, Point(x1*(sqrt(2) - 1), 0)) ic = (250 - 125*sqrt(2))/50 assert t1.incenter == Point(ic, ic) # Inradius assert t1.inradius == t1.incircle.radius == 5 - 5*sqrt(2)/2 assert t2.inradius == t2.incircle.radius == 5*sqrt(3)/6 assert t3.inradius == t3.incircle.radius == x1**2/((2 + sqrt(2))*Abs(x1)) # Exradius assert t1.exradii[t1.sides[2]] == 5*sqrt(2)/2 # Circumcircle assert t1.circumcircle.center == Point(2.5, 2.5) # Medians + Centroid m = t1.medians assert t1.centroid == Point(Rational(5, 3), Rational(5, 3)) assert m[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) assert t3.medians[p1] == Segment(p1, Point(x1/2, x1/2)) assert intersection(m[p1], m[p2], m[p3]) == [t1.centroid] assert t1.medial == Triangle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5)) # Nine-point circle assert t1.nine_point_circle == Circle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5)) assert t1.nine_point_circle == Circle(Point(0, 0), Point(0, 2.5), Point(2.5, 2.5)) # Perpendicular altitudes = t1.altitudes assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) assert altitudes[p2].equals(s1[0]) assert altitudes[p3] == s1[2] assert t1.orthocenter == p1 t = S('''Triangle( Point(100080156402737/5000000000000, 79782624633431/500000000000), Point(39223884078253/2000000000000, 156345163124289/1000000000000), Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''') assert t.orthocenter == S('''Point(-780660869050599840216997''' '''79471538701955848721853/80368430960602242240789074233100000000000000,''' '''20151573611150265741278060334545897615974257/16073686192120448448157''' '''8148466200000000000)''') # Ensure assert len(intersection(*bisectors.values())) == 1 assert len(intersection(*altitudes.values())) == 1 assert len(intersection(*m.values())) == 1 # Distance p1 = Polygon( Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1)) p2 = Polygon( Point(0, Rational(5)/4), Point(1, Rational(5)/4), Point(1, Rational(9)/4), Point(0, Rational(9)/4)) p3 = Polygon( Point(1, 2), Point(2, 2), Point(2, 1)) p4 = Polygon( Point(1, 1), Point(Rational(6)/5, 1), Point(1, Rational(6)/5)) pt1 = Point(half, half) pt2 = Point(1, 1) '''Polygon to Point''' assert p1.distance(pt1) == half assert p1.distance(pt2) == 0 assert p2.distance(pt1) == Rational(3)/4 assert p3.distance(pt2) == sqrt(2)/2 '''Polygon to Polygon''' # p1.distance(p2) emits a warning with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): assert p1.distance(p2) == half/2 assert p1.distance(p3) == sqrt(2)/2 # p3.distance(p4) emits a warning with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): assert p3.distance(p4) == (sqrt(2)/2 - sqrt(Rational(2)/25)/2)
def test_dimension_normalization(): with warns(UserWarning): assert Ray((1, 1), (2, 1, 2)) == Ray((1, 1, 0), (2, 1, 2))
def test_point3D(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) x2 = Symbol('x2', real=True) x3 = Symbol('x3', real=True) y1 = Symbol('y1', real=True) y2 = Symbol('y2', real=True) y3 = Symbol('y3', real=True) half = Rational(1, 2) 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) 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) 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)) 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(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float # Test length property returns correctly assert p.length == 0 assert p1_1.length == 0 assert p1_2.length == 0 # Test are_colinear type error raises(TypeError, lambda: Point3D.are_collinear(p, x)) # Test are_coplanar assert Point.are_coplanar() assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0)) assert Point.are_coplanar((1, 2, 0), (1, 2, 3)) with warns(UserWarning): raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3))) assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3)) assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False planar2 = Point3D(1, -1, 1) planar3 = Point3D(-1, 1, 1) assert Point3D.are_coplanar(p, planar2, planar3) == True assert Point3D.are_coplanar(p, planar2, planar3, p3) == False assert Point.are_coplanar(p, planar2) planar2 = Point3D(1, 1, 2) planar3 = Point3D(1, 1, 3) assert Point3D.are_coplanar(p, planar2, planar3) # line, not plane plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2)) assert Point.are_coplanar(*[plane.projection(((-1)**i, i)) for i in range(4)]) # all 2D points are coplanar assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(y, x + 2)) is True # 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) raises(ValueError, lambda: p.transform(p)) raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]]))) # Test Equals assert p.equals(x1) == False # Test __sub__ p_4d = Point(0, 0, 0, 1) with warns(UserWarning): assert p - p_4d == Point(1, 1, 1, -1) p_4d3d = Point(0, 0, 1, 0) with warns(UserWarning): assert p - p_4d3d == Point(1, 1, 0, 0)
def test_point(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) x2 = Symbol('x2', real=True) y1 = Symbol('y1', real=True) y2 = Symbol('y2', real=True) half = Rational(1, 2) p1 = Point(x1, x2) p2 = Point(y1, y2) p3 = Point(0, 0) p4 = Point(1, 1) p5 = Point(0, 1) line = Line(Point(1,0), slope = 1) 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) raises(ValueError, lambda: Point(3, I)) raises(ValueError, lambda: Point(2*I, I)) 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) # distance should be symmetric assert p1.distance(line) == line.distance(p1) assert p4.distance(line) == line.distance(p4) assert Point.taxicab_distance(p4, p3) == 2 assert Point.canberra_distance(p4, p5) == 1 p1_1 = Point(x1, x1) p1_2 = Point(y2, y2) p1_3 = Point(x1 + 1, x1) assert Point.is_collinear(p3) with warns(UserWarning): assert Point.is_collinear(p3, Point(p3, dim=4)) assert p3.is_collinear() 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 raises(TypeError, lambda: Point.is_collinear(line)) 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) for pts in permutations((p2_1, p2_2, p2_3, p2_5)): assert Point.is_concyclic(*pts) is False assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) 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) 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)) 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 raises(ValueError, lambda: p3.transform(p3)) raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
def test_warns_catches_warning(): with warnings.catch_warnings(record=True) as w: with warns(UserWarning): warnings.warn('this is the warning message') assert len(w) == 0
def test_issue_11617(): p1 = Point3D(1,0,2) p2 = Point2D(2,0) with warns(UserWarning): assert p1.distance(p2) == sqrt(5)
def test_polygon(): x = Symbol('x', real=True) y = Symbol('y', real=True) q = Symbol('q', real=True) u = Symbol('u', real=True) v = Symbol('v', real=True) w = Symbol('w', real=True) x1 = Symbol('x1', real=True) half = Rational(1, 2) a, b, c = Point(0, 0), Point(2, 0), Point(3, 3) t = Triangle(a, b, c) assert Polygon(a, Point(1, 0), b, c) == t assert Polygon(Point(1, 0), b, c, a) == t assert Polygon(b, c, a, Point(1, 0)) == t # 2 "remove folded" tests assert Polygon(a, Point(3, 0), b, c) == t assert Polygon(a, b, Point(3, -1), b, c) == t # remove multiple collinear points assert Polygon(Point(-4, 15), Point(-11, 15), Point(-15, 15), Point(-15, 33/5), Point(-15, -87/10), Point(-15, -15), Point(-42/5, -15), Point(-2, -15), Point(7, -15), Point(15, -15), Point(15, -3), Point(15, 10), Point(15, 15)) == \ Polygon(Point(-15,-15), Point(15,-15), Point(15,15), Point(-15,15)) p1 = Polygon( Point(0, 0), Point(3, -1), Point(6, 0), Point(4, 5), Point(2, 3), Point(0, 3)) p2 = Polygon( Point(6, 0), Point(3, -1), Point(0, 0), Point(0, 3), Point(2, 3), Point(4, 5)) p3 = Polygon( Point(0, 0), Point(3, 0), Point(5, 2), Point(4, 4)) p4 = Polygon( Point(0, 0), Point(4, 4), Point(5, 2), Point(3, 0)) p5 = Polygon( Point(0, 0), Point(4, 4), Point(0, 4)) p6 = Polygon( Point(-11, 1), Point(-9, 6.6), Point(-4, -3), Point(-8.4, -8.7)) p7 = Polygon( Point(x, y), Point(q, u), Point(v, w)) p8 = Polygon( Point(x, y), Point(v, w), Point(q, u)) p9 = Polygon( Point(0, 0), Point(4, 4), Point(3, 0), Point(5, 2)) p10 = Polygon( Point(0, 2), Point(2, 2), Point(0, 0), Point(2, 0)) p11 = Polygon(Point(0, 0), 1, n=3) r = Ray(Point(-9,6.6), Point(-9,5.5)) # # General polygon # assert p1 == p2 assert len(p1.args) == 6 assert len(p1.sides) == 6 assert p1.perimeter == 5 + 2*sqrt(10) + sqrt(29) + sqrt(8) assert p1.area == 22 assert not p1.is_convex() assert Polygon((-1, 1), (2, -1), (2, 1), (-1, -1), (3, 0) ).is_convex() is False # ensure convex for both CW and CCW point specification assert p3.is_convex() assert p4.is_convex() dict5 = p5.angles assert dict5[Point(0, 0)] == pi / 4 assert dict5[Point(0, 4)] == pi / 2 assert p5.encloses_point(Point(x, y)) is None assert p5.encloses_point(Point(1, 3)) assert p5.encloses_point(Point(0, 0)) is False assert p5.encloses_point(Point(4, 0)) is False assert p1.encloses(Circle(Point(2.5,2.5),5)) is False assert p1.encloses(Ellipse(Point(2.5,2),5,6)) is False p5.plot_interval('x') == [x, 0, 1] assert p5.distance( Polygon(Point(10, 10), Point(14, 14), Point(10, 14))) == 6 * sqrt(2) assert p5.distance( Polygon(Point(1, 8), Point(5, 8), Point(8, 12), Point(1, 12))) == 4 with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance( Polygon(Point(0, 0), Point(0, 1), Point(1, 1))) assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4))) assert hash(p1) == hash(p2) assert hash(p7) == hash(p8) assert hash(p3) != hash(p9) assert p5 == Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) assert Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) in p5 assert p5 != Point(0, 4) assert Point(0, 1) in p5 assert p5.arbitrary_point('t').subs(Symbol('t', real=True), 0) == \ Point(0, 0) raises(ValueError, lambda: Polygon( Point(x, 0), Point(0, y), Point(x, y)).arbitrary_point('x')) assert p6.intersection(r) == [Point(-9, -S(84)/13), Point(-9, S(33)/5)] assert p10.area == 0 assert p11 == RegularPolygon(Point(0, 0), 1, 3, 0) assert p11.vertices[0] == Point(1, 0) assert p11.args[0] == Point(0, 0) p11.spin(pi/2) assert p11.vertices[0] == Point(0, 1) # # Regular polygon # p1 = RegularPolygon(Point(0, 0), 10, 5) p2 = RegularPolygon(Point(0, 0), 5, 5) raises(GeometryError, lambda: RegularPolygon(Point(0, 0), Point(0, 1), Point(1, 1))) raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2)) raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5)) assert p1 != p2 assert p1.interior_angle == 3*pi/5 assert p1.exterior_angle == 2*pi/5 assert p2.apothem == 5*cos(pi/5) assert p2.circumcenter == p1.circumcenter == Point(0, 0) assert p1.circumradius == p1.radius == 10 assert p2.circumcircle == Circle(Point(0, 0), 5) assert p2.incircle == Circle(Point(0, 0), p2.apothem) assert p2.inradius == p2.apothem == (5 * (1 + sqrt(5)) / 4) p2.spin(pi / 10) dict1 = p2.angles assert dict1[Point(0, 5)] == 3 * pi / 5 assert p1.is_convex() assert p1.rotation == 0 assert p1.encloses_point(Point(0, 0)) assert p1.encloses_point(Point(11, 0)) is False assert p2.encloses_point(Point(0, 4.9)) p1.spin(pi/3) assert p1.rotation == pi/3 assert p1.vertices[0] == Point(5, 5*sqrt(3)) for var in p1.args: if isinstance(var, Point): assert var == Point(0, 0) else: assert var == 5 or var == 10 or var == pi / 3 assert p1 != Point(0, 0) assert p1 != p5 # while spin works in place (notice that rotation is 2pi/3 below) # rotate returns a new object p1_old = p1 assert p1.rotate(pi/3) == RegularPolygon(Point(0, 0), 10, 5, 2*pi/3) assert p1 == p1_old assert p1.area == (-250*sqrt(5) + 1250)/(4*tan(pi/5)) assert p1.length == 20*sqrt(-sqrt(5)/8 + S(5)/8) assert p1.scale(2, 2) == \ RegularPolygon(p1.center, p1.radius*2, p1._n, p1.rotation) assert RegularPolygon((0, 0), 1, 4).scale(2, 3) == \ Polygon(Point(2, 0), Point(0, 3), Point(-2, 0), Point(0, -3)) assert repr(p1) == str(p1) # # Angles # angles = p4.angles assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) angles = p3.angles assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483")) assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544")) assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388")) assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449")) # # Triangle # p1 = Point(0, 0) p2 = Point(5, 0) p3 = Point(0, 5) t1 = Triangle(p1, p2, p3) t2 = Triangle(p1, p2, Point(Rational(5, 2), sqrt(Rational(75, 4)))) t3 = Triangle(p1, Point(x1, 0), Point(0, x1)) s1 = t1.sides assert Triangle(p1, p2, p1) == Polygon(p1, p2, p1) == Segment(p1, p2) raises(GeometryError, lambda: Triangle(Point(0, 0))) # Basic stuff assert Triangle(p1, p1, p1) == p1 assert Triangle(p2, p2*2, p2*3) == Segment(p2, p2*3) assert t1.area == Rational(25, 2) assert t1.is_right() assert t2.is_right() is False assert t3.is_right() assert p1 in t1 assert t1.sides[0] in t1 assert Segment((0, 0), (1, 0)) in t1 assert Point(5, 5) not in t2 assert t1.is_convex() assert feq(t1.angles[p1].evalf(), pi.evalf()/2) assert t1.is_equilateral() is False assert t2.is_equilateral() assert t3.is_equilateral() is False assert are_similar(t1, t2) is False assert are_similar(t1, t3) assert are_similar(t2, t3) is False assert t1.is_similar(Point(0, 0)) is False assert t1.is_similar(t2) is False # Bisectors bisectors = t1.bisectors() assert bisectors[p1] == Segment( p1, Point(Rational(5, 2), Rational(5, 2))) assert t2.bisectors()[p2] == Segment( Point(5, 0), Point(Rational(5, 4), 5*sqrt(3)/4)) p4 = Point(0, x1) assert t3.bisectors()[p4] == Segment(p4, Point(x1*(sqrt(2) - 1), 0)) ic = (250 - 125*sqrt(2))/50 assert t1.incenter == Point(ic, ic) # Inradius assert t1.inradius == t1.incircle.radius == 5 - 5*sqrt(2)/2 assert t2.inradius == t2.incircle.radius == 5*sqrt(3)/6 assert t3.inradius == t3.incircle.radius == x1**2/((2 + sqrt(2))*Abs(x1)) # Exradius assert t1.exradii[t1.sides[2]] == 5*sqrt(2)/2 # Circumcircle assert t1.circumcircle.center == Point(2.5, 2.5) # Medians + Centroid m = t1.medians assert t1.centroid == Point(Rational(5, 3), Rational(5, 3)) assert m[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) assert t3.medians[p1] == Segment(p1, Point(x1/2, x1/2)) assert intersection(m[p1], m[p2], m[p3]) == [t1.centroid] assert t1.medial == Triangle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5)) # Nine-point circle assert t1.nine_point_circle == Circle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5)) assert t1.nine_point_circle == Circle(Point(0, 0), Point(0, 2.5), Point(2.5, 2.5)) # Perpendicular altitudes = t1.altitudes assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) assert altitudes[p2].equals(s1[0]) assert altitudes[p3] == s1[2] assert t1.orthocenter == p1 t = S('''Triangle( Point(100080156402737/5000000000000, 79782624633431/500000000000), Point(39223884078253/2000000000000, 156345163124289/1000000000000), Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''') assert t.orthocenter == S('''Point(-780660869050599840216997''' '''79471538701955848721853/80368430960602242240789074233100000000000000,''' '''20151573611150265741278060334545897615974257/16073686192120448448157''' '''8148466200000000000)''') # Ensure assert len(intersection(*bisectors.values())) == 1 assert len(intersection(*altitudes.values())) == 1 assert len(intersection(*m.values())) == 1 # Distance p1 = Polygon( Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1)) p2 = Polygon( Point(0, Rational(5)/4), Point(1, Rational(5)/4), Point(1, Rational(9)/4), Point(0, Rational(9)/4)) p3 = Polygon( Point(1, 2), Point(2, 2), Point(2, 1)) p4 = Polygon( Point(1, 1), Point(Rational(6)/5, 1), Point(1, Rational(6)/5)) pt1 = Point(half, half) pt2 = Point(1, 1) '''Polygon to Point''' assert p1.distance(pt1) == half assert p1.distance(pt2) == 0 assert p2.distance(pt1) == Rational(3)/4 assert p3.distance(pt2) == sqrt(2)/2 '''Polygon to Polygon''' # p1.distance(p2) emits a warning with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): assert p1.distance(p2) == half/2 assert p1.distance(p3) == sqrt(2)/2 # p3.distance(p4) emits a warning with warns(UserWarning, \ match="Polygons may intersect producing erroneous output"): assert p3.distance(p4) == (sqrt(2)/2 - sqrt(Rational(2)/25)/2)
def test_point(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) x2 = Symbol('x2', real=True) y1 = Symbol('y1', real=True) y2 = Symbol('y2', real=True) half = S.Half p1 = Point(x1, x2) p2 = Point(y1, y2) p3 = Point(0, 0) p4 = Point(1, 1) p5 = Point(0, 1) line = Line(Point(1, 0), slope=1) 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 -p2 == Point(-y1, -y2) raises(ValueError, lambda: Point(3, I)) raises(ValueError, lambda: Point(2 * I, I)) 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) # distance should be symmetric assert p1.distance(line) == line.distance(p1) assert p4.distance(line) == line.distance(p4) assert Point.taxicab_distance(p4, p3) == 2 assert Point.canberra_distance(p4, p5) == 1 p1_1 = Point(x1, x1) p1_2 = Point(y2, y2) p1_3 = Point(x1 + 1, x1) assert Point.is_collinear(p3) with warns(UserWarning): assert Point.is_collinear(p3, Point(p3, dim=4)) assert p3.is_collinear() 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 raises(TypeError, lambda: Point.is_collinear(line)) 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) for pts in permutations((p2_1, p2_2, p2_3, p2_5)): assert Point.is_concyclic(*pts) is False assert Point.is_concyclic(p4, p4 * 2, p4 * 3) is False assert Point(0, 0).is_concyclic((1, 1), (2, 2), (2, 1)) 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) assert 5 * p4 == Point(5, 5) 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 = S.Half, Rational(1, 3) assert Point(a, b).evalf(2) == \ Point(a.n(2), b.n(2), evaluate=False) 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 raises(ValueError, lambda: p3.transform(p3)) raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
def test_warns_match_matching(): with warnings.catch_warnings(record=True) as w: with warns(UserWarning, match='this is the warning message'): warnings.warn('this is the warning message', UserWarning) assert len(w) == 0
def test_dimension_normalization(): with warns(UserWarning): assert Ray((1, 1), (2, 1, 2)) == Ray((1, 1, 0), (2, 1, 2))
def test_warns_catches_warning(): with warnings.catch_warnings(record=True) as w: with warns(UserWarning): warnings.warn('this is the warning message') assert len(w) == 0
def test_warns_raises_without_warning(): with raises(Failed): with warns(UserWarning): pass
def test_warns_match_matching(): with warnings.catch_warnings(record=True) as w: with warns(UserWarning, match='this is the warning message'): warnings.warn('this is the warning message', UserWarning) assert len(w) == 0
def test_point3D(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) x2 = Symbol('x2', real=True) x3 = Symbol('x3', real=True) y1 = Symbol('y1', real=True) y2 = Symbol('y2', real=True) y3 = Symbol('y3', real=True) half = S.Half 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 -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) 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) assert 5 * p4 == Point3D(5, 5, 5) raises(ValueError, lambda: Point3D(0, 0, 0) + 10) # Test coordinate properties assert p1.coordinates == (x1, x2, x3) assert p2.coordinates == (y1, y2, y3) assert p3.coordinates == (0, 0, 0) assert p4.coordinates == (1, 1, 1) assert p5.coordinates == (0, 1, 2) assert p5.x == 0 assert p5.y == 1 assert p5.z == 2 # 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, c = S.Half, Rational(1, 3), Rational(1, 4) assert Point3D(a, b, c).evalf(2) == \ Point(a.n(2), b.n(2), c.n(2), evaluate=False) raises(ValueError, lambda: Point3D(1, 2, 3) + 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(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float # Test length property returns correctly assert p.length == 0 assert p1_1.length == 0 assert p1_2.length == 0 # Test are_colinear type error raises(TypeError, lambda: Point3D.are_collinear(p, x)) # Test are_coplanar assert Point.are_coplanar() assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0)) assert Point.are_coplanar((1, 2, 0), (1, 2, 3)) with warns(UserWarning): raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3))) assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3)) assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False planar2 = Point3D(1, -1, 1) planar3 = Point3D(-1, 1, 1) assert Point3D.are_coplanar(p, planar2, planar3) == True assert Point3D.are_coplanar(p, planar2, planar3, p3) == False assert Point.are_coplanar(p, planar2) planar2 = Point3D(1, 1, 2) planar3 = Point3D(1, 1, 3) assert Point3D.are_coplanar(p, planar2, planar3) # line, not plane plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2)) assert Point.are_coplanar( *[plane.projection(((-1)**i, i)) for i in range(4)]) # all 2D points are coplanar assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point( y, x + 2)) is True # 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) raises(ValueError, lambda: p.transform(p)) raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]]))) # Test Equals assert p.equals(x1) == False # Test __sub__ p_4d = Point(0, 0, 0, 1) with warns(UserWarning): assert p - p_4d == Point(1, 1, 1, -1) p_4d3d = Point(0, 0, 1, 0) with warns(UserWarning): assert p - p_4d3d == Point(1, 1, 0, 0)
def test_min_module_version_python3_basestring_error(): with warns(UserWarning): import_module('mpmath', min_module_version='1000.0.1')
def test_issue_11617(): p1 = Point3D(1, 0, 2) p2 = Point2D(2, 0) with warns(UserWarning): assert p1.distance(p2) == sqrt(5)
def test_min_module_version_python3_basestring_error(): with warns(UserWarning): import_module('mpmath', min_module_version='1000.0.1')
def test_warns_match_non_matching(): with warnings.catch_warnings(record=True) as w: with raises(Failed): with warns(UserWarning, match='this is the warning message'): warnings.warn('this is not the expected warning message', UserWarning) assert len(w) == 0
def test_warns_raises_without_warning(): with raises(Failed): with warns(UserWarning): pass