def test_evalf_bugs(): assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10) assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10) assert NS('log(1+1/10**50)', 20) == '1.0000000000000000000e-50' assert NS('log(10**100,10)', 10) == '100.0000000' assert NS('log(2)', 10) == '0.6931471806' assert NS( '(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667' assert NS(sin(1) + Rational( 1, 10**100)*I, 15) == '0.841470984807897 + 1.00000000000000e-100*I' assert x.evalf() == x assert NS((1 + I)**2*I, 6) == '-2.00000' d = {n: ( -1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)} assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I' assert NS(((-I - sqrt(2)*I)**2).evalf()) == '-5.82842712474619' assert NS((1 + I)**2*I, 15) == '-2.00000000000000' # issue sympy/sympy#4758 (1/2): assert NS(Float(pi.evalf(69), 100) - pi) == '-4.43863937855894e-71' assert NS(pi.evalf(69) - pi) == '-0.e-71' # issue sympy/sympy#4758 (2/2): With the bug present, this still only fails if the # terms are in the order given here. This is not generally the case, # because the order depends on the hashes of the terms. assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n, subs={n: .01}) == '19.8100000000000' assert NS(((x - 1)*((1 - x))**1000).n() ) == '(-x + 1.00000000000000)**1000*(x - 1.00000000000000)' assert NS((-x).n()) == '-x' assert NS((-2*x).n()) == '-2.00000000000000*x' assert NS((-2*x*y).n()) == '-2.00000000000000*x*y' assert cos(x).n(subs={x: 1+I}) == cos(x).subs(x, 1+I).n() # issue sympy/sympy#6660. Also NaN != mpmath.nan # In this order: # 0*nan, 0/nan, 0*inf, 0/inf # 0+nan, 0-nan, 0+inf, 0-inf # >>> n = Some Number # n*nan, n/nan, n*inf, n/inf # n+nan, n-nan, n+inf, n-inf assert (0*sin(oo)).n() == S.Zero assert (0/sin(oo)).n() == S.Zero assert (0*E**(oo)).n() == S.NaN assert (0/E**(oo)).n() == S.Zero assert (0+sin(oo)).n() == S.NaN assert (0-sin(oo)).n() == S.NaN assert (0+E**(oo)).n() == S.Infinity assert (0-E**(oo)).n() == S.NegativeInfinity assert (5*sin(oo)).n() == S.NaN assert (5/sin(oo)).n() == S.NaN assert (5*E**(oo)).n() == S.Infinity assert (5/E**(oo)).n() == S.Zero assert (5+sin(oo)).n() == S.NaN assert (5-sin(oo)).n() == S.NaN assert (5+E**(oo)).n() == S.Infinity assert (5-E**(oo)).n() == S.NegativeInfinity # issue sympy/sympy#7416 assert as_mpmath(0.0, 10, {'chop': True}) == 0
def test_fcode_NumberSymbol(): p = FCodePrinter() assert fcode( Catalan ) == ' parameter (Catalan = 0.915965594177219d0)\n Catalan' assert fcode( EulerGamma ) == ' parameter (EulerGamma = 0.577215664901533d0)\n EulerGamma' assert fcode(E) == ' parameter (E = 2.71828182845905d0)\n E' assert fcode( GoldenRatio ) == ' parameter (GoldenRatio = 1.61803398874989d0)\n GoldenRatio' assert fcode(pi) == ' parameter (pi = 3.14159265358979d0)\n pi' assert fcode(pi, precision=5) == ' parameter (pi = 3.1416d0)\n pi' assert fcode(Catalan, human=False) == ({(Catalan, p._print(Catalan.evalf(15)))}, set(), ' Catalan') assert fcode(EulerGamma, human=False) == ({ (EulerGamma, p._print(EulerGamma.evalf(15))) }, set(), ' EulerGamma') assert fcode(E, human=False) == ({(E, p._print(E.evalf(15)))}, set(), ' E') assert fcode(GoldenRatio, human=False) == ({ (GoldenRatio, p._print(GoldenRatio.evalf(15))) }, set(), ' GoldenRatio') assert fcode(pi, human=False) == ({(pi, p._print(pi.evalf(15)))}, set(), ' pi') assert fcode(pi, precision=5, human=False) == ({(pi, p._print(pi.evalf(5)))}, set(), ' pi')
def test_sympyissue_8821(): s = str(pi.evalf(128)) p = N(s) assert abs(sin(p)) < 1e-15 p = N(s, 64) assert abs(sin(p)) < 1e-64 s = str(pi.evalf(128)) p = sympify(s) assert abs(sin(p)) < 1e-127
def test_Float(): # NOTE prec is the whole number of decimal digits assert str(Float('1.23', prec=1 + 2)) == '1.23' assert str(Float('1.23456789', prec=1 + 8)) == '1.23456789' assert str(Float('1.234567890123456789', prec=1 + 18)) == '1.234567890123456789' assert str(pi.evalf(1 + 2)) == '3.14' assert str(pi.evalf(1 + 14)) == '3.14159265358979' assert str(pi.evalf(1 + 64)) == ('3.141592653589793238462643383279' '5028841971693993751058209749445923') assert str(pi.round(-1)) == '0.' assert str((pi**400 - (pi**400).round(1)).n(2)) == '-0.e+88'
def test_Float(): # NOTE prec is the whole number of decimal digits assert str(Float('1.23', dps=1 + 2)) == '1.23' assert str(Float('1.23456789', dps=1 + 8)) == '1.23456789' assert str( Float('1.234567890123456789', dps=1 + 18)) == '1.234567890123456789' assert str(pi.evalf(1 + 2)) == '3.14' assert str(pi.evalf(1 + 14)) == '3.14159265358979' assert str(pi.evalf(1 + 64)) == ('3.141592653589793238462643383279' '5028841971693993751058209749445923') assert str(pi.round(-1)) == '0.' assert str((pi**400 - (pi**400).round(1)).evalf(2, strict=False)) == '-0.e+9'
def test_fcode_NumberSymbol(): p = FCodePrinter() assert fcode(Catalan) == ' parameter (Catalan = 0.915965594177219d0)\n Catalan' assert fcode(EulerGamma) == ' parameter (EulerGamma = 0.577215664901533d0)\n EulerGamma' assert fcode(E) == ' parameter (E = 2.71828182845905d0)\n E' assert fcode(GoldenRatio) == ' parameter (GoldenRatio = 1.61803398874989d0)\n GoldenRatio' assert fcode(pi) == ' parameter (pi = 3.14159265358979d0)\n pi' assert fcode( pi, precision=5) == ' parameter (pi = 3.1416d0)\n pi' assert fcode(Catalan, human=False) == ({(Catalan, p._print( Catalan.evalf(15)))}, set(), ' Catalan') assert fcode(EulerGamma, human=False) == ({(EulerGamma, p._print( EulerGamma.evalf(15)))}, set(), ' EulerGamma') assert fcode(E, human=False) == ( {(E, p._print(E.evalf(15)))}, set(), ' E') assert fcode(GoldenRatio, human=False) == ({(GoldenRatio, p._print( GoldenRatio.evalf(15)))}, set(), ' GoldenRatio') assert fcode(pi, human=False) == ( {(pi, p._print(pi.evalf(15)))}, set(), ' pi') assert fcode(pi, precision=5, human=False) == ( {(pi, p._print(pi.evalf(5)))}, set(), ' pi')
def test_nsolve(): # onedimensional x = Symbol('x') assert nsolve(sin(x), 2) - pi.evalf() < 1e-15 assert nsolve(Eq(2 * x, 2), x, -10) == nsolve(2 * x - 2, -10) # Testing checks on number of inputs pytest.raises(TypeError, lambda: nsolve(Eq(2 * x, 2))) pytest.raises(TypeError, lambda: nsolve(Eq(2 * x, 2), x, 1, 2)) # issue 4829 assert nsolve(x**2 / (1 - x) / (1 - 2 * x)**2 - 100, x, 0) # doesn't fail # multidimensional x1 = Symbol('x1') x2 = Symbol('x2') f1 = 3 * x1**2 - 2 * x2**2 - 1 f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8 f = Matrix((f1, f2)).T F = lambdify((x1, x2), f.T, modules='mpmath') for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]: x = nsolve(f, (x1, x2), x0, tol=1.e-8) assert mnorm(F(*x), 1) <= 1.e-10 # The Chinese mathematician Zhu Shijie was the very first to solve this # nonlinear system 700 years ago (z was added to make it 3-dimensional) x = Symbol('x') y = Symbol('y') z = Symbol('z') f1 = -x + 2 * y f2 = (x**2 + x * (y**2 - 2) - 4 * y) / (x + 4) f3 = sqrt(x**2 + y**2) * z f = Matrix((f1, f2, f3)).T F = lambdify((x, y, z), f.T, modules='mpmath') def getroot(x0): root = nsolve(f, (x, y, z), x0) assert mnorm(F(*root), 1) <= 1.e-8 return root assert list(map(round, getroot((1, 1, 1)))) == [2.0, 1.0, 0.0] assert nsolve([Eq(f1), Eq(f2), Eq(f3)], [x, y, z], (1, 1, 1)) # just see that it works a = Symbol('a') assert nsolve(1 / (0.001 + a)**3 - 6 / (0.9 - a)**3, a, 0.3).ae(mpf('0.31883011387318591'))
def test_sympyissue_8821_highprec_from_str(): s = str(pi.evalf(128)) p = sympify(s) assert Abs(sin(p)) < 1e-127
def test_polygon(): a, b, c = Point(0, 0), Point(2, 0), Point(3, 3) t = Triangle(a, b, c) assert Polygon(a) == a assert Polygon(a, a) == a assert Polygon(a, b, b, c) == Polygon(a, b, c) assert Polygon(a, 1, 1, n=4) == RegularPolygon(a, 1, 4, 1) 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 pytest.raises(GeometryError, lambda: Polygon((0, 0), (1, 0), (0, 1), (1, 1))) # 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)) 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 p1.contains(Segment((0, 0), (1, 2))) is False assert p1.contains(Ray((0, 0), angle=pi / 3)) 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 assert 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 p7 = Polygon(Point(1, 2), Point(3, 7), Point(0, 1)) assert p5.distance(p7) == 9 * sqrt(29) / 29 l1 = Line(Point(0, 0), Point(1, 0)) assert p5.reflect(l1).distance(p7.reflect(l1)) == 9 * sqrt(29) / 29 warnings.filterwarnings( 'error', message='Polygons may intersect producing erroneous output') pytest.raises( UserWarning, lambda: Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance( Polygon(Point(0, 0), Point(0, 1), Point(1, 1)))) warnings.filterwarnings( 'ignore', message='Polygons may intersect producing erroneous output') assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4))) 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', extended_real=True): 0}) == \ Point(0, 0) pytest.raises( ValueError, lambda: Polygon(Point(x, 0), Point(0, y), Point(x, y)). arbitrary_point('x')) assert p6.intersection(r) == [Point(-9, 33 / 5), Point(-9, -84 / 13)] # # Regular polygon # p1 = RegularPolygon(Point(0, 0), 10, 5) p2 = RegularPolygon(Point(0, 0), 5, 5) pytest.raises( GeometryError, lambda: RegularPolygon(Point(0, 0), Point(0, 1), Point(1, 1))) pytest.raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2)) pytest.raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5)) assert Polygon(Point(0, 0), 10, 5, pi, n=5) == RegularPolygon(Point(0, 0), 10, 5, pi) 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 in (5, 10, 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 + 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')) assert (Polygon((0, 0), (10, 0), (2, 1), (0, 3)).angles == { Point(0, 0): pi / 2, Point(0, 3): pi / 4, Point(2, 1): -acos(-9 * sqrt(130) / 130) + 2 * pi, Point(10, 0): acos(8 * sqrt(65) / 65) }) # # 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) pytest.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 # Bisectors bisectors = t1.bisectors() assert bisectors[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) 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)) # 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)) # Perpendicular altitudes = t1.altitudes assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2))) assert altitudes[p2] == s1[0] assert altitudes[p3] == s1[2] assert t1.orthocenter == p1 t = Triangle( Point(Rational(100080156402737, 5000000000000), Rational(79782624633431, 500000000000)), Point(Rational(39223884078253, 2000000000000), Rational(156345163124289, 1000000000000)), Point(Rational(31241359188437, 1250000000000), Rational(338338270939941, 1000000000000000))) assert t.orthocenter == \ Point(Rational(-78066086905059984021699779471538701955848721853, 80368430960602242240789074233100000000000000), Rational(20151573611150265741278060334545897615974257, 160736861921204484481578148466200000000000)) # 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(0.5, 0.5) pt2 = Point(1, 1) # Polygon to Point assert p1.distance(pt1) == Rational(1, 2) 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 # First, test the warning warnings.filterwarnings( 'error', message='Polygons may intersect producing erroneous output') pytest.raises(UserWarning, lambda: p1.distance(p2)) # now test the actual output warnings.filterwarnings( 'ignore', message='Polygons may intersect producing erroneous output') assert p1.distance(p2) == Rational(1, 4) assert p1.distance(p3) == sqrt(2) / 2 assert p3.distance(p4) == 2 * sqrt(2) / 5 r = Polygon(Point(0, 0), 1, n=3) assert r.vertices[0] == Point(1, 0) mid = Point(1, 1) assert Polygon((0, 2), (2, 2), mid, (0, 0), (2, 0), mid).area == 0 t1 = Triangle(Point(0, 0), Point(4, 0), Point(2, 4)) assert t1.is_isosceles() is True t1 = Triangle(Point(0, 0), Point(4, 0), Point(1, 4)) assert t1.is_scalene() is True assert t1.is_isosceles() is False p1 = Polygon((1, 0), (2, 0), (2, 2), (-4, 3)) p2 = Polygon((1, 0), (2, 0), (3, 2), (-4, 3)) assert (p1 == p2) is False
def test_sympyissue_8821_highprec_from_str(): s = str(pi.evalf(128)) p = N(s) assert Abs(sin(p)) < 1e-15 p = N(s, 64) assert Abs(sin(p)) < 1e-64
def test_evalf_arguments(): pytest.raises(TypeError, lambda: pi.evalf(method="garbage"))
def test_evalf_bugs(): assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10) assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10) assert NS('log(1+1/10**50)', 20) == '1.0000000000000000000e-50' assert NS('log(10**100,10)', 10) == '100.0000000' assert NS('log(2)', 10) == '0.6931471806' assert NS( '(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667' assert NS(sin(1) + I/10**100, 15) == '0.841470984807897 + 1.00000000000000e-100*I' assert x.evalf(strict=False) == x assert NS((1 + I)**2*I, 6) == '-2.00000' d = {n: ( -1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)} assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I' assert NS(((-I - sqrt(2)*I)**2).evalf(), strict=False) == '-5.82842712474619' assert NS((1 + I)**2*I, 15) == '-2.00000000000000' # issue sympy/sympy#4758 (1/2): assert NS(Float(pi.evalf(69), 100) - pi) == '-4.43863937855894e-71' assert NS(pi.evalf(69) - pi, strict=False) == '-0.e-71' # issue sympy/sympy#4758 (2/2): With the bug present, this still only fails if the # terms are in the order given here. This is not generally the case, # because the order depends on the hashes of the terms. assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n, subs={n: .01}, strict=False) == '19.8100000000000' assert NS(((x - 1)*((1 - x))**1000).evalf(strict=False), strict=False) == '(-x + 1.00000000000000)**1000*(x - 1.00000000000000)' assert NS((-x).evalf(strict=False)) == '-x' assert NS((-2*x).evalf(strict=False), strict=False) == '-2.00000000000000*x' assert NS((-2*x*y).evalf(strict=False), strict=False) == '-2.00000000000000*x*y' assert cos(x).evalf(subs={x: 1+I}) == cos(x).subs({x: 1 + I}).evalf() # issue sympy/sympy#6660. Also NaN != mpmath.nan # In this order: # 0*nan, 0/nan, 0*inf, 0/inf # 0+nan, 0-nan, 0+inf, 0-inf # >>> n = Some Number # n*nan, n/nan, n*inf, n/inf # n+nan, n-nan, n+inf, n-inf assert (0*sin(oo)).evalf() == 0 assert (0/sin(oo)).evalf() == 0 assert (0*E**oo).evalf() == nan assert (0/E**oo).evalf() == 0 assert (0+sin(oo)).evalf() == nan assert (0-sin(oo)).evalf() == nan assert (0+E**oo).evalf() == +oo assert (0-E**oo).evalf() == -oo assert (5*sin(oo)).evalf() == nan assert (5/sin(oo)).evalf() == nan assert (5*E**oo).evalf() == oo assert (5/E**oo).evalf() == 0 assert (5+sin(oo)).evalf() == nan assert (5-sin(oo)).evalf() == nan assert (5+E**oo).evalf() == +oo assert (5-E**oo).evalf() == -oo # issue sympy/sympy#7416 assert as_mpmath(0.0, 10, {'chop': True}) == 0 # issue sympy/sympy#5412 assert (oo*I).evalf() == oo*I assert (oo + oo*I).evalf() == oo + oo*I
def test_issue_8821_highprec_from_str(): s = str(pi.evalf(128)) p = N(s) assert Abs(sin(p)) < 1e-15 p = N(s, 64) assert Abs(sin(p)) < 1e-64
def test_line_geom(): p1 = Point(0, 0) p2 = Point(1, 1) p3 = Point(x1, x1) p4 = Point(y1, y1) p5 = Point(x1, 1 + x1) p6 = Point(1, 0) p7 = Point(0, 1) p8 = Point(2, 0) p9 = Point(2, 1) l1 = Line(p1, p2) l2 = Line(p3, p4) l3 = Line(p3, p5) l4 = Line(p1, p6) l5 = Line(p1, p7) l6 = Line(p8, p9) l7 = Line(p2, p9) pytest.raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0))) # Basic stuff assert Line((1, 1), slope=1) == Line((1, 1), (2, 2)) assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2)) assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2)) pytest.raises(ValueError, lambda: Line((1, 1), 1)) assert Line(p1, p2) == Line(p1, p2) assert Line(p1, p2) != Line(p2, p1) assert l1 != l2 assert l1 != l3 assert l1.slope == 1 assert l1.length == oo assert l3.slope == oo assert l4.slope == 0 assert l4.coefficients == (0, 1, 0) assert l4.equation(x=x, y=y) == y assert l5.slope == oo assert l5.coefficients == (1, 0, 0) assert l5.equation() == x assert l6.equation() == x - 2 assert l7.equation() == y - 1 assert p1 in l1 # is p1 on the line l1? assert p1 not in l3 assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0) assert simplify(l1.equation()) in (x - y, y - x) assert simplify(l3.equation()) in (x - x1, x1 - x) assert Line(p1, p2).scale(2, 1) == Line(p1, p9) assert l2.arbitrary_point() in l2 for ind in range(5): assert l3.random_point() in l3 pytest.raises(ValueError, lambda: l3.arbitrary_point('x1')) assert Line(Point(0, 0), Point(1, 0)).is_similar( Line(Point(1, 0), Point(2, 0))) is True assert l1.equal(l1) is True assert l1.equal(l2) is True assert l1.equal(l3) is False assert l1.equal(object()) is False # Orthogonality p1_1 = Point(-x1, x1) l1_1 = Line(p1, p1_1) assert l1.perpendicular_line(p1.args) == Line(Point(0, 0), Point(1, -1)) assert l1.perpendicular_line(p1) == Line(Point(0, 0), Point(1, -1)) assert Line.is_perpendicular(l1, l1_1) assert Line.is_perpendicular(l1, l2) is False p = l1.random_point() assert l1.perpendicular_segment(p) == p assert l4.perpendicular_line(p2) == Line(Point(1, 1), Point(1, 0)) # Parallelity l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1) == Line(Point(-x1, x1), Point(-y1, 2 * x1 - y1)) assert l2_1.parallel_line(p1.args) == Line(Point(0, 0), Point(0, -1)) assert l2_1.parallel_line(p1) == Line(Point(0, 0), Point(0, -1)) assert Line.is_parallel(l1, l2) assert Line.is_parallel(l2, l3) is False assert Line.is_parallel(l2, l2.parallel_line(p1_1)) assert Line.is_parallel(l2_1, l2_1.parallel_line(p1)) # Intersection assert intersection(l1, p1) == [p1] assert intersection(l1, p5) == [] assert intersection(l1, l2) in [[l1], [l2]] assert intersection(l1, l1.parallel_line(p5)) == [] # Concurrency l3_1 = Line(Point(5, x1), Point(-Rational(3, 5), x1)) assert Line.are_concurrent(l1) is False assert Line.are_concurrent(l1, l3) assert Line.are_concurrent(l1, l3, l3_1) assert Line.are_concurrent(l1, l1_1, l3) is False # Projection assert l2.projection(p4) == p4 assert l1.projection(p1_1) == p1 assert l3.projection(p2) == Point(x1, 1) pytest.raises( GeometryError, lambda: Line(Point(0, 0), Point(1, 0)).projection( Circle(Point(0, 0), 1))) # Finding angles l1_1 = Line(p1, Point(5, 0)) assert feq(Line.angle_between(l1, l1_1).evalf(), pi.evalf() / 4) # Testing Rays and Segments (very similar to Lines) pytest.raises(ValueError, lambda: Ray((1, 1), I)) pytest.raises(ValueError, lambda: Ray(p1, p1)) pytest.raises(ValueError, lambda: Ray(p1)) assert Ray((1, 1), angle=pi / 4) == Ray((1, 1), (2, 2)) assert Ray((1, 1), angle=pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=-pi / 2) == Ray((1, 1), (1, 0)) assert Ray((1, 1), angle=-3 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5.0 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=3.0 * pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=4.0 * pi) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=4.05 * pi) == Ray( Point(1, 1), Point( 2, -sqrt(5) * sqrt(2 * sqrt(5) + 10) / 4 - sqrt(2 * sqrt(5) + 10) / 4 + 2 + sqrt(5))) assert Ray((1, 1), angle=4.02 * pi) == Ray(Point(1, 1), Point(2, 1 + tan(4.02 * pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5))) pytest.raises(ValueError, lambda: Ray((1, 1), 1)) # issue sympy/sympy#7963 r = Ray((0, 0), angle=x) assert r.subs({x: 3 * pi / 4}) == Ray((0, 0), (-1, 1)) assert r.subs({x: 5 * pi / 4}) == Ray((0, 0), (-1, -1)) assert r.subs({x: -pi / 4}) == Ray((0, 0), (1, -1)) assert r.subs({x: pi / 2}) == Ray((0, 0), (0, 1)) assert r.subs({x: -pi / 2}) == Ray((0, 0), (0, -1)) r1 = Ray(p1, Point(-1, 5)) r2 = Ray(p1, Point(-1, 1)) r3 = Ray(p3, p5) r4 = Ray(p1, p2) r5 = Ray(p2, p1) r6 = Ray(Point(0, 1), Point(1, 2)) r7 = Ray(Point(0.5, 0.5), Point(1, 1)) assert l1.projection(r1) == Ray(Point(0, 0), Point(2, 2)) assert l1.projection(r2) == p1 assert r3 != r1 t = Symbol('t', extended_real=True) assert Ray((1, 1), angle=pi/4).arbitrary_point() == \ Point(t + 1, t + 1) r8 = Ray(Point(0, 0), Point(0, 4)) r9 = Ray(Point(0, 1), Point(0, -1)) assert r8.intersection(r9) == [Segment(Point(0, 0), Point(0, 1))] s1 = Segment(p1, p2) s2 = Segment(p1, p1_1) assert s1.midpoint == Point(Rational(1, 2), Rational(1, 2)) assert s2.length == sqrt(2 * (x1**2)) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2 * t) assert s1.perpendicular_bisector() == \ Line(Point(1/2, 1/2), Point(3/2, -1/2)) # intersections assert s1.intersection(Line(p6, p9)) == [] s3 = Segment(Point(0.25, 0.25), Point(0.5, 0.5)) assert s1.intersection(s3) == [s1] assert s3.intersection(s1) == [s3] assert r4.intersection(s3) == [s3] assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == [] assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] s3 = Segment(Point(1, 1), Point(2, 2)) assert s1.intersection(s3) == [Point(1, 1)] s3 = Segment(Point(0.5, 0.5), Point(1.5, 1.5)) assert s1.intersection(s3) == [Segment(Point(0.5, 0.5), p2)] assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == [] assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1] assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] assert r4.intersection(r5) == [s1] assert r5.intersection(r6) == [] assert r4.intersection(r7) == r7.intersection(r4) == [r7] # Segment contains a, b = symbols('a,b') s = Segment((0, a), (0, b)) assert Point(0, (a + b) / 2) in s s = Segment((a, 0), (b, 0)) assert Point((a + b) / 2, 0) in s pytest.raises(Undecidable, lambda: Point(2 * a, 0) in s) # Testing distance from a Segment to an object s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) pt1 = Point(0, 0) pt2 = Point(Rational(3, 2), Rational(3, 2)) assert s1.distance(pt1) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(pt1) == 2**half / 2 assert s2.distance(pt2) == 2**half # Line to point p1, p2 = Point(0, 0), Point(1, 1) s = Line(p1, p2) assert s.distance(Point(-1, 1)) == sqrt(2) assert s.distance(Point(1, -1)) == sqrt(2) assert s.distance(Point(2, 2)) == 0 assert s.distance((-1, 1)) == sqrt(2) assert Line((0, 0), (0, 1)).distance(p1) == 0 assert Line((0, 0), (0, 1)).distance(p2) == 1 assert Line((0, 0), (1, 0)).distance(p1) == 0 assert Line((0, 0), (1, 0)).distance(p2) == 1 m = symbols('m') l = Line((0, 5), slope=m) p = Point(2, 3) assert l.distance(p) == 2 * abs(m + 1) / sqrt(m**2 + 1) # Ray to point r = Ray(p1, p2) assert r.distance(Point(-1, -1)) == sqrt(2) assert r.distance(Point(1, 1)) == 0 assert r.distance(Point(-1, 1)) == sqrt(2) assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3 * sqrt(2) / 4 assert r.distance((1, 1)) == 0 assert r.distance((-1, Rational(1, 2))) == sqrt(5) / 2 # Line contains p1, p2 = Point(0, 1), Point(3, 4) l = Line(p1, p2) assert l.contains(p1) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False assert l.contains(Circle(p1, 1)) is False assert l.contains(Ray(p1, p1 + p2)) is False # Ray contains p1, p2 = Point(0, 0), Point(4, 4) r = Ray(p1, p2) assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False assert r.contains(object()) is False s = Segment((1, 1), (2, 2)) assert r.contains(s) is True s = Segment((1, 2), (2, 5)) assert r.contains(s) is False r1 = Ray((2, 2), (3, 3)) assert r.contains(r1) is True r1 = Ray((2, 2), (3, 5)) assert r.contains(r1) is False r1 = Ray(p1, angle=-pi) assert r1.contains(Point(1, 0)) is False r1 = Ray(p1, angle=-pi / 2) assert r1.contains(Point(0, 1)) is False pytest.raises(Undecidable, lambda: r1.contains(Point(0, x))) # Special cases of projection and intersection r1 = Ray(Point(1, 1), Point(2, 2)) r2 = Ray(Point(2, 2), Point(0, 0)) r3 = Ray(Point(1, 1), Point(-1, -1)) r4 = Ray(Point(0, 4), Point(-1, -5)) r5 = Ray(Point(2, 2), Point(3, 3)) assert intersection(r1, r2) == [Segment(Point(1, 1), Point(2, 2))] assert intersection(r1, r3) == [Point(1, 1)] assert r1.projection(r3) == Point(1, 1) assert r1.projection(r4) == Segment(Point(1, 1), Point(2, 2)) r5 = Ray(Point(0, 0), Point(0, 1)) r6 = Ray(Point(0, 0), Point(0, 2)) assert r5 in r6 assert r6 in r5 s1 = Segment(Point(0, 0), Point(2, 2)) s2 = Segment(Point(-1, 5), Point(-5, -10)) s3 = Segment(Point(0, 4), Point(-2, 2)) assert intersection(r1, s1) == [Segment(Point(1, 1), Point(2, 2))] assert r1.projection(s2) == Segment(Point(1, 1), Point(2, 2)) assert s3.projection(r1) == Segment(Point(0, 4), Point(-1, 3)) l1 = Line(Point(0, 0), Point(3, 4)) r1 = Ray(Point(0, 0), Point(3, 4)) s1 = Segment(Point(0, 0), Point(3, 4)) assert intersection(l1, l1) == [l1] assert intersection(l1, r1) == [r1] assert intersection(l1, s1) == [s1] assert intersection(r1, l1) == [r1] assert intersection(s1, l1) == [s1] entity1 = Segment(Point(-10, 10), Point(10, 10)) entity2 = Segment(Point(-5, -5), Point(-5, 5)) assert intersection(entity1, entity2) == [] r1 = Ray(p1, Point(0, 1)) r2 = Ray(Point(0, 1), p1) r3 = Ray(p1, p2) r4 = Ray(p2, p1) s1 = Segment(p1, Point(0, 1)) assert Line(r1.source, r1.random_point()).slope == r1.slope assert Line(r2.source, r2.random_point()).slope == r2.slope assert Segment(Point(0, -1), s1.random_point()).slope == s1.slope p_r3 = r3.random_point() p_r4 = r4.random_point() assert p_r3.x >= p1.x and p_r3.y >= p1.y assert p_r4.x <= p2.x and p_r4.y <= p2.y p10 = Point(2000, 2000) s1 = Segment(p1, p10) p_s1 = s1.random_point() assert p1.x <= p_s1.x and p_s1.x <= p10.x and \ p1.y <= p_s1.y and p_s1.y <= p10.y s2 = Segment(p10, p1) assert hash(s1) == hash(s2) p11 = p10.scale(2, 2) assert s1.is_similar(Segment(p10, p11)) assert s1.is_similar(r1) is False assert (r1 in s1) is False assert Segment(p1, p2) in s1 assert s1.plot_interval() == [t, 0, 1] assert s1 in Line(p1, p10) assert Line(p1, p10) != Line(p10, p1) assert Line(p1, p10) != p1 assert Line(p1, p10).plot_interval() == [t, -5, 5] assert Ray((0, 0), angle=pi/4).plot_interval() == \ [t, 0, 10] p1, p2 = Point(0, 0), Point(4, 1) r1 = Ray(p1, p2) assert r1.direction == p2 p1, p2, p3 = Point(0, 0), Point(-1, -1), Point(-1, 0) r1, r2 = Ray(p1, p2), Ray(p1, p3) assert r1.ydirection == -oo assert r2.ydirection == 0 p1, p2, p3 = Point(0, 0), Point(6, 6), Point(5, 1) s1 = Segment(p1, p2) assert s1.perpendicular_bisector() == Line(Point(3, 3), Point(9, -3)) assert s1.perpendicular_bisector(p3) == Segment(Point(3, 3), Point(5, 1))
def test_mpmath_precision(): mpmath.mp.dps = 100 assert str(lambdify((), pi.evalf(100), 'mpmath')()) == str(pi.evalf(100))
def test_sympyissue_19988(): c = pi.evalf(100) check(c)
def test_line_geom(): p1 = Point(0, 0) p2 = Point(1, 1) p3 = Point(x1, x1) p4 = Point(y1, y1) p5 = Point(x1, 1 + x1) p6 = Point(1, 0) p7 = Point(0, 1) p8 = Point(2, 0) p9 = Point(2, 1) l1 = Line(p1, p2) l2 = Line(p3, p4) l3 = Line(p3, p5) l4 = Line(p1, p6) l5 = Line(p1, p7) l6 = Line(p8, p9) l7 = Line(p2, p9) pytest.raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0))) # Basic stuff assert Line((1, 1), slope=1) == Line((1, 1), (2, 2)) assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2)) assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2)) pytest.raises(ValueError, lambda: Line((1, 1), 1)) assert Line(p1, p2) == Line(p1, p2) assert Line(p1, p2) != Line(p2, p1) assert l1 != l2 assert l1 != l3 assert l1.slope == 1 assert l1.length == oo assert l3.slope == oo assert l4.slope == 0 assert l4.coefficients == (0, 1, 0) assert l4.equation(x=x, y=y) == y assert l5.slope == oo assert l5.coefficients == (1, 0, 0) assert l5.equation() == x assert l6.equation() == x - 2 assert l7.equation() == y - 1 assert p1 in l1 # is p1 on the line l1? assert p1 not in l3 assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0) assert simplify(l1.equation()) in (x - y, y - x) assert simplify(l3.equation()) in (x - x1, x1 - x) assert Line(p1, p2).scale(2, 1) == Line(p1, p9) assert l2.arbitrary_point() in l2 for ind in range(5): assert l3.random_point() in l3 # Orthogonality p1_1 = Point(-x1, x1) l1_1 = Line(p1, p1_1) assert l1.perpendicular_line(p1.args) == Line(Point(0, 0), Point(1, -1)) assert l1.perpendicular_line(p1) == Line(Point(0, 0), Point(1, -1)) assert Line.is_perpendicular(l1, l1_1) assert Line.is_perpendicular(l1, l2) is False p = l1.random_point() assert l1.perpendicular_segment(p) == p # Parallelity l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1) == Line(Point(-x1, x1), Point(-y1, 2*x1 - y1)) assert l2_1.parallel_line(p1.args) == Line(Point(0, 0), Point(0, -1)) assert l2_1.parallel_line(p1) == Line(Point(0, 0), Point(0, -1)) assert Line.is_parallel(l1, l2) assert Line.is_parallel(l2, l3) is False assert Line.is_parallel(l2, l2.parallel_line(p1_1)) assert Line.is_parallel(l2_1, l2_1.parallel_line(p1)) # Intersection assert intersection(l1, p1) == [p1] assert intersection(l1, p5) == [] assert intersection(l1, l2) in [[l1], [l2]] assert intersection(l1, l1.parallel_line(p5)) == [] # Concurrency l3_1 = Line(Point(5, x1), Point(-Rational(3, 5), x1)) assert Line.are_concurrent(l1) is False assert Line.are_concurrent(l1, l3) assert Line.are_concurrent(l1, l3, l3_1) assert Line.are_concurrent(l1, l1_1, l3) is False # Projection assert l2.projection(p4) == p4 assert l1.projection(p1_1) == p1 assert l3.projection(p2) == Point(x1, 1) pytest.raises(GeometryError, lambda: Line(Point(0, 0), Point(1, 0)) .projection(Circle(Point(0, 0), 1))) # Finding angles l1_1 = Line(p1, Point(5, 0)) assert feq(Line.angle_between(l1, l1_1).evalf(), pi.evalf()/4) # Testing Rays and Segments (very similar to Lines) pytest.raises(ValueError, lambda: Ray((1, 1), I)) assert Ray((1, 1), angle=pi/4) == Ray((1, 1), (2, 2)) assert Ray((1, 1), angle=pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=-pi/2) == Ray((1, 1), (1, 0)) assert Ray((1, 1), angle=-3*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5.0*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=3.0*pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=4.0*pi) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=4.05*pi) == Ray(Point(1, 1), Point(2, -sqrt(5)*sqrt(2*sqrt(5) + 10)/4 - sqrt(2*sqrt(5) + 10)/4 + 2 + sqrt(5))) assert Ray((1, 1), angle=4.02*pi) == Ray(Point(1, 1), Point(2, 1 + tan(4.02*pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5))) pytest.raises(ValueError, lambda: Ray((1, 1), 1)) # issue sympy/sympy#7963 r = Ray((0, 0), angle=x) assert r.subs({x: 3*pi/4}) == Ray((0, 0), (-1, 1)) assert r.subs({x: 5*pi/4}) == Ray((0, 0), (-1, -1)) assert r.subs({x: -pi/4}) == Ray((0, 0), (1, -1)) assert r.subs({x: pi/2}) == Ray((0, 0), (0, 1)) assert r.subs({x: -pi/2}) == Ray((0, 0), (0, -1)) r1 = Ray(p1, Point(-1, 5)) r2 = Ray(p1, Point(-1, 1)) r3 = Ray(p3, p5) r4 = Ray(p1, p2) r5 = Ray(p2, p1) r6 = Ray(Point(0, 1), Point(1, 2)) r7 = Ray(Point(0.5, 0.5), Point(1, 1)) assert l1.projection(r1) == Ray(Point(0, 0), Point(2, 2)) assert l1.projection(r2) == p1 assert r3 != r1 t = Symbol('t', extended_real=True) assert Ray((1, 1), angle=pi/4).arbitrary_point() == \ Point(t + 1, t + 1) r8 = Ray(Point(0, 0), Point(0, 4)) r9 = Ray(Point(0, 1), Point(0, -1)) assert r8.intersection(r9) == [Segment(Point(0, 0), Point(0, 1))] s1 = Segment(p1, p2) s2 = Segment(p1, p1_1) assert s1.midpoint == Point(Rational(1, 2), Rational(1, 2)) assert s2.length == sqrt( 2*(x1**2) ) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2*t) assert s1.perpendicular_bisector() == \ Line(Point(1/2, 1/2), Point(3/2, -1/2)) # intersections assert s1.intersection(Line(p6, p9)) == [] s3 = Segment(Point(0.25, 0.25), Point(0.5, 0.5)) assert s1.intersection(s3) == [s1] assert s3.intersection(s1) == [s3] assert r4.intersection(s3) == [s3] assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == [] assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] s3 = Segment(Point(1, 1), Point(2, 2)) assert s1.intersection(s3) == [Point(1, 1)] s3 = Segment(Point(0.5, 0.5), Point(1.5, 1.5)) assert s1.intersection(s3) == [Segment(Point(0.5, 0.5), p2)] assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == [] assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1] assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] assert r4.intersection(r5) == [s1] assert r5.intersection(r6) == [] assert r4.intersection(r7) == r7.intersection(r4) == [r7] # Segment contains a, b = symbols('a,b') s = Segment((0, a), (0, b)) assert Point(0, (a + b)/2) in s s = Segment((a, 0), (b, 0)) assert Point((a + b)/2, 0) in s pytest.raises(Undecidable, lambda: Point(2*a, 0) in s) # Testing distance from a Segment to an object s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) pt1 = Point(0, 0) pt2 = Point(Rational(3, 2), Rational(3, 2)) assert s1.distance(pt1) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(pt1) == 2**half/2 assert s2.distance(pt2) == 2**half # Line to point p1, p2 = Point(0, 0), Point(1, 1) s = Line(p1, p2) assert s.distance(Point(-1, 1)) == sqrt(2) assert s.distance(Point(1, -1)) == sqrt(2) assert s.distance(Point(2, 2)) == 0 assert s.distance((-1, 1)) == sqrt(2) assert Line((0, 0), (0, 1)).distance(p1) == 0 assert Line((0, 0), (0, 1)).distance(p2) == 1 assert Line((0, 0), (1, 0)).distance(p1) == 0 assert Line((0, 0), (1, 0)).distance(p2) == 1 m = symbols('m') l = Line((0, 5), slope=m) p = Point(2, 3) assert l.distance(p) == 2*abs(m + 1)/sqrt(m**2 + 1) # Ray to point r = Ray(p1, p2) assert r.distance(Point(-1, -1)) == sqrt(2) assert r.distance(Point(1, 1)) == 0 assert r.distance(Point(-1, 1)) == sqrt(2) assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3*sqrt(2)/4 assert r.distance((1, 1)) == 0 # Line contains p1, p2 = Point(0, 1), Point(3, 4) l = Line(p1, p2) assert l.contains(p1) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False # Ray contains p1, p2 = Point(0, 0), Point(4, 4) r = Ray(p1, p2) assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False s = Segment((1, 1), (2, 2)) assert r.contains(s) is True s = Segment((1, 2), (2, 5)) assert r.contains(s) is False r1 = Ray((2, 2), (3, 3)) assert r.contains(r1) is True r1 = Ray((2, 2), (3, 5)) assert r.contains(r1) is False # Special cases of projection and intersection r1 = Ray(Point(1, 1), Point(2, 2)) r2 = Ray(Point(2, 2), Point(0, 0)) r3 = Ray(Point(1, 1), Point(-1, -1)) r4 = Ray(Point(0, 4), Point(-1, -5)) r5 = Ray(Point(2, 2), Point(3, 3)) assert intersection(r1, r2) == [Segment(Point(1, 1), Point(2, 2))] assert intersection(r1, r3) == [Point(1, 1)] assert r1.projection(r3) == Point(1, 1) assert r1.projection(r4) == Segment(Point(1, 1), Point(2, 2)) r5 = Ray(Point(0, 0), Point(0, 1)) r6 = Ray(Point(0, 0), Point(0, 2)) assert r5 in r6 assert r6 in r5 s1 = Segment(Point(0, 0), Point(2, 2)) s2 = Segment(Point(-1, 5), Point(-5, -10)) s3 = Segment(Point(0, 4), Point(-2, 2)) assert intersection(r1, s1) == [Segment(Point(1, 1), Point(2, 2))] assert r1.projection(s2) == Segment(Point(1, 1), Point(2, 2)) assert s3.projection(r1) == Segment(Point(0, 4), Point(-1, 3)) l1 = Line(Point(0, 0), Point(3, 4)) r1 = Ray(Point(0, 0), Point(3, 4)) s1 = Segment(Point(0, 0), Point(3, 4)) assert intersection(l1, l1) == [l1] assert intersection(l1, r1) == [r1] assert intersection(l1, s1) == [s1] assert intersection(r1, l1) == [r1] assert intersection(s1, l1) == [s1] entity1 = Segment(Point(-10, 10), Point(10, 10)) entity2 = Segment(Point(-5, -5), Point(-5, 5)) assert intersection(entity1, entity2) == [] r1 = Ray(p1, Point(0, 1)) r2 = Ray(Point(0, 1), p1) r3 = Ray(p1, p2) r4 = Ray(p2, p1) s1 = Segment(p1, Point(0, 1)) assert Line(r1.source, r1.random_point()).slope == r1.slope assert Line(r2.source, r2.random_point()).slope == r2.slope assert Segment(Point(0, -1), s1.random_point()).slope == s1.slope p_r3 = r3.random_point() p_r4 = r4.random_point() assert p_r3.x >= p1.x and p_r3.y >= p1.y assert p_r4.x <= p2.x and p_r4.y <= p2.y p10 = Point(2000, 2000) s1 = Segment(p1, p10) p_s1 = s1.random_point() assert p1.x <= p_s1.x and p_s1.x <= p10.x and \ p1.y <= p_s1.y and p_s1.y <= p10.y s2 = Segment(p10, p1) assert hash(s1) == hash(s2) p11 = p10.scale(2, 2) assert s1.is_similar(Segment(p10, p11)) assert s1.is_similar(r1) is False assert (r1 in s1) is False assert Segment(p1, p2) in s1 assert s1.plot_interval() == [t, 0, 1] assert s1 in Line(p1, p10) assert Line(p1, p10) != Line(p10, p1) assert Line(p1, p10) != p1 assert Line(p1, p10).plot_interval() == [t, -5, 5] assert Ray((0, 0), angle=pi/4).plot_interval() == \ [t, 0, 10]