本文整理汇总了Python中sympy.sinh函数的典型用法代码示例。如果您正苦于以下问题：Python sinh函数的具体用法？Python sinh怎么用？Python sinh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sinh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: Lorentz_Tranformation_in_Geometric_Algebra
def Lorentz_Tranformation_in_Geometric_Algebra():
Print_Function()
(alpha, beta, gamma) = symbols('alpha beta gamma')
(x, t, xp, tp) = symbols("x t x' t'")
(g0, g1) = MV.setup('gamma*t|x', metric='[1,-1]')
from sympy import sinh, cosh
R = cosh(alpha/2) + sinh(alpha/2)*(g0 ^ g1)
X = t*g0 + x*g1
Xp = tp*g0 + xp*g1
print('R =', R)
print(r"#%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} = t'\bm{\gamma'_{t}}+x'\bm{\gamma'_{x}} = R\lp t'\bm{\gamma_{t}}+x'\bm{\gamma_{x}}\rp R^{\dagger}")
Xpp = R*Xp*R.rev()
Xpp = Xpp.collect([xp, tp])
Xpp = Xpp.subs({2*sinh(alpha/2)*cosh(alpha/2): sinh(alpha), sinh(alpha/2)**2 + cosh(alpha/2)**2: cosh(alpha)})
print(r"%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} =", Xpp)
Xpp = Xpp.subs({sinh(alpha): gamma*beta, cosh(alpha): gamma})
print(r'%\f{\sinh}{\alpha} = \gamma\beta')
print(r'%\f{\cosh}{\alpha} = \gamma')
print(r"%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} =", Xpp.collect(gamma))
return
开发者ID:AALEKH，项目名称:sympy，代码行数:26，代码来源:physics_check_latex.py
示例2: test_issue_1572_1364_1368
def test_issue_1572_1364_1368():
assert solve((sqrt(x**2 - 1) - 2)) in ([sqrt(5), -sqrt(5)],
[-sqrt(5), sqrt(5)])
assert set(solve((2**exp(y**2/x) + 2)/(x**2 + 15), y)) == set([
-sqrt(x)*sqrt(-log(log(2)) + log(log(2) + I*pi)),
sqrt(x)*sqrt(-log(log(2)) + log(log(2) + I*pi))])
C1, C2 = symbols('C1 C2')
f = Function('f')
assert solve(C1 + C2/x**2 - exp(-f(x)), f(x)) == [log(x**2/(C1*x**2 + C2))]
a = Symbol('a')
E = S.Exp1
assert solve(1 - log(a + 4*x**2), x) in (
[-sqrt(-a + E)/2, sqrt(-a + E)/2],
[sqrt(-a + E)/2, -sqrt(-a + E)/2]
)
assert solve(log(a**(-3) - x**2)/a, x) in (
[-sqrt(-1 + a**(-3)), sqrt(-1 + a**(-3))],
[sqrt(-1 + a**(-3)), -sqrt(-1 + a**(-3))],)
assert solve(1 - log(a + 4*x**2), x) in (
[-sqrt(-a + E)/2, sqrt(-a + E)/2],
[sqrt(-a + E)/2, -sqrt(-a + E)/2],)
assert set(solve((
a**2 + 1) * (sin(a*x) + cos(a*x)), x)) == set([-pi/(4*a), 3*pi/(4*a)])
assert solve(3 - (sinh(a*x) + cosh(a*x)), x) == [2*atanh(S.Half)/a]
assert set(solve(3 - (sinh(a*x) + cosh(a*x)**2), x)) == \
set([
2*atanh(-1 + sqrt(2))/a,
2*atanh(S(1)/2 + sqrt(5)/2)/a,
2*atanh(-sqrt(2) - 1)/a,
2*atanh(-sqrt(5)/2 + S(1)/2)/a
])
assert solve(atan(x) - 1) == [tan(1)]
开发者ID:Maihj，项目名称:sympy，代码行数:33，代码来源:test_solvers.py
示例3: Lorentz_Tranformation_in_Geog_Algebra
def Lorentz_Tranformation_in_Geog_Algebra():
Print_Function()
(alpha,beta,gamma) = symbols('alpha beta gamma')
(x,t,xp,tp) = symbols("x t x' t'",real=True)
(st2d,g0,g1) = Ga.build('gamma*t|x',g=[1,-1])
from sympy import sinh,cosh
R = cosh(alpha/2)+sinh(alpha/2)*(g0^g1)
X = t*g0+x*g1
Xp = tp*g0+xp*g1
print 'R =',R
print r"#%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} = t'\bm{\gamma'_{t}}+x'\bm{\gamma'_{x}} = R\lp t'\bm{\gamma_{t}}+x'\bm{\gamma_{x}}\rp R^{\dagger}"
Xpp = R*Xp*R.rev()
Xpp = Xpp.collect()
Xpp = Xpp.trigsimp()
print r"%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} =",Xpp
Xpp = Xpp.subs({sinh(alpha):gamma*beta,cosh(alpha):gamma})
print r'%\f{\sinh}{\alpha} = \gamma\beta'
print r'%\f{\cosh}{\alpha} = \gamma'
print r"%t\bm{\gamma_{t}}+x\bm{\gamma_{x}} =",Xpp.collect()
return
开发者ID:Ignat99，项目名称:galgebra，代码行数:26，代码来源:physics_check_latex.py
示例4: test_ode_solutions
def test_ode_solutions():
# only a few examples here, the rest will be tested in the actual dsolve tests
assert constant_renumber(constantsimp(C1*exp(2*x) + exp(x)*(C2 + C3), [C1, C2, C3])) == \
constant_renumber((C1*exp(x) + C2*exp(2*x)))
assert constant_renumber(
constantsimp(Eq(f(x), I*C1*sinh(x/3) + C2*cosh(x/3)), [C1, C2])
) == constant_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)))
assert constant_renumber(constantsimp(Eq(f(x), acos((-C1)/cos(x))), [C1])) == \
Eq(f(x), acos(C1/cos(x)))
assert constant_renumber(
constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), [C1])
) == Eq(log(C1*f(x)) + 2*exp(x/f(x)), 0)
assert constant_renumber(constantsimp(Eq(log(x*sqrt(2)*sqrt(1/x)*sqrt(f(x))
/C1) + x**2/(2*f(x)**2), 0), [C1])) == \
Eq(log(C1*sqrt(x)*sqrt(f(x))) + x**2/(2*f(x)**2), 0)
assert constant_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) -
cos(f(x)/x)*exp(-f(x)/x)/2, 0), [C1])) == \
Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x)*
exp(-f(x)/x)/2, 0)
assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2),
(u2, _a, x/f(x))) + log(f(x)/C1), 0), [C1])) == \
Eq(-Integral(-1/(u2*sqrt(1 - u2**2)), (u2, _a, x/f(x))) +
log(C1*f(x)), 0)
assert [constantsimp(i, [C1]) for i in [Eq(f(x), sqrt(-C1*x + x**2)), Eq(f(x), -sqrt(-C1*x + x**2))]] == \
[Eq(f(x), sqrt(x*(C1 + x))), Eq(f(x), -sqrt(x*(C1 + x)))]
开发者ID:asmeurer，项目名称:sympy，代码行数:25，代码来源:test_constantsimp.py
示例5: 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)
for func in (sinh, cosh, tanh, coth):
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), y) == cosh(x)
assert i(sin(x*y), y) == sinh(x)/I
assert i(tan(x*y), y) == tanh(x)/I
assert i(cot(x*y), y) == coth(x)*I
assert i(sec(x*y), y) == 1/cosh(x)
assert i(csc(x*y), y) == I/sinh(x)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:26，代码来源:test_fu.py
示例6: 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7: test_ode_solutions
def test_ode_solutions():
# only a few examples here, the rest will be tested in the actual dsolve tests
assert ode_renumber(constantsimp(C1*exp(2*x)+exp(x)*(C2+C3), x, 3), 'C', 1, 3) == \
ode_renumber(C1*exp(x)+C2*exp(2*x), 'C', 1, 2)
assert ode_renumber(constantsimp(Eq(f(x),I*C1*sinh(x/3) + C2*cosh(x/3)), x, 2),
'C', 1, 2) == ode_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)), 'C', 1, 2)
assert ode_renumber(constantsimp(Eq(f(x),acos((-C1)/cos(x))), x, 1), 'C', 1, 1) == \
Eq(f(x),acos(C1/cos(x)))
assert ode_renumber(constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), x, 1),
'C', 1, 1) == Eq(log(C1*f(x)) + 2*exp(x/f(x)), 0)
assert ode_renumber(constantsimp(Eq(log(x*2**Rational(1,2)*(1/x)**Rational(1,2)*f(x)\
**Rational(1,2)/C1) + x**2/(2*f(x)**2), 0), x, 1), 'C', 1, 1) == \
Eq(log(C1*x*(1/x)**Rational(1,2)*f(x)**Rational(1,2)) + x**2/(2*f(x)**2), 0)
assert ode_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) - \
cos(f(x)/x)*exp(-f(x)/x)/2, 0), x, 1), 'C', 1, 1) == \
Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x)*exp(-f(x)/x)/2, 0)
u2 = Symbol('u2')
_a = Symbol('_a')
assert ode_renumber(constantsimp(Eq(-Integral(-1/((1 - u2**2)**Rational(1,2)*u2), \
(u2, _a, x/f(x))) + log(f(x)/C1), 0), x, 1), 'C', 1, 1) == \
Eq(-Integral(-1/(u2*(1 - u2**2)**Rational(1,2)), (u2, _a, x/f(x))) + \
log(C1*f(x)), 0)
assert map(lambda i: ode_renumber(constantsimp(i, x, 1), 'C', 1, 1),
[Eq(f(x), (-C1*x + x**2)**Rational(1,2)), Eq(f(x), -(-C1*x +
x**2)**Rational(1,2))]) == [Eq(f(x), (C1*x + x**2)**Rational(1,2)),
Eq(f(x), -(C1*x + x**2)**Rational(1,2))]
开发者ID:KevinGoodsell，项目名称:sympy，代码行数:26，代码来源:test_constantsimp.py
示例8: test_issue_8368
def test_issue_8368():
assert integrate(exp(-s*x)*cosh(x), (x, 0, oo)) == \
Piecewise(
( pi*Piecewise(
( -s/(pi*(-s**2 + 1)),
Abs(s**2) < 1),
( 1/(pi*s*(1 - 1/s**2)),
Abs(s**(-2)) < 1),
( meijerg(
((S(1)/2,), (0, 0)),
((0, S(1)/2), (0,)),
polar_lift(s)**2),
True)
),
And(
Abs(periodic_argument(polar_lift(s)**2, oo)) < pi,
cos(Abs(periodic_argument(polar_lift(s)**2, oo))/2)*sqrt(Abs(s**2)) - 1 > 0,
Ne(s**2, 1))
),
(
Integral(exp(-s*x)*cosh(x), (x, 0, oo)),
True))
assert integrate(exp(-s*x)*sinh(x), (x, 0, oo)) == \
Piecewise(
( -1/(s + 1)/2 - 1/(-s + 1)/2,
And(
Ne(1/s, 1),
Abs(periodic_argument(s, oo)) < pi/2,
Abs(periodic_argument(s, oo)) <= pi/2,
cos(Abs(periodic_argument(s, oo)))*Abs(s) - 1 > 0)),
( Integral(exp(-s*x)*sinh(x), (x, 0, oo)),
True))
开发者ID:baoqchau，项目名称:sympy，代码行数:32，代码来源:test_integrals.py
示例9: test_coth_rewrite
def test_coth_rewrite():
x = Symbol('x')
assert coth(x).rewrite(exp) == (exp(x) + exp(-x))/(exp(x) - exp(-x)) \
== coth(x).rewrite('tractable')
assert coth(x).rewrite(sinh) == -I*sinh(I*pi/2 - x)/sinh(x)
assert coth(x).rewrite(cosh) == -I*cosh(x)/cosh(I*pi/2 - x)
assert coth(x).rewrite(tanh) == 1/tanh(x)
开发者ID:Bercio，项目名称:sympy，代码行数:7，代码来源:test_hyperbolic.py
示例10: test_ode_solutions
def test_ode_solutions():
# only a few examples here, the rest will be tested in the actual dsolve tests
assert constant_renumber(constantsimp(C1*exp(2*x)+exp(x)*(C2+C3), x, 3), 'C', 1, 3) == \
constant_renumber(C1*exp(x)+C2*exp(2*x), 'C', 1, 2)
assert constant_renumber(constantsimp(Eq(f(x),I*C1*sinh(x/3) + C2*cosh(x/3)), x, 2),
'C', 1, 2) == constant_renumber(Eq(f(x), C1*sinh(x/3) + C2*cosh(x/3)), 'C', 1, 2)
assert constant_renumber(constantsimp(Eq(f(x),acos((-C1)/cos(x))), x, 1), 'C', 1, 1) == \
Eq(f(x),acos(C1/cos(x)))
assert constant_renumber(constantsimp(Eq(log(f(x)/C1) + 2*exp(x/f(x)), 0), x, 1),
'C', 1, 1) == Eq(log(C1*f(x)) + 2*exp(x/f(x)), 0)
assert constant_renumber(constantsimp(Eq(log(x*sqrt(2)*sqrt(1/x)*sqrt(f(x))\
/C1) + x**2/(2*f(x)**2), 0), x, 1), 'C', 1, 1) == \
Eq(log(C1*x*sqrt(1/x)*sqrt(f(x))) + x**2/(2*f(x)**2), 0)
assert constant_renumber(constantsimp(Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(x/C1) - \
cos(f(x)/x)*exp(-f(x)/x)/2, 0), x, 1), 'C', 1, 1) == \
Eq(-exp(-f(x)/x)*sin(f(x)/x)/2 + log(C1*x) - cos(f(x)/x)*exp(-f(x)/x)/2, 0)
u2 = Symbol('u2')
_a = Symbol('_a')
assert constant_renumber(constantsimp(Eq(-Integral(-1/(sqrt(1 - u2**2)*u2), \
(u2, _a, x/f(x))) + log(f(x)/C1), 0), x, 1), 'C', 1, 1) == \
Eq(-Integral(-1/(u2*sqrt(1 - u2**2)), (u2, _a, x/f(x))) + \
log(C1*f(x)), 0)
assert [constant_renumber(constantsimp(i, x, 1), 'C', 1, 1) for i in
[Eq(f(x), sqrt(-C1*x + x**2)), Eq(f(x), -sqrt(-C1*x +
x**2))]] == [Eq(f(x), sqrt(C1*x + x**2)),
Eq(f(x), -sqrt(C1*x + x**2))]
开发者ID:ALGHeArT，项目名称:sympy，代码行数:26，代码来源:test_constantsimp.py
示例11: test_exp_rewrite
def test_exp_rewrite():
assert exp(x).rewrite(sin) == sinh(x) + cosh(x)
assert exp(x*I).rewrite(cos) == cos(x) + I*sin(x)
assert exp(1).rewrite(cos) == sinh(1) + cosh(1)
assert exp(1).rewrite(sin) == sinh(1) + cosh(1)
assert exp(1).rewrite(sin) == sinh(1) + cosh(1)
assert exp(x).rewrite(tanh) == (1 + tanh(x/2))/(1 - tanh(x/2))
开发者ID:aprasanna，项目名称:sympy，代码行数:7，代码来源:test_exponential.py
示例12: _w
def _w(self, section):
q0 = self.q0
a = self.a
aa = self.alpha
bb = self.beta
A11 = self.laminate.abd[0,0]
B11 = self.laminate.abd[0,3]
D11 = self.laminate.abd[3,3]
n0 = self.n0
x = self._x
if ((section is 'left') or (section is 'right')):
res = ((1/(4.*n0**2))*q0*
(-4*(1/sympy.cosh((1/2.)*a*bb))*
sympy.sinh((1/2.)*(a-2*(-x))*bb)*
sympy.sinh((1/2.)*a*aa*bb)*D11+a*(a-2*(-x))*aa*n0))
if section is 'right':
res = res.subs(self._x, -self._x)
elif section is 'mid':
res = ((1/(8.*n0**2))*q0*
(8*(-1+
sympy.cosh(x*bb)*sympy.cosh((1/2.)*a*(-1+aa)*bb)*
(1/sympy.cosh((1/2.)*a*bb)))*D11-
(4*x**2+a**2*(-2+aa)*aa)*n0))
return res
开发者ID:tbhartman，项目名称:eng，代码行数:25，代码来源:clpt.py
示例13: test_manualintegrate_special
def test_manualintegrate_special():
f, F = 4*exp(-x**2/3), 2*sqrt(3)*sqrt(pi)*erf(sqrt(3)*x/3)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = 3*exp(4*x**2), 3*sqrt(pi)*erfi(2*x)/4
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = x**(S(1)/3)*exp(-x/8), -16*uppergamma(S(4)/3, x/8)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = exp(2*x)/x, Ei(2*x)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = exp(1 + 2*x - x**2), sqrt(pi)*exp(2)*erf(x - 1)/2
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f = sin(x**2 + 4*x + 1)
F = (sqrt(2)*sqrt(pi)*(-sin(3)*fresnelc(sqrt(2)*(2*x + 4)/(2*sqrt(pi))) +
cos(3)*fresnels(sqrt(2)*(2*x + 4)/(2*sqrt(pi))))/2)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = cos(4*x**2), sqrt(2)*sqrt(pi)*fresnelc(2*sqrt(2)*x/sqrt(pi))/4
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = sin(3*x + 2)/x, sin(2)*Ci(3*x) + cos(2)*Si(3*x)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = sinh(3*x - 2)/x, -sinh(2)*Chi(3*x) + cosh(2)*Shi(3*x)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = 5*cos(2*x - 3)/x, 5*cos(3)*Ci(2*x) + 5*sin(3)*Si(2*x)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = cosh(x/2)/x, Chi(x/2)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = cos(x**2)/x, Ci(x**2)/2
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = 1/log(2*x + 1), li(2*x + 1)/2
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = polylog(2, 5*x)/x, polylog(3, 5*x)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = 5/sqrt(3 - 2*sin(x)**2), 5*sqrt(3)*elliptic_f(x, S(2)/3)/3
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
f, F = sqrt(4 + 9*sin(x)**2), 2*elliptic_e(x, -S(9)/4)
assert manualintegrate(f, x) == F and F.diff(x).equals(f)
开发者ID:gamechanger98，项目名称:sympy，代码行数:35，代码来源:test_manual.py
示例14: test_tan_rewrite
def test_tan_rewrite():
neg_exp, pos_exp = exp(-x*I), exp(x*I)
assert tan(x).rewrite(exp) == I*(neg_exp - pos_exp)/(neg_exp + pos_exp)
assert tan(x).rewrite(sin) == 2*sin(x)**2/sin(2*x)
assert tan(x).rewrite(cos) == -cos(x + S.Pi/2)/cos(x)
assert tan(x).rewrite(cot) == 1/cot(x)
assert tan(sinh(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sinh(3)).n()
assert tan(cosh(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cosh(3)).n()
assert tan(tanh(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tanh(3)).n()
assert tan(coth(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, coth(3)).n()
assert tan(sin(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, sin(3)).n()
assert tan(cos(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cos(3)).n()
assert tan(tan(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, tan(3)).n()
assert tan(cot(x)).rewrite(
exp).subs(x, 3).n() == tan(x).rewrite(exp).subs(x, cot(3)).n()
assert tan(log(x)).rewrite(Pow) == I*(x**-I - x**I)/(x**-I + x**I)
assert 0 == (cos(pi/15)*tan(pi/15) - sin(pi/15)).rewrite(pow)
assert tan(pi/19).rewrite(pow) == tan(pi/19)
assert tan(8*pi/19).rewrite(sqrt) == tan(8*pi/19)
开发者ID:mattpap，项目名称:sympy，代码行数:26，代码来源:test_trigonometric.py
示例15: test_cosine_transform
def test_cosine_transform():
from sympy import sinh, cosh, Si, Ci
t = symbols("t")
w = symbols("w")
a = symbols("a")
f = Function("f")
# Test unevaluated form
assert cosine_transform(f(t), t, w) == CosineTransform(f(t), t, w)
assert inverse_cosine_transform(f(w), w, t) == InverseCosineTransform(f(w), w, t)
assert cosine_transform(1/sqrt(t), t, w) == 1/sqrt(w)
assert inverse_cosine_transform(1/sqrt(w), w, t) == 1/sqrt(t)
assert cosine_transform(1/(a**2+t**2), t, w) == sqrt(2)*sqrt(pi)*(-sinh(a*w) + cosh(a*w))/(2*a)
assert cosine_transform(t**(-a), t, w) == 2**(-a + S(1)/2)*w**(a - 1)*gamma((-a + 1)/2)/gamma(a/2)
assert inverse_cosine_transform(2**(-a + S(1)/2)*w**(a - 1)*gamma(-a/2 + S(1)/2)/gamma(a/2), w, t) == t**(-a)
assert cosine_transform(exp(-a*t), t, w) == sqrt(2)*a/(sqrt(pi)*(a**2 + w**2))
assert inverse_cosine_transform(sqrt(2)*a/(sqrt(pi)*(a**2 + w**2)), w, t) == -sinh(a*t) + cosh(a*t)
assert cosine_transform(exp(-a*sqrt(t))*cos(a*sqrt(t)), t, w) == a*(-sinh(a**2/(2*w)) + cosh(a**2/(2*w)))/(2*w**(S(3)/2))
assert cosine_transform(1/(a+t), t, w) == -sqrt(2)*((2*Si(a*w) - pi)*sin(a*w) + 2*cos(a*w)*Ci(a*w))/(2*sqrt(pi))
assert inverse_cosine_transform(sqrt(2)*meijerg(((S(1)/2, 0), ()), ((S(1)/2, 0, 0), (S(1)/2,)), a**2*w**2/4)/(2*pi), w, t) == 1/(a + t)
assert cosine_transform(1/sqrt(a**2+t**2), t, w) == sqrt(2)*meijerg(((S(1)/2,), ()), ((0, 0), (S(1)/2,)), a**2*w**2/4)/(2*sqrt(pi))
assert inverse_cosine_transform(sqrt(2)*meijerg(((S(1)/2,), ()), ((0, 0), (S(1)/2,)), a**2*w**2/4)/(2*sqrt(pi)), w, t) == 1/(t*sqrt(a**2/t**2 + 1))
开发者ID:rishabh11，项目名称:sympy，代码行数:30，代码来源:test_transforms.py
示例16: test_sinh_rewrite
def test_sinh_rewrite():
x = Symbol('x')
assert sinh(x).rewrite(exp) == (exp(x)-exp(-x))/2
assert sinh(x).rewrite(cosh) == -I*cosh(x+I*pi/2)
tanh_half = tanh(S.Half*x)
assert sinh(x).rewrite(tanh) == 2*tanh_half/(1-tanh_half**2)
coth_half = coth(S.Half*x)
assert sinh(x).rewrite(coth) == 2*coth_half/(coth_half**2-1)
开发者ID:Aang，项目名称:sympy，代码行数:8，代码来源:test_hyperbolic.py
示例17: test_heurisch_hyperbolic
def test_heurisch_hyperbolic():
assert heurisch(sinh(x), x) == cosh(x)
assert heurisch(cosh(x), x) == sinh(x)
assert heurisch(x*sinh(x), x) == x*cosh(x) - sinh(x)
assert heurisch(x*cosh(x), x) == x*sinh(x) - cosh(x)
assert heurisch(x*asinh(x/2), x) == x**2*asinh(x/2)/2 + asinh(x/2) - x*sqrt(4+x**2)/4
开发者ID:ALGHeArT，项目名称:sympy，代码行数:8，代码来源:test_risch.py
示例18: test_sec
def test_sec():
x = symbols('x', real=True)
z = symbols('z')
assert sec.nargs == FiniteSet(1)
assert sec(0) == 1
assert sec(pi) == -1
assert sec(pi/2) == zoo
assert sec(-pi/2) == zoo
assert sec(pi/6) == 2*sqrt(3)/3
assert sec(pi/3) == 2
assert sec(5*pi/2) == zoo
assert sec(9*pi/7) == -sec(2*pi/7)
assert sec(I) == 1/cosh(1)
assert sec(x*I) == 1/cosh(x)
assert sec(-x) == sec(x)
assert sec(x).rewrite(exp) == 1/(exp(I*x)/2 + exp(-I*x)/2)
assert sec(x).rewrite(sin) == sec(x)
assert sec(x).rewrite(cos) == 1/cos(x)
assert sec(x).rewrite(tan) == (tan(x/2)**2 + 1)/(-tan(x/2)**2 + 1)
assert sec(x).rewrite(pow) == sec(x)
assert sec(x).rewrite(sqrt) == sec(x)
assert sec(z).conjugate() == sec(conjugate(z))
assert (sec(z).as_real_imag() ==
(cos(re(z))*cosh(im(z))/(sin(re(z))**2*sinh(im(z))**2 +
cos(re(z))**2*cosh(im(z))**2),
sin(re(z))*sinh(im(z))/(sin(re(z))**2*sinh(im(z))**2 +
cos(re(z))**2*cosh(im(z))**2)))
assert sec(x).expand(trig=True) == 1/cos(x)
assert sec(2*x).expand(trig=True) == 1/(2*cos(x)**2 - 1)
assert sec(x).is_real == True
assert sec(z).is_real == None
assert sec(x).as_leading_term() == sec(x)
assert sec(0).is_bounded == True
assert sec(x).is_bounded == None
assert sec(pi/2).is_bounded == False
assert series(sec(x), x, x0=0, n=6) == 1 + x**2/2 + 5*x**4/24 + O(x**6)
# https://github.com/sympy/sympy/issues/7166
assert series(sqrt(sec(x))) == 1 + x**2/4 + 7*x**4/96 + O(x**6)
assert sec(x).diff(x) == tan(x)*sec(x)
# Taylor Term checks
assert sec(z).taylor_term(4, z) == 5*z**4/24
assert sec(z).taylor_term(6, z) == 61*z**6/720
assert sec(z).taylor_term(5, z) == 0
开发者ID:waytai，项目名称:sympy，代码行数:56，代码来源:test_trigonometric.py
示例19: test_csc
def test_csc():
x = symbols('x', real=True)
z = symbols('z')
# https://github.com/sympy/sympy/issues/6707
cosecant = csc('x')
alternate = 1/sin('x')
assert cosecant.equals(alternate) == True
assert alternate.equals(cosecant) == True
assert csc.nargs == FiniteSet(1)
assert csc(0) == zoo
assert csc(pi) == zoo
assert csc(pi/2) == 1
assert csc(-pi/2) == -1
assert csc(pi/6) == 2
assert csc(pi/3) == 2*sqrt(3)/3
assert csc(5*pi/2) == 1
assert csc(9*pi/7) == -csc(2*pi/7)
assert csc(I) == -I/sinh(1)
assert csc(x*I) == -I/sinh(x)
assert csc(-x) == -csc(x)
assert csc(x).rewrite(exp) == 2*I/(exp(I*x) - exp(-I*x))
assert csc(x).rewrite(sin) == 1/sin(x)
assert csc(x).rewrite(cos) == csc(x)
assert csc(x).rewrite(tan) == (tan(x/2)**2 + 1)/(2*tan(x/2))
assert csc(z).conjugate() == csc(conjugate(z))
assert (csc(z).as_real_imag() ==
(sin(re(z))*cosh(im(z))/(sin(re(z))**2*cosh(im(z))**2 +
cos(re(z))**2*sinh(im(z))**2),
-cos(re(z))*sinh(im(z))/(sin(re(z))**2*cosh(im(z))**2 +
cos(re(z))**2*sinh(im(z))**2)))
assert csc(x).expand(trig=True) == 1/sin(x)
assert csc(2*x).expand(trig=True) == 1/(2*sin(x)*cos(x))
assert csc(x).is_real == True
assert csc(z).is_real == None
assert csc(x).as_leading_term() == csc(x)
assert csc(0).is_bounded == False
assert csc(x).is_bounded == None
assert csc(pi/2).is_bounded == True
assert series(csc(x), x, x0=pi/2, n=6) == \
1 + (x - pi/2)**2/2 + 5*(x - pi/2)**4/24 + O((x - pi/2)**6, (x, pi/2))
assert series(csc(x), x, x0=0, n=6) == \
1/x + x/6 + 7*x**3/360 + 31*x**5/15120 + O(x**6)
assert csc(x).diff(x) == -cot(x)*csc(x)
开发者ID:Eskatrem，项目名称:sympy，代码行数:56，代码来源:test_trigonometric.py
示例20: 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 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:Bercio，项目名称:sympy，代码行数:10，代码来源:test_hyperbolic.py
注：本文中的sympy.sinh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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