本文整理汇总了Python中sympy.Symbol.conjugate方法的典型用法代码示例。如果您正苦于以下问题：Python Symbol.conjugate方法的具体用法？Python Symbol.conjugate怎么用？Python Symbol.conjugate使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sympy.Symbol的用法示例。
在下文中一共展示了Symbol.conjugate方法的7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，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_K
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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
)示例2: test_E
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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)示例3: test_K
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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)示例4: test_E
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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
)示例5: test_P
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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)示例6: test_F
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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)示例7: test_F
# 需要导入模块: from sympy import Symbol [as 别名]
# 或者: from sympy.Symbol import conjugate [as 别名]
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)