本文整理汇总了Python中sympy.sech函数的典型用法代码示例。如果您正苦于以下问题：Python sech函数的具体用法？Python sech怎么用？Python sech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sech函数的11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_sech_rewrite
def test_sech_rewrite():
x = Symbol("x")
assert sech(x).rewrite(exp) == 1 / (exp(x) / 2 + exp(-x) / 2) == sech(x).rewrite("tractable")
assert sech(x).rewrite(sinh) == I / sinh(x + I * pi / 2)
tanh_half = tanh(S.Half * x) ** 2
assert sech(x).rewrite(tanh) == (1 - tanh_half) / (1 + tanh_half)
coth_half = coth(S.Half * x) ** 2
assert sech(x).rewrite(coth) == (coth_half - 1) / (coth_half + 1)
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_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5: 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6: test_rewrite_trigh
def test_rewrite_trigh():
# if this import passes then the test below should also pass
from sympy import sech
assert solveset_real(sinh(x) + sech(x), x) == FiniteSet(
2*atanh(-S.Half + sqrt(5)/2 - sqrt(-2*sqrt(5) + 2)/2),
2*atanh(-S.Half + sqrt(5)/2 + sqrt(-2*sqrt(5) + 2)/2),
2*atanh(-sqrt(5)/2 - S.Half + sqrt(2 + 2*sqrt(5))/2),
2*atanh(-sqrt(2 + 2*sqrt(5))/2 - sqrt(5)/2 - S.Half))
开发者ID:nickle8424，项目名称:sympy，代码行数:8，代码来源:test_solveset.py
示例7: 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8: test_asech
def test_asech():
x = Symbol('x')
assert asech(-x) == asech(-x)
# values at fixed points
assert asech(1) == 0
assert asech(-1) == pi*I
assert asech(0) == oo
assert asech(2) == I*pi/3
assert asech(-2) == 2*I*pi / 3
# at infinites
assert asech(oo) == I*pi/2
assert asech(-oo) == I*pi/2
assert asech(zoo) == nan
assert asech(I) == log(1 + sqrt(2)) - I*pi/2
assert asech(-I) == log(1 + sqrt(2)) + I*pi/2
assert asech(sqrt(2) - sqrt(6)) == 11*I*pi / 12
assert asech(sqrt(2 - 2/sqrt(5))) == I*pi / 10
assert asech(-sqrt(2 - 2/sqrt(5))) == 9*I*pi / 10
assert asech(2 / sqrt(2 + sqrt(2))) == I*pi / 8
assert asech(-2 / sqrt(2 + sqrt(2))) == 7*I*pi / 8
assert asech(sqrt(5) - 1) == I*pi / 5
assert asech(1 - sqrt(5)) == 4*I*pi / 5
assert asech(-sqrt(2*(2 + sqrt(2)))) == 5*I*pi / 8
# properties
# asech(x) == acosh(1/x)
assert asech(sqrt(2)) == acosh(1/sqrt(2))
assert asech(2/sqrt(3)) == acosh(sqrt(3)/2)
assert asech(2/sqrt(2 + sqrt(2))) == acosh(sqrt(2 + sqrt(2))/2)
assert asech(S(2)) == acosh(1/S(2))
# asech(x) == I*acos(1/x)
# (Note: the exact formula is asech(x) == +/- I*acos(1/x))
assert asech(-sqrt(2)) == I*acos(-1/sqrt(2))
assert asech(-2/sqrt(3)) == I*acos(-sqrt(3)/2)
assert asech(-S(2)) == I*acos(-S.Half)
assert asech(-2/sqrt(2)) == I*acos(-sqrt(2)/2)
# sech(asech(x)) / x == 1
assert expand_mul(sech(asech(sqrt(6) - sqrt(2))) / (sqrt(6) - sqrt(2))) == 1
assert expand_mul(sech(asech(sqrt(6) + sqrt(2))) / (sqrt(6) + sqrt(2))) == 1
assert (sech(asech(sqrt(2 + 2/sqrt(5)))) / (sqrt(2 + 2/sqrt(5)))).simplify() == 1
assert (sech(asech(-sqrt(2 + 2/sqrt(5)))) / (-sqrt(2 + 2/sqrt(5)))).simplify() == 1
assert (sech(asech(sqrt(2*(2 + sqrt(2))))) / (sqrt(2*(2 + sqrt(2))))).simplify() == 1
assert expand_mul(sech(asech((1 + sqrt(5)))) / ((1 + sqrt(5)))) == 1
assert expand_mul(sech(asech((-1 - sqrt(5)))) / ((-1 - sqrt(5)))) == 1
assert expand_mul(sech(asech((-sqrt(6) - sqrt(2)))) / ((-sqrt(6) - sqrt(2)))) == 1
# numerical evaluation
assert str(asech(5*I).n(6)) == '0.19869 - 1.5708*I'
assert str(asech(-5*I).n(6)) == '0.19869 + 1.5708*I'
开发者ID:certik，项目名称:sympy，代码行数:55，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_sech_series
def test_sech_series():
x = Symbol('x')
assert sech(x).series(x, 0, 10) == \
1 - x**2/2 + 5*x**4/24 - 61*x**6/720 + 277*x**8/8064 + O(x**10)
开发者ID:certik，项目名称:sympy，代码行数:4，代码来源:test_hyperbolic.py
示例11: test_sech
def test_sech():
x, y = symbols('x, y')
k = Symbol('k', integer=True)
n = Symbol('n', positive=True)
assert sech(nan) == nan
assert sech(zoo) == nan
assert sech(oo) == 0
assert sech(-oo) == 0
assert sech(0) == 1
assert sech(-1) == sech(1)
assert sech(-x) == sech(x)
assert sech(pi*I) == sec(pi)
assert sech(-pi*I) == sec(pi)
assert sech(-2**1024 * E) == sech(2**1024 * E)
assert sech(pi*I/2) == zoo
assert sech(-pi*I/2) == zoo
assert sech((-3*10**73 + 1)*pi*I/2) == zoo
assert sech((7*10**103 + 1)*pi*I/2) == zoo
assert sech(pi*I) == -1
assert sech(-pi*I) == -1
assert sech(5*pi*I) == -1
assert sech(8*pi*I) == 1
assert sech(pi*I/3) == 2
assert sech(-2*pi*I/3) == -2
assert sech(pi*I/4) == sqrt(2)
assert sech(-pi*I/4) == sqrt(2)
assert sech(5*pi*I/4) == -sqrt(2)
assert sech(-5*pi*I/4) == -sqrt(2)
assert sech(pi*I/6) == 2/sqrt(3)
assert sech(-pi*I/6) == 2/sqrt(3)
assert sech(7*pi*I/6) == -2/sqrt(3)
assert sech(-5*pi*I/6) == -2/sqrt(3)
assert sech(pi*I/105) == 1/cos(pi/105)
assert sech(-pi*I/105) == 1/cos(pi/105)
assert sech(x*I) == 1/cos(x)
assert sech(k*pi*I) == 1/cos(k*pi)
assert sech(17*k*pi*I) == 1/cos(17*k*pi)
assert sech(n).is_real is True
开发者ID:certik，项目名称:sympy，代码行数:54，代码来源:test_hyperbolic.py
注：本文中的sympy.sech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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