本文整理汇总了Python中sympy.csch函数的典型用法代码示例。如果您正苦于以下问题：Python csch函数的具体用法？Python csch怎么用？Python csch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csch函数的10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_simplifications
def test_simplifications():
x = Symbol('x')
assert sinh(asinh(x)) == x
assert sinh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1)
assert sinh(atanh(x)) == x/sqrt(1 - x**2)
assert sinh(acoth(x)) == 1/(sqrt(x - 1) * sqrt(x + 1))
assert cosh(asinh(x)) == sqrt(1 + x**2)
assert cosh(acosh(x)) == x
assert cosh(atanh(x)) == 1/sqrt(1 - x**2)
assert cosh(acoth(x)) == x/(sqrt(x - 1) * sqrt(x + 1))
assert tanh(asinh(x)) == x/sqrt(1 + x**2)
assert tanh(acosh(x)) == sqrt(x - 1) * sqrt(x + 1) / x
assert tanh(atanh(x)) == x
assert tanh(acoth(x)) == 1/x
assert coth(asinh(x)) == sqrt(1 + x**2)/x
assert coth(acosh(x)) == x/(sqrt(x - 1) * sqrt(x + 1))
assert coth(atanh(x)) == 1/x
assert coth(acoth(x)) == x
assert csch(asinh(x)) == 1/x
assert csch(acosh(x)) == 1/(sqrt(x - 1) * sqrt(x + 1))
assert csch(atanh(x)) == sqrt(1 - x**2)/x
assert csch(acoth(x)) == sqrt(x - 1) * sqrt(x + 1)
assert sech(asinh(x)) == 1/sqrt(1 + x**2)
assert sech(acosh(x)) == 1/x
assert sech(atanh(x)) == sqrt(1 - x**2)
assert sech(acoth(x)) == sqrt(x - 1) * sqrt(x + 1)/x
开发者ID:certik，项目名称:sympy，代码行数:31，代码来源:test_hyperbolic.py
示例2: test_hyper_as_trig
def test_hyper_as_trig():
from sympy.simplify.fu import _osborne as o, _osbornei as i, TR12
eq = sinh(x)**2 + cosh(x)**2
t, f = hyper_as_trig(eq)
assert f(fu(t)) == cosh(2*x)
e, f = hyper_as_trig(tanh(x + y))
assert f(TR12(e)) == (tanh(x) + tanh(y))/(tanh(x)*tanh(y) + 1)
d = Dummy()
assert o(sinh(x), d) == I*sin(x*d)
assert o(tanh(x), d) == I*tan(x*d)
assert o(coth(x), d) == cot(x*d)/I
assert o(cosh(x), d) == cos(x*d)
assert o(sech(x), d) == sec(x*d)
assert o(csch(x), d) == csc(x*d)/I
for func in (sinh, cosh, tanh, coth, sech, csch):
h = func(pi)
assert i(o(h, d), d) == h
# /!\ the _osborne functions are not meant to work
# in the o(i(trig, d), d) direction so we just check
# that they work as they are supposed to work
assert i(cos(x*y + z), y) == cosh(x + z*I)
assert i(sin(x*y + z), y) == sinh(x + z*I)/I
assert i(tan(x*y + z), y) == tanh(x + z*I)/I
assert i(cot(x*y + z), y) == coth(x + z*I)*I
assert i(sec(x*y + z), y) == sech(x + z*I)
assert i(csc(x*y + z), y) == csch(x + z*I)*I
开发者ID:baoqchau，项目名称:sympy，代码行数:28，代码来源:test_fu.py
示例3: test_csch_rewrite
def test_csch_rewrite():
x = Symbol("x")
assert csch(x).rewrite(exp) == 1 / (exp(x) / 2 - exp(-x) / 2) == csch(x).rewrite("tractable")
assert csch(x).rewrite(cosh) == I / cosh(x + I * pi / 2)
tanh_half = tanh(S.Half * x)
assert csch(x).rewrite(tanh) == (1 - tanh_half ** 2) / (2 * tanh_half)
coth_half = coth(S.Half * x)
assert csch(x).rewrite(coth) == (coth_half ** 2 - 1) / (2 * coth_half)
开发者ID:ashutoshsaboo，项目名称:sympy，代码行数:8，代码来源:test_hyperbolic.py
示例4: test_acsch
def test_acsch():
x = Symbol('x')
assert acsch(-x) == acsch(-x)
assert acsch(x) == -acsch(-x)
# values at fixed points
assert acsch(1) == log(1 + sqrt(2))
assert acsch(-1) == - log(1 + sqrt(2))
assert acsch(0) == zoo
assert acsch(2) == log((1+sqrt(5))/2)
assert acsch(-2) == - log((1+sqrt(5))/2)
assert acsch(I) == - I*pi/2
assert acsch(-I) == I*pi/2
assert acsch(-I*(sqrt(6) + sqrt(2))) == I*pi / 12
assert acsch(I*(sqrt(2) + sqrt(6))) == -I*pi / 12
assert acsch(-I*(1 + sqrt(5))) == I*pi / 10
assert acsch(I*(1 + sqrt(5))) == -I*pi / 10
assert acsch(-I*2 / sqrt(2 - sqrt(2))) == I*pi / 8
assert acsch(I*2 / sqrt(2 - sqrt(2))) == -I*pi / 8
assert acsch(-I*2) == I*pi / 6
assert acsch(I*2) == -I*pi / 6
assert acsch(-I*sqrt(2 + 2/sqrt(5))) == I*pi / 5
assert acsch(I*sqrt(2 + 2/sqrt(5))) == -I*pi / 5
assert acsch(-I*sqrt(2)) == I*pi / 4
assert acsch(I*sqrt(2)) == -I*pi / 4
assert acsch(-I*(sqrt(5)-1)) == 3*I*pi / 10
assert acsch(I*(sqrt(5)-1)) == -3*I*pi / 10
assert acsch(-I*2 / sqrt(3)) == I*pi / 3
assert acsch(I*2 / sqrt(3)) == -I*pi / 3
assert acsch(-I*2 / sqrt(2 + sqrt(2))) == 3*I*pi / 8
assert acsch(I*2 / sqrt(2 + sqrt(2))) == -3*I*pi / 8
assert acsch(-I*sqrt(2 - 2/sqrt(5))) == 2*I*pi / 5
assert acsch(I*sqrt(2 - 2/sqrt(5))) == -2*I*pi / 5
assert acsch(-I*(sqrt(6) - sqrt(2))) == 5*I*pi / 12
assert acsch(I*(sqrt(6) - sqrt(2))) == -5*I*pi / 12
# properties
# acsch(x) == asinh(1/x)
assert acsch(-I*sqrt(2)) == asinh(I/sqrt(2))
assert acsch(-I*2 / sqrt(3)) == asinh(I*sqrt(3) / 2)
# acsch(x) == -I*asin(I/x)
assert acsch(-I*sqrt(2)) == -I*asin(-1/sqrt(2))
assert acsch(-I*2 / sqrt(3)) == -I*asin(-sqrt(3)/2)
# csch(acsch(x)) / x == 1
assert expand_mul(csch(acsch(-I*(sqrt(6) + sqrt(2)))) / (-I*(sqrt(6) + sqrt(2)))) == 1
assert expand_mul(csch(acsch(I*(1 + sqrt(5)))) / ((I*(1 + sqrt(5))))) == 1
assert (csch(acsch(I*sqrt(2 - 2/sqrt(5)))) / (I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
assert (csch(acsch(-I*sqrt(2 - 2/sqrt(5)))) / (-I*sqrt(2 - 2/sqrt(5)))).simplify() == 1
# numerical evaluation
assert str(acsch(5*I+1).n(6)) == '0.0391819 - 0.193363*I'
assert str(acsch(-5*I+1).n(6)) == '0.0391819 + 0.193363*I'
开发者ID:certik，项目名称:sympy，代码行数:56，代码来源:test_hyperbolic.py
示例5: test_derivs
def test_derivs():
x = Symbol('x')
assert coth(x).diff(x) == -sinh(x)**(-2)
assert sinh(x).diff(x) == cosh(x)
assert cosh(x).diff(x) == sinh(x)
assert tanh(x).diff(x) == -tanh(x)**2 + 1
assert csch(x).diff(x) == -coth(x)*csch(x)
assert sech(x).diff(x) == -tanh(x)*sech(x)
assert acoth(x).diff(x) == 1/(-x**2 + 1)
assert asinh(x).diff(x) == 1/sqrt(x**2 + 1)
assert acosh(x).diff(x) == 1/sqrt(x**2 - 1)
assert atanh(x).diff(x) == 1/(-x**2 + 1)
开发者ID:JoshLipsmeyer，项目名称:sympy，代码行数:12，代码来源:test_hyperbolic.py
示例6: test_sign_assumptions
def test_sign_assumptions():
p = Symbol('p', positive=True)
n = Symbol('n', negative=True)
assert sinh(n).is_negative is True
assert sinh(p).is_positive is True
assert cosh(n).is_positive is True
assert cosh(p).is_positive is True
assert tanh(n).is_negative is True
assert tanh(p).is_positive is True
assert csch(n).is_negative is True
assert csch(p).is_positive is True
assert sech(n).is_positive is True
assert sech(p).is_positive is True
assert coth(n).is_negative is True
assert coth(p).is_positive is True
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:15，代码来源:test_hyperbolic.py
示例7: test_csch_series
def test_csch_series():
x = Symbol("x")
assert csch(x).series(
x, 0, 10
) == 1 / x - x / 6 + 7 * x ** 3 / 360 - 31 * x ** 5 / 15120 + 127 * x ** 7 / 604800 - 73 * x ** 9 / 3421440 + O(
x ** 10
)
开发者ID:ashutoshsaboo，项目名称:sympy，代码行数:7，代码来源:test_hyperbolic.py
示例8: test_real_assumptions
def test_real_assumptions():
z = Symbol('z', real=False)
assert sinh(z).is_real is None
assert cosh(z).is_real is None
assert tanh(z).is_real is None
assert sech(z).is_real is None
assert csch(z).is_real is None
assert coth(z).is_real is None
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:8，代码来源:test_hyperbolic.py
示例9: test_complex
def test_complex():
a, b = symbols('a,b', real=True)
z = a + b*I
for func in [sinh, cosh, tanh, coth, sech, csch]:
assert func(z).conjugate() == func(a - b*I)
for deep in [True, False]:
assert sinh(z).expand(
complex=True, deep=deep) == sinh(a)*cos(b) + I*cosh(a)*sin(b)
assert cosh(z).expand(
complex=True, deep=deep) == cosh(a)*cos(b) + I*sinh(a)*sin(b)
assert tanh(z).expand(complex=True, deep=deep) == sinh(a)*cosh(
a)/(cos(b)**2 + sinh(a)**2) + I*sin(b)*cos(b)/(cos(b)**2 + sinh(a)**2)
assert coth(z).expand(complex=True, deep=deep) == sinh(a)*cosh(
a)/(sin(b)**2 + sinh(a)**2) - I*sin(b)*cos(b)/(sin(b)**2 + sinh(a)**2)
assert csch(z).expand(complex=True, deep=deep) == cos(b) * sinh(a) / (sin(b)**2\
*cosh(a)**2 + cos(b)**2 * sinh(a)**2) - I*sin(b) * cosh(a) / (sin(b)**2\
*cosh(a)**2 + cos(b)**2 * sinh(a)**2)
assert sech(z).expand(complex=True, deep=deep) == cos(b) * cosh(a) / (sin(b)**2\
*sinh(a)**2 + cos(b)**2 * cosh(a)**2) - I*sin(b) * sinh(a) / (sin(b)**2\
*sinh(a)**2 + cos(b)**2 * cosh(a)**2)
开发者ID:certik，项目名称:sympy，代码行数:20，代码来源:test_hyperbolic.py
示例10: test_csch
def test_csch():
x, y = symbols('x,y')
k = Symbol('k', integer=True)
n = Symbol('n', positive=True)
assert csch(nan) == nan
assert csch(zoo) == nan
assert csch(oo) == 0
assert csch(-oo) == 0
assert csch(0) == zoo
assert csch(-1) == -csch(1)
assert csch(-x) == -csch(x)
assert csch(-pi) == -csch(pi)
assert csch(-2**1024 * E) == -csch(2**1024 * E)
assert csch(pi*I) == zoo
assert csch(-pi*I) == zoo
assert csch(2*pi*I) == zoo
assert csch(-2*pi*I) == zoo
assert csch(-3*10**73*pi*I) == zoo
assert csch(7*10**103*pi*I) == zoo
assert csch(pi*I/2) == -I
assert csch(-pi*I/2) == I
assert csch(5*pi*I/2) == -I
assert csch(7*pi*I/2) == I
assert csch(pi*I/3) == -2/sqrt(3)*I
assert csch(-2*pi*I/3) == 2/sqrt(3)*I
assert csch(pi*I/4) == -sqrt(2)*I
assert csch(-pi*I/4) == sqrt(2)*I
assert csch(7*pi*I/4) == sqrt(2)*I
assert csch(-3*pi*I/4) == sqrt(2)*I
assert csch(pi*I/6) == -2*I
assert csch(-pi*I/6) == 2*I
assert csch(7*pi*I/6) == 2*I
assert csch(-7*pi*I/6) == -2*I
assert csch(-5*pi*I/6) == 2*I
assert csch(pi*I/105) == -1/sin(pi/105)*I
assert csch(-pi*I/105) == 1/sin(pi/105)*I
assert csch(x*I) == -1/sin(x)*I
assert csch(k*pi*I) == zoo
assert csch(17*k*pi*I) == zoo
assert csch(k*pi*I/2) == -1/sin(k*pi/2)*I
assert csch(n).is_real is True
开发者ID:certik，项目名称:sympy，代码行数:57，代码来源:test_hyperbolic.py
注：本文中的sympy.csch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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