本文整理汇总了Python中sympy.utilities.randtest.td函数的典型用法代码示例。如果您正苦于以下问题：Python td函数的具体用法？Python td怎么用？Python td使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了td函数的20个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: test_E
def test_E():
assert E(z, 0) == z
assert E(0, m) == 0
assert E(i*pi/2, m) == i*E(m)
assert E(z, oo) == zoo
assert E(z, -oo) == zoo
assert E(0) == pi/2
assert E(1) == 1
assert E(oo) == I*oo
assert E(-oo) == oo
assert E(zoo) == zoo
assert E(-z, m) == -E(z, m)
assert E(z, m).diff(z) == sqrt(1 - m*sin(z)**2)
assert E(z, m).diff(m) == (E(z, m) - F(z, m))/(2*m)
assert E(z).diff(z) == (E(z) - K(z))/(2*z)
r = randcplx()
assert td(E(r, m), m)
assert td(E(z, r), z)
assert td(E(z), z)
mi = Symbol('m', real=False)
assert E(z, mi).conjugate() == E(z.conjugate(), mi.conjugate())
mr = Symbol('m', real=True, negative=True)
assert E(z, mr).conjugate() == E(z.conjugate(), mr)
assert E(z).rewrite(hyper) == (pi/2)*hyper((-S.Half, S.Half), (S.One,), z)
assert tn(E(z), (pi/2)*hyper((-S.Half, S.Half), (S.One,), z))
assert E(z).rewrite(meijerg) == \
-meijerg(((S.Half, S(3)/2), []), ((S.Zero,), (S.Zero,)), -z)/4
assert tn(E(z), -meijerg(((S.Half, S(3)/2), []), ((S.Zero,), (S.Zero,)), -z)/4)
开发者ID:Maihj，项目名称:sympy，代码行数:32，代码来源:test_elliptic_integrals.py
示例2: test_uppergamma
def test_uppergamma():
from sympy import meijerg, exp_polar, I, expint
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y**(x-1)*exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == \
uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi)*(1 - erf(sqrt(x)))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False),
uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False),
uppergamma(S.Half - 3, x), x)
assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
assert tn_branch(-3, uppergamma)
assert tn_branch(-4, uppergamma)
assert tn_branch(S(1)/3, uppergamma)
assert tn_branch(pi, uppergamma)
assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x)
assert uppergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + gamma(y)*(1-exp(4*pi*I*y))
assert uppergamma(-2, exp_polar(5*pi*I)*x) == \
uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I
assert uppergamma(-2, x) == expint(3, x)/x**2
assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y)
开发者ID:BDGLunde，项目名称:sympy，代码行数:32，代码来源:test_gamma_functions.py
示例3: test_lowergamma
def test_lowergamma():
from sympy import meijerg, exp_polar, I, expint
assert lowergamma(x, y).diff(y) == y ** (x - 1) * exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert td(lowergamma(x, randcplx()), x)
assert lowergamma(x, y).diff(x) == gamma(x) * polygamma(0, x) - uppergamma(x, y) * log(y) - meijerg(
[], [1, 1], [0, 0, x], [], y
)
assert lowergamma(S.Half, x) == sqrt(pi) * erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False), lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False), lowergamma(S.Half - 3, x), x)
assert tn_branch(-3, lowergamma)
assert tn_branch(-4, lowergamma)
assert tn_branch(S(1) / 3, lowergamma)
assert tn_branch(pi, lowergamma)
assert lowergamma(3, exp_polar(4 * pi * I) * x) == lowergamma(3, x)
assert lowergamma(y, exp_polar(5 * pi * I) * x) == exp(4 * I * pi * y) * lowergamma(y, x * exp_polar(pi * I))
assert lowergamma(-2, exp_polar(5 * pi * I) * x) == lowergamma(-2, x * exp_polar(I * pi)) + 2 * pi * I
assert conjugate(lowergamma(x, y)) == lowergamma(conjugate(x), conjugate(y))
assert conjugate(lowergamma(x, 0)) == conjugate(lowergamma(x, 0))
assert conjugate(lowergamma(x, -oo)) == conjugate(lowergamma(x, -oo))
assert lowergamma(x, y).rewrite(expint) == -y ** x * expint(-x + 1, y) + gamma(x)
k = Symbol("k", integer=True)
assert lowergamma(k, y).rewrite(expint) == -y ** k * expint(-k + 1, y) + gamma(k)
k = Symbol("k", integer=True, positive=False)
assert lowergamma(k, y).rewrite(expint) == lowergamma(k, y)
assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
开发者ID:melsophos，项目名称:sympy，代码行数:35，代码来源:test_gamma_functions.py
示例4: test_meijer
def test_meijer():
raises(TypeError, lambda: meijerg(1, z))
raises(TypeError, lambda: meijerg(((1,), (2,)), (3,), (4,), z))
assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == \
meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z)
g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z)
assert g.an == Tuple(1, 2)
assert g.ap == Tuple(1, 2, 3, 4, 5)
assert g.aother == Tuple(3, 4, 5)
assert g.bm == Tuple(6, 7, 8, 9)
assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14)
assert g.bother == Tuple(10, 11, 12, 13, 14)
assert g.argument == z
assert g.nu == 75
assert g.delta == -1
assert g.is_commutative is True
assert meijerg([1, 2], [3], [4], [5], z).delta == S(1)/2
# just a few checks to make sure that all arguments go where they should
assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z)
assert tn(sqrt(pi)*meijerg(Tuple(), Tuple(),
Tuple(0), Tuple(S(1)/2), z**2/4), cos(z), z)
assert tn(meijerg(Tuple(1, 1), Tuple(), Tuple(1), Tuple(0), z),
log(1 + z), z)
# differentiation
g = meijerg((randcplx(),), (randcplx() + 2*I,), Tuple(),
(randcplx(), randcplx()), z)
assert td(g, z)
g = meijerg(Tuple(), (randcplx(),), Tuple(),
(randcplx(), randcplx()), z)
assert td(g, z)
g = meijerg(Tuple(), Tuple(), Tuple(randcplx()),
Tuple(randcplx(), randcplx()), z)
assert td(g, z)
a1, a2, b1, b2, c1, c2, d1, d2 = symbols('a1:3, b1:3, c1:3, d1:3')
assert meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == \
(meijerg((a1 - 1, a2), (b1, b2), (c1, c2), (d1, d2), z)
+ (a1 - 1)*meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z))/z
assert meijerg([z, z], [], [], [], z).diff(z) == \
Derivative(meijerg([z, z], [], [], [], z), z)
# meijerg is unbranched wrt parameters
from sympy import polar_lift as pl
assert meijerg([pl(a1)], [pl(a2)], [pl(b1)], [pl(b2)], pl(z)) == \
meijerg([a1], [a2], [b1], [b2], pl(z))
# integrand
from sympy.abc import a, b, c, d, s
assert meijerg([a], [b], [c], [d], z).integrand(s) == \
z**s*gamma(c - s)*gamma(-a + s + 1)/(gamma(b - s)*gamma(-d + s + 1))
开发者ID:B-Rich，项目名称:sympy，代码行数:58，代码来源:test_hyper.py
示例5: test_derivatives
def test_derivatives():
from sympy import Derivative
assert zeta(x, a).diff(x) == Derivative(zeta(x, a), x)
assert zeta(x, a).diff(a) == -x*zeta(x + 1, a)
assert lerchphi(z, s, a).diff(z) == (lerchphi(z, s-1, a) - a*lerchphi(z, s, a))/z
assert lerchphi(z, s, a).diff(a) == -s*lerchphi(z, s+1, a)
assert polylog(s, z).diff(z) == polylog(s - 1, z)/z
b = randcplx()
c = randcplx()
assert td(zeta(b, x), x)
assert td(polylog(b, z), z)
assert td(lerchphi(c, b, x), x)
assert td(lerchphi(x, b, c), x)
开发者ID:ALGHeArT，项目名称:sympy，代码行数:14，代码来源:test_zeta_functions.py
示例6: test_uppergamma
def test_uppergamma():
from sympy import meijerg
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y ** (x - 1) * exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == uppergamma(x, y) * log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi) * (1 - erf(sqrt(x)))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False), uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False), uppergamma(S.Half - 3, x), x)
开发者ID:hitej，项目名称:meta-core，代码行数:15，代码来源:test_gamma_functions.py
示例7: test_lowergamma
def test_lowergamma():
from sympy import meijerg, exp_polar, I
assert lowergamma(x, y).diff(y) == y**(x-1)*exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert lowergamma(x, y).diff(x) == \
gamma(x)*polygamma(0, x) - uppergamma(x, y)*log(y) \
+ meijerg([], [1, 1], [0, 0, x], [], y)
assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False),
lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False),
lowergamma(S.Half - 3, x), x)
assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
assert tn_branch(-3, lowergamma)
assert tn_branch(-4, lowergamma)
assert tn_branch(S(1)/3, lowergamma)
assert tn_branch(pi, lowergamma)
assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x)
assert lowergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I))
assert lowergamma(-2, exp_polar(5*pi*I)*x) == \
lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I
开发者ID:Kimay，项目名称:sympy，代码行数:28，代码来源:test_gamma_functions.py
示例8: test_K
def test_K():
assert K(0) == pi / 2
assert K(S(1) / 2) == 8 * pi ** (S(3) / 2) / gamma(-S(1) / 4) ** 2
assert K(1) == zoo
assert K(-1) == gamma(S(1) / 4) ** 2 / (4 * sqrt(2 * pi))
assert K(oo) == 0
assert K(-oo) == 0
assert K(I * oo) == 0
assert K(-I * oo) == 0
assert K(zoo) == 0
assert K(z).diff(z) == (E(z) - (1 - z) * K(z)) / (2 * z * (1 - z))
assert td(K(z), z)
zi = Symbol("z", real=False)
assert K(zi).conjugate() == K(zi.conjugate())
zr = Symbol("z", real=True, negative=True)
assert K(zr).conjugate() == K(zr)
assert K(z).rewrite(hyper) == (pi / 2) * hyper((S.Half, S.Half), (S.One,), z)
assert tn(K(z), (pi / 2) * hyper((S.Half, S.Half), (S.One,), z))
assert K(z).rewrite(meijerg) == meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z) / 2
assert tn(K(z), meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z) / 2)
assert K(z).series(
z
) == pi / 2 + pi * z / 8 + 9 * pi * z ** 2 / 128 + 25 * pi * z ** 3 / 512 + 1225 * pi * z ** 4 / 32768 + 3969 * pi * z ** 5 / 131072 + O(
z ** 6
)
开发者ID:Carreau，项目名称:sympy，代码行数:29，代码来源:test_elliptic_integrals.py
示例9: test_hyper
def test_hyper():
raises(TypeError, lambda: hyper(1, 2, z))
assert hyper((1, 2), (1,), z) == hyper(Tuple(1, 2), Tuple(1), z)
h = hyper((1, 2), (3, 4, 5), z)
assert h.ap == Tuple(1, 2)
assert h.bq == Tuple(3, 4, 5)
assert h.argument == z
assert h.is_commutative is True
# just a few checks to make sure that all arguments go where they should
assert tn(hyper(Tuple(), Tuple(), z), exp(z), z)
assert tn(z*hyper((1, 1), Tuple(2), -z), log(1 + z), z)
# differentiation
h = hyper(
(randcplx(), randcplx(), randcplx()), (randcplx(), randcplx()), z)
assert td(h, z)
a1, a2, b1, b2, b3 = symbols('a1:3, b1:4')
assert hyper((a1, a2), (b1, b2, b3), z).diff(z) == \
a1*a2/(b1*b2*b3) * hyper((a1 + 1, a2 + 1), (b1 + 1, b2 + 1, b3 + 1), z)
# differentiation wrt parameters is not supported
assert hyper([z], [], z).diff(z) == Derivative(hyper([z], [], z), z)
# hyper is unbranched wrt parameters
from sympy import polar_lift
assert hyper([polar_lift(z)], [polar_lift(k)], polar_lift(x)) == \
hyper([z], [k], polar_lift(x))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:31，代码来源:test_hyper.py
示例10: test_hyper
def test_hyper():
raises(TypeError, 'hyper(1, 2, z)')
assert hyper((1, 2),(1,), z) == hyper(Tuple(1, 2), Tuple(1), z)
h = hyper((1, 2), (3, 4, 5), z)
assert h.ap == Tuple(1, 2)
assert h.bq == Tuple(3, 4, 5)
assert h.argument == z
assert h.is_commutative is True
# just a few checks to make sure that all arguments go where they should
assert tn(hyper(Tuple(), Tuple(), z), exp(z), z)
assert tn(z*hyper((1, 1), Tuple(2), -z), log(1 + z), z)
# differentiation
h = hyper((randcplx(), randcplx(), randcplx()), (randcplx(), randcplx()), z)
assert td(h, z)
a1, a2, b1, b2, b3 = symbols('a1:3, b1:4')
assert hyper((a1, a2), (b1, b2, b3), z).diff(z) == \
a1*a2/(b1*b2*b3) * hyper((a1+1, a2+1), (b1+1, b2+1, b3+1), z)
# differentiation wrt parameters is not supported
raises(NotImplementedError, 'hyper((z,), (), z).diff(z)')
开发者ID:AlexandruFlorescu，项目名称:sympy，代码行数:25，代码来源:test_hyper.py
示例11: test_K
def test_K():
assert K(0) == pi/2
assert K(S(1)/2) == 8*pi**(S(3)/2)/gamma(-S(1)/4)**2
assert K(1) == zoo
assert K(-1) == gamma(S(1)/4)**2/(4*sqrt(2*pi))
assert K(oo) == 0
assert K(-oo) == 0
assert K(I*oo) == 0
assert K(-I*oo) == 0
assert K(zoo) == 0
assert K(z).diff(z) == (E(z) - (1 - z)*K(z))/(2*z*(1 - z))
assert td(K(z), z)
zi = Symbol('z', real=False)
assert K(zi).conjugate() == K(zi.conjugate())
zr = Symbol('z', real=True, negative=True)
assert K(zr).conjugate() == K(zr)
assert K(z).rewrite(hyper) == \
(pi/2)*hyper((S.Half, S.Half), (S.One,), z)
assert tn(K(z), (pi/2)*hyper((S.Half, S.Half), (S.One,), z))
assert K(z).rewrite(meijerg) == \
meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2
assert tn(K(z), meijerg(((S.Half, S.Half), []), ((S.Zero,), (S.Zero,)), -z)/2)
开发者ID:Maihj，项目名称:sympy，代码行数:25，代码来源:test_elliptic_integrals.py
示例12: test_meijer
def test_meijer():
raises(TypeError, 'meijerg(1, z)')
raises(TypeError, 'meijerg(((1,), (2,)), (3,), (4,), z)')
assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == \
meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z)
g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z)
assert g.an == Tuple(1, 2)
assert g.ap == Tuple(1, 2, 3, 4, 5)
assert g.aother == Tuple(3, 4, 5)
assert g.bm == Tuple(6, 7, 8, 9)
assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14)
assert g.bother == Tuple(10, 11, 12, 13, 14)
assert g.argument == z
assert g.nu == 75
assert g.delta == -1
assert g.is_commutative is True
assert meijerg([1, 2], [3], [4], [5], z).delta == S(1)/2
# just a few checks to make sure that all arguments go where they should
assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z)
assert tn(sqrt(pi)*meijerg(Tuple(), Tuple(),
Tuple(0), Tuple(S(1)/2), z**2/4), cos(z), z)
assert tn(meijerg(Tuple(1, 1),Tuple(), Tuple(1), Tuple(0), z),
log(1 + z), z)
# differentiation
g = meijerg((randcplx(),), (randcplx() + 2*I,), Tuple(),
(randcplx(), randcplx()), z)
assert td(g, z)
g = meijerg(Tuple(), (randcplx(),), Tuple(),
(randcplx(), randcplx()), z)
assert td(g, z)
g = meijerg(Tuple(), Tuple(), Tuple(randcplx()),
Tuple(randcplx(), randcplx()), z)
assert td(g, z)
a1, a2, b1, b2, c1, c2, d1, d2 = symbols('a1:3, b1:3, c1:3, d1:3')
assert meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == \
(meijerg((a1-1, a2), (b1, b2), (c1, c2), (d1, d2), z) \
+ (a1 - 1)*meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z))/z
raises(NotImplementedError, 'meijerg((z,), (), (), (), z).diff(z)')
开发者ID:AlexandruFlorescu，项目名称:sympy，代码行数:47，代码来源:test_hyper.py
示例13: test_bessel_rand
def test_bessel_rand():
assert td(besselj(randcplx(), z), z)
assert td(bessely(randcplx(), z), z)
assert td(besseli(randcplx(), z), z)
assert td(besselk(randcplx(), z), z)
assert td(hankel1(randcplx(), z), z)
assert td(hankel2(randcplx(), z), z)
assert td(jn(randcplx(), z), z)
assert td(yn(randcplx(), z), z)
开发者ID:Abhityagi16，项目名称:sympy，代码行数:9，代码来源:test_bessel.py
示例14: test_P
def test_P():
assert P(0, z, m) == F(z, m)
assert P(1, z, m) == F(z, m) + (sqrt(1 - m * sin(z) ** 2) * tan(z) - E(z, m)) / (1 - m)
assert P(n, i * pi / 2, m) == i * P(n, m)
assert P(n, z, 0) == atanh(sqrt(n - 1) * tan(z)) / sqrt(n - 1)
assert P(n, z, n) == F(z, n) - P(1, z, n) + tan(z) / sqrt(1 - n * sin(z) ** 2)
assert P(oo, z, m) == 0
assert P(-oo, z, m) == 0
assert P(n, z, oo) == 0
assert P(n, z, -oo) == 0
assert P(0, m) == K(m)
assert P(1, m) == zoo
assert P(n, 0) == pi / (2 * sqrt(1 - n))
assert P(2, 1) == -oo
assert P(-1, 1) == oo
assert P(n, n) == E(n) / (1 - n)
assert P(n, -z, m) == -P(n, z, m)
ni, mi = Symbol("n", real=False), Symbol("m", real=False)
assert P(ni, z, mi).conjugate() == P(ni.conjugate(), z.conjugate(), mi.conjugate())
nr, mr = Symbol("n", real=True, negative=True), Symbol("m", real=True, negative=True)
assert P(nr, z, mr).conjugate() == P(nr, z.conjugate(), mr)
assert P(n, m).conjugate() == P(n.conjugate(), m.conjugate())
assert P(n, z, m).diff(n) == (
E(z, m)
+ (m - n) * F(z, m) / n
+ (n ** 2 - m) * P(n, z, m) / n
- n * sqrt(1 - m * sin(z) ** 2) * sin(2 * z) / (2 * (1 - n * sin(z) ** 2))
) / (2 * (m - n) * (n - 1))
assert P(n, z, m).diff(z) == 1 / (sqrt(1 - m * sin(z) ** 2) * (1 - n * sin(z) ** 2))
assert P(n, z, m).diff(m) == (
E(z, m) / (m - 1) + P(n, z, m) - m * sin(2 * z) / (2 * (m - 1) * sqrt(1 - m * sin(z) ** 2))
) / (2 * (n - m))
assert P(n, m).diff(n) == (E(m) + (m - n) * K(m) / n + (n ** 2 - m) * P(n, m) / n) / (2 * (m - n) * (n - 1))
assert P(n, m).diff(m) == (E(m) / (m - 1) + P(n, m)) / (2 * (n - m))
rx, ry = randcplx(), randcplx()
assert td(P(n, rx, ry), n)
assert td(P(rx, z, ry), z)
assert td(P(rx, ry, m), m)
assert P(n, z, m).series(z) == z + z ** 3 * (m / 6 + n / 3) + z ** 5 * (
3 * m ** 2 / 40 + m * n / 10 - m / 30 + n ** 2 / 5 - n / 15
) + O(z ** 6)
开发者ID:Carreau，项目名称:sympy，代码行数:45，代码来源:test_elliptic_integrals.py
示例15: test_lowergamma
def test_lowergamma():
from sympy import meijerg, exp_polar, I, expint
assert lowergamma(x, 0) == 0
assert lowergamma(x, y).diff(y) == y**(x - 1)*exp(-y)
assert td(lowergamma(randcplx(), y), y)
assert td(lowergamma(x, randcplx()), x)
assert lowergamma(x, y).diff(x) == \
gamma(x)*polygamma(0, x) - uppergamma(x, y)*log(y) \
- meijerg([], [1, 1], [0, 0, x], [], y)
assert lowergamma(S.Half, x) == sqrt(pi)*erf(sqrt(x))
assert not lowergamma(S.Half - 3, x).has(lowergamma)
assert not lowergamma(S.Half + 3, x).has(lowergamma)
assert lowergamma(S.Half, x, evaluate=False).has(lowergamma)
assert tn(lowergamma(S.Half + 3, x, evaluate=False),
lowergamma(S.Half + 3, x), x)
assert tn(lowergamma(S.Half - 3, x, evaluate=False),
lowergamma(S.Half - 3, x), x)
assert tn_branch(-3, lowergamma)
assert tn_branch(-4, lowergamma)
assert tn_branch(S(1)/3, lowergamma)
assert tn_branch(pi, lowergamma)
assert lowergamma(3, exp_polar(4*pi*I)*x) == lowergamma(3, x)
assert lowergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*lowergamma(y, x*exp_polar(pi*I))
assert lowergamma(-2, exp_polar(5*pi*I)*x) == \
lowergamma(-2, x*exp_polar(I*pi)) + 2*pi*I
assert conjugate(lowergamma(x, y)) == lowergamma(conjugate(x), conjugate(y))
assert conjugate(lowergamma(x, 0)) == conjugate(lowergamma(x, 0))
assert conjugate(lowergamma(x, -oo)) == conjugate(lowergamma(x, -oo))
assert lowergamma(
x, y).rewrite(expint) == -y**x*expint(-x + 1, y) + gamma(x)
k = Symbol('k', integer=True)
assert lowergamma(
k, y).rewrite(expint) == -y**k*expint(-k + 1, y) + gamma(k)
k = Symbol('k', integer=True, positive=False)
assert lowergamma(k, y).rewrite(expint) == lowergamma(k, y)
assert lowergamma(x, y).rewrite(uppergamma) == gamma(x) - uppergamma(x, y)
assert lowergamma(70, 6) == factorial(69) - 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320 * exp(-6)
assert (lowergamma(S(77) / 2, 6) - lowergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
assert (lowergamma(-S(77) / 2, 6) - lowergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
开发者ID:carstimon，项目名称:sympy，代码行数:45，代码来源:test_gamma_functions.py
示例16: test_meijerg_derivative
def test_meijerg_derivative():
assert meijerg([], [1, 1], [0, 0, x], [], z).diff(x) == \
log(z)*meijerg([], [1, 1], [0, 0, x], [], z) \
+ 2*meijerg([], [1, 1, 1], [0, 0, x, 0], [], z)
y = randcplx()
a = 5 # mpmath chokes with non-real numbers, and Mod1 with floats
assert td(meijerg([x], [], [], [], y), x)
assert td(meijerg([x**2], [], [], [], y), x)
assert td(meijerg([], [x], [], [], y), x)
assert td(meijerg([], [], [x], [], y), x)
assert td(meijerg([], [], [], [x], y), x)
assert td(meijerg([x], [a], [a + 1], [], y), x)
assert td(meijerg([x], [a + 1], [a], [], y), x)
assert td(meijerg([x, a], [], [], [a + 1], y), x)
assert td(meijerg([x, a + 1], [], [], [a], y), x)
b = S(3)/2
assert td(meijerg([a + 2], [b], [b - 3, x], [a], y), x)
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:18，代码来源:test_hyper.py
示例17: test_F
def test_F():
assert F(z, 0) == z
assert F(0, m) == 0
assert F(pi*i/2, m) == i*K(m)
assert F(z, oo) == 0
assert F(z, -oo) == 0
assert F(-z, m) == -F(z, m)
assert F(z, m).diff(z) == 1/sqrt(1 - m*sin(z)**2)
assert F(z, m).diff(m) == E(z, m)/(2*m*(1 - m)) - F(z, m)/(2*m) - \
sin(2*z)/(4*(1 - m)*sqrt(1 - m*sin(z)**2))
r = randcplx()
assert td(F(z, r), z)
assert td(F(r, m), m)
mi = Symbol('m', real=False)
assert F(z, mi).conjugate() == F(z.conjugate(), mi.conjugate())
mr = Symbol('m', real=True, negative=True)
assert F(z, mr).conjugate() == F(z.conjugate(), mr)
开发者ID:Maihj，项目名称:sympy，代码行数:20，代码来源:test_elliptic_integrals.py
示例18: test_uppergamma
def test_uppergamma():
from sympy import meijerg, exp_polar, I, expint
assert uppergamma(4, 0) == 6
assert uppergamma(x, y).diff(y) == -y**(x - 1)*exp(-y)
assert td(uppergamma(randcplx(), y), y)
assert uppergamma(x, y).diff(x) == \
uppergamma(x, y)*log(y) + meijerg([], [1, 1], [0, 0, x], [], y)
assert td(uppergamma(x, randcplx()), x)
assert uppergamma(S.Half, x) == sqrt(pi)*erfc(sqrt(x))
assert not uppergamma(S.Half - 3, x).has(uppergamma)
assert not uppergamma(S.Half + 3, x).has(uppergamma)
assert uppergamma(S.Half, x, evaluate=False).has(uppergamma)
assert tn(uppergamma(S.Half + 3, x, evaluate=False),
uppergamma(S.Half + 3, x), x)
assert tn(uppergamma(S.Half - 3, x, evaluate=False),
uppergamma(S.Half - 3, x), x)
assert tn_branch(-3, uppergamma)
assert tn_branch(-4, uppergamma)
assert tn_branch(S(1)/3, uppergamma)
assert tn_branch(pi, uppergamma)
assert uppergamma(3, exp_polar(4*pi*I)*x) == uppergamma(3, x)
assert uppergamma(y, exp_polar(5*pi*I)*x) == \
exp(4*I*pi*y)*uppergamma(y, x*exp_polar(pi*I)) + \
gamma(y)*(1 - exp(4*pi*I*y))
assert uppergamma(-2, exp_polar(5*pi*I)*x) == \
uppergamma(-2, x*exp_polar(I*pi)) - 2*pi*I
assert uppergamma(-2, x) == expint(3, x)/x**2
assert conjugate(uppergamma(x, y)) == uppergamma(conjugate(x), conjugate(y))
assert conjugate(uppergamma(x, 0)) == gamma(conjugate(x))
assert conjugate(uppergamma(x, -oo)) == conjugate(uppergamma(x, -oo))
assert uppergamma(x, y).rewrite(expint) == y**x*expint(-x + 1, y)
assert uppergamma(x, y).rewrite(lowergamma) == gamma(x) - lowergamma(x, y)
assert uppergamma(70, 6) == 69035724522603011058660187038367026272747334489677105069435923032634389419656200387949342530805432320*exp(-6)
assert (uppergamma(S(77) / 2, 6) - uppergamma(S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
assert (uppergamma(-S(77) / 2, 6) - uppergamma(-S(77) / 2, 6, evaluate=False)).evalf() < 1e-16
开发者ID:carstimon，项目名称:sympy，代码行数:41，代码来源:test_gamma_functions.py
示例19: test_E
def test_E():
assert E(z, 0) == z
assert E(0, m) == 0
assert E(i * pi / 2, m) == i * E(m)
assert E(z, oo) == zoo
assert E(z, -oo) == zoo
assert E(0) == pi / 2
assert E(1) == 1
assert E(oo) == I * oo
assert E(-oo) == oo
assert E(zoo) == zoo
assert E(-z, m) == -E(z, m)
assert E(z, m).diff(z) == sqrt(1 - m * sin(z) ** 2)
assert E(z, m).diff(m) == (E(z, m) - F(z, m)) / (2 * m)
assert E(z).diff(z) == (E(z) - K(z)) / (2 * z)
r = randcplx()
assert td(E(r, m), m)
assert td(E(z, r), z)
assert td(E(z), z)
mi = Symbol("m", real=False)
assert E(z, mi).conjugate() == E(z.conjugate(), mi.conjugate())
assert E(mi).conjugate() == E(mi.conjugate())
mr = Symbol("m", real=True, negative=True)
assert E(z, mr).conjugate() == E(z.conjugate(), mr)
assert E(mr).conjugate() == E(mr)
assert E(z).rewrite(hyper) == (pi / 2) * hyper((-S.Half, S.Half), (S.One,), z)
assert tn(E(z), (pi / 2) * hyper((-S.Half, S.Half), (S.One,), z))
assert E(z).rewrite(meijerg) == -meijerg(((S.Half, S(3) / 2), []), ((S.Zero,), (S.Zero,)), -z) / 4
assert tn(E(z), -meijerg(((S.Half, S(3) / 2), []), ((S.Zero,), (S.Zero,)), -z) / 4)
assert E(z, m).series(z) == z + z ** 5 * (-m ** 2 / 40 + m / 30) - m * z ** 3 / 6 + O(z ** 6)
assert E(z).series(
z
) == pi / 2 - pi * z / 8 - 3 * pi * z ** 2 / 128 - 5 * pi * z ** 3 / 512 - 175 * pi * z ** 4 / 32768 - 441 * pi * z ** 5 / 131072 + O(
z ** 6
)
开发者ID:Carreau，项目名称:sympy，代码行数:40，代码来源:test_elliptic_integrals.py
示例20: test_F
def test_F():
assert F(z, 0) == z
assert F(0, m) == 0
assert F(pi * i / 2, m) == i * K(m)
assert F(z, oo) == 0
assert F(z, -oo) == 0
assert F(-z, m) == -F(z, m)
assert F(z, m).diff(z) == 1 / sqrt(1 - m * sin(z) ** 2)
assert F(z, m).diff(m) == E(z, m) / (2 * m * (1 - m)) - F(z, m) / (2 * m) - sin(2 * z) / (
4 * (1 - m) * sqrt(1 - m * sin(z) ** 2)
)
r = randcplx()
assert td(F(z, r), z)
assert td(F(r, m), m)
mi = Symbol("m", real=False)
assert F(z, mi).conjugate() == F(z.conjugate(), mi.conjugate())
mr = Symbol("m", real=True, negative=True)
assert F(z, mr).conjugate() == F(z.conjugate(), mr)
assert F(z, m).series(z) == z + z ** 5 * (3 * m ** 2 / 40 - m / 30) + m * z ** 3 / 6 + O(z ** 6)
开发者ID:Carreau，项目名称:sympy，代码行数:23，代码来源:test_elliptic_integrals.py
注：本文中的sympy.utilities.randtest.td函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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