本文整理汇总了Python中sympy.atanh函数的典型用法代码示例。如果您正苦于以下问题：Python atanh函数的具体用法？Python atanh怎么用？Python atanh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。
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示例1: test_issue_10847
def test_issue_10847():
assert manualintegrate(x**2 / (x**2 - c), x) == c*Piecewise((atan(x/sqrt(-c))/sqrt(-c), -c > 0), \
(-acoth(x/sqrt(c))/sqrt(c), And(-c < 0, x**2 > c)), \
(-atanh(x/sqrt(c))/sqrt(c), And(-c < 0, x**2 < c))) + x
assert manualintegrate(sqrt(x - y) * log(z / x), x) == 4*y**2*Piecewise((atan(sqrt(x - y)/sqrt(y))/sqrt(y), y > 0), \
(-acoth(sqrt(x - y)/sqrt(-y))/sqrt(-y), \
And(x - y > -y, y < 0)), \
(-atanh(sqrt(x - y)/sqrt(-y))/sqrt(-y), \
And(x - y < -y, y < 0)))/3 \
- 4*y*sqrt(x - y)/3 + 2*(x - y)**(S(3)/2)*log(z/x)/3 \
+ 4*(x - y)**(S(3)/2)/9
assert manualintegrate(sqrt(x) * log(x), x) == 2*x**(S(3)/2)*log(x)/3 - 4*x**(S(3)/2)/9
assert manualintegrate(sqrt(a*x + b) / x, x) == -2*b*Piecewise((-atan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b), -b > 0), \
(acoth(sqrt(a*x + b)/sqrt(b))/sqrt(b), And(-b < 0, a*x + b > b)), \
(atanh(sqrt(a*x + b)/sqrt(b))/sqrt(b), And(-b < 0, a*x + b < b))) \
+ 2*sqrt(a*x + b)
assert expand(manualintegrate(sqrt(a*x + b) / (x + c), x)) == -2*a*c*Piecewise((atan(sqrt(a*x + b)/sqrt(a*c - b))/sqrt(a*c - b), \
a*c - b > 0), (-acoth(sqrt(a*x + b)/sqrt(-a*c + b))/sqrt(-a*c + b), And(a*c - b < 0, a*x + b > -a*c + b)), \
(-atanh(sqrt(a*x + b)/sqrt(-a*c + b))/sqrt(-a*c + b), And(a*c - b < 0, a*x + b < -a*c + b))) \
+ 2*b*Piecewise((atan(sqrt(a*x + b)/sqrt(a*c - b))/sqrt(a*c - b), a*c - b > 0), \
(-acoth(sqrt(a*x + b)/sqrt(-a*c + b))/sqrt(-a*c + b), And(a*c - b < 0, a*x + b > -a*c + b)), \
(-atanh(sqrt(a*x + b)/sqrt(-a*c + b))/sqrt(-a*c + b), And(a*c - b < 0, a*x + b < -a*c + b))) + 2*sqrt(a*x + b)
assert manualintegrate((4*x**4 + 4*x**3 + 16*x**2 + 12*x + 8) \
/ (x**6 + 2*x**5 + 3*x**4 + 4*x**3 + 3*x**2 + 2*x + 1), x) == \
2*x/(x**2 + 1) + 3*atan(x) - 1/(x**2 + 1) - 3/(x + 1)
assert manualintegrate(sqrt(2*x + 3) / (x + 1), x) == 2*sqrt(2*x + 3) - log(sqrt(2*x + 3) + 1) + log(sqrt(2*x + 3) - 1)
assert manualintegrate(sqrt(2*x + 3) / 2 * x, x) == (2*x + 3)**(S(5)/2)/20 - (2*x + 3)**(S(3)/2)/4
assert manualintegrate(x**Rational(3,2) * log(x), x) == 2*x**Rational(5,2)*log(x)/5 - 4*x**Rational(5,2)/25
assert manualintegrate(x**(-3) * log(x), x) == -log(x)/(2*x**2) - 1/(4*x**2)
assert manualintegrate(log(y)/(y**2*(1 - 1/y)), y) == \
log(y)*log(-1 + 1/y) - Integral(log(-1 + 1/y)/y, y)
开发者ID:gamechanger98，项目名称:sympy，代码行数:34，代码来源:test_manual.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: 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4: 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 cosh(asinh(x)) == sqrt(1 + x ** 2)
assert cosh(acosh(x)) == x
assert cosh(atanh(x)) == 1 / sqrt(1 - x ** 2)
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
开发者ID:rkern，项目名称:sympy-rkern，代码行数:13，代码来源:test_hyperbolic.py
示例5: test_issue_6746
def test_issue_6746():
y = Symbol('y')
n = Symbol('n')
assert manualintegrate(y**x, x) == \
Piecewise((x, Eq(log(y), 0)), (y**x/log(y), True))
assert manualintegrate(y**(n*x), x) == \
Piecewise(
(x, Eq(n, 0)),
(Piecewise(
(n*x, Eq(log(y), 0)),
(y**(n*x)/log(y), True))/n, True))
assert manualintegrate(exp(n*x), x) == \
Piecewise((x, Eq(n, 0)), (exp(n*x)/n, True))
y = Symbol('y', positive=True)
assert manualintegrate((y + 1)**x, x) == (y + 1)**x/log(y + 1)
y = Symbol('y', zero=True)
assert manualintegrate((y + 1)**x, x) == x
y = Symbol('y')
n = Symbol('n', nonzero=True)
assert manualintegrate(y**(n*x), x) == \
Piecewise((n*x, Eq(log(y), 0)), (y**(n*x)/log(y), True))/n
y = Symbol('y', positive=True)
assert manualintegrate((y + 1)**(n*x), x) == \
(y + 1)**(n*x)/(n*log(y + 1))
a = Symbol('a', negative=True)
assert manualintegrate(1 / (a + b*x**2), x) == \
Piecewise((atan(x/sqrt(a/b))/(b*sqrt(a/b)), a/b > 0), \
(-acoth(x/sqrt(-a/b))/(b*sqrt(-a/b)), And(a/b < 0, x**2 > -a/b)), \
(-atanh(x/sqrt(-a/b))/(b*sqrt(-a/b)), And(a/b < 0, x**2 < -a/b)))
开发者ID:sixpearls，项目名称:sympy，代码行数:30，代码来源:test_manual.py
示例6: 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
示例7: test_hyperbolic
def test_hyperbolic():
x = Symbol("x")
assert sinh(x).nseries(x, 0, 6) == x + x**3/6 + x**5/120 + O(x**6)
assert cosh(x).nseries(x, 0, 5) == 1 + x**2/2 + x**4/24 + O(x**5)
assert tanh(x).nseries(x, 0, 6) == x - x**3/3 + 2*x**5/15 + O(x**6)
assert coth(x).nseries(x, 0, 6) == 1/x - x**3/45 + x/3 + 2*x**5/945 + O(x**6)
assert asinh(x).nseries(x, 0, 6) == x - x**3/6 + 3*x**5/40 + O(x**6)
assert acosh(x).nseries(x, 0, 6) == pi*I/2 - I*x - 3*I*x**5/40 - I*x**3/6 + O(x**6)
assert atanh(x).nseries(x, 0, 6) == x + x**3/3 + x**5/5 + O(x**6)
assert acoth(x).nseries(x, 0, 6) == x + x**3/3 + x**5/5 + pi*I/2 + O(x**6)
开发者ID:jcockayne，项目名称:sympy-rkern，代码行数:10，代码来源:test_nseries.py
示例8: test_inverses
def test_inverses():
x = Symbol('x')
assert sinh(x).inverse() == asinh
raises(AttributeError, lambda: cosh(x).inverse())
assert tanh(x).inverse() == atanh
assert coth(x).inverse() == acoth
assert asinh(x).inverse() == sinh
assert acosh(x).inverse() == cosh
assert atanh(x).inverse() == tanh
assert acoth(x).inverse() == coth
开发者ID:Bercio，项目名称:sympy，代码行数:10，代码来源:test_hyperbolic.py
示例9: test_conv12b
def test_conv12b():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
assert sympify(sympy.sinh(x/3)) == sinh(Symbol("x") / 3)
assert sympify(sympy.cosh(x/3)) == cosh(Symbol("x") / 3)
assert sympify(sympy.tanh(x/3)) == tanh(Symbol("x") / 3)
assert sympify(sympy.coth(x/3)) == coth(Symbol("x") / 3)
assert sympify(sympy.asinh(x/3)) == asinh(Symbol("x") / 3)
assert sympify(sympy.acosh(x/3)) == acosh(Symbol("x") / 3)
assert sympify(sympy.atanh(x/3)) == atanh(Symbol("x") / 3)
assert sympify(sympy.acoth(x/3)) == acoth(Symbol("x") / 3)
开发者ID:cbehan，项目名称:symengine.py，代码行数:11，代码来源:test_sympy_conv.py
示例10: 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11: test_hyperexpand_bases
def test_hyperexpand_bases():
assert hyperexpand(hyper([2], [a], z)) == \
a + z**(-a + 1)*(-a**2 + 3*a + z*(a - 1) - 2)*exp(z)*lowergamma(a - 1, z) - 1
# TODO [a+1, a-S.Half], [2*a]
assert hyperexpand(hyper([1, 2], [3], z)) == -2/z - 2*log(-z + 1)/z**2
assert hyperexpand(hyper([S.Half, 2], [S(3)/2], z)) == \
-1/(2*z - 2) + atanh(sqrt(z))/sqrt(z)/2
assert hyperexpand(hyper([S(1)/2, S(1)/2], [S(5)/2], z)) == \
(-3*z + 3)/4/(z*sqrt(-z + 1)) \
+ (6*z - 3)*asin(sqrt(z))/(4*z**(S(3)/2))
assert hyperexpand(hyper([1, 2], [S(3)/2], z)) == -1/(2*z - 2) \
- asin(sqrt(z))/(sqrt(z)*(2*z - 2)*sqrt(-z + 1))
assert hyperexpand(hyper([-S.Half - 1, 1, 2], [S.Half, 3], z)) == \
sqrt(z)*(6*z/7 - S(6)/5)*atanh(sqrt(z)) \
+ (-30*z**2 + 32*z - 6)/35/z - 6*log(-z + 1)/(35*z**2)
assert hyperexpand(hyper([1+S.Half, 1, 1], [2, 2], z)) == \
-4*log(sqrt(-z + 1)/2 + S(1)/2)/z
# TODO hyperexpand(hyper([a], [2*a + 1], z))
# TODO [S.Half, a], [S(3)/2, a+1]
assert hyperexpand(hyper([2], [b, 1], z)) == \
z**(-b/2 + S(1)/2)*besseli(b - 1, 2*sqrt(z))*gamma(b) \
+ z**(-b/2 + 1)*besseli(b, 2*sqrt(z))*gamma(b)
开发者ID:BDGLunde，项目名称:sympy，代码行数:22，代码来源:test_hyperexpand.py
示例12: test_atanh
def test_atanh():
# TODO please write more tests -- see #652
# From http://functions.wolfram.com/ElementaryFunctions/ArcTanh/03/01/
# at specific points
x = Symbol('x')
#at specific points
assert atanh(0) == 0
assert atanh(I) == I*pi/4
assert atanh(-I) == -I*pi/4
assert atanh(1) == oo
assert atanh(-1) == -oo
# at infinites
assert atanh(I*oo) == I*pi/2
assert atanh(-I*oo) == -I*pi/2
#properties
assert atanh(-x) == -atanh(x)
开发者ID:Aang，项目名称:sympy，代码行数:19，代码来源:test_hyperbolic.py
示例13: 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)
assert asech(x).diff(x) == -1/(x*sqrt(1 - x**2))
assert acsch(x).diff(x) == -1/(x**2*sqrt(1 + x**(-2)))
开发者ID:certik，项目名称:sympy，代码行数:14，代码来源:test_hyperbolic.py
示例14: test_atan
def test_atan():
assert atan(nan) == nan
assert atan(oo) == pi/2
assert atan(-oo) == -pi/2
assert atan(0) == 0
assert atan(1) == pi/4
assert atan(sqrt(3)) == pi/3
assert atan(oo) == pi/2
assert atan(x).diff(x) == 1/(1 + x**2)
assert atan(r).is_real is True
assert atan(-2*I) == -I*atanh(2)
开发者ID:mattpap，项目名称:sympy，代码行数:15，代码来源:test_trigonometric.py
示例15: 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16: test_atan
def test_atan():
x = Symbol('x')
r = Symbol('r', real=True)
assert atan(nan) == nan
assert atan(oo) == pi/2
assert atan(-oo) == -pi/2
assert atan(0) == 0
assert atan(1) == pi/4
assert atan(sqrt(3)) == pi/3
assert atan(oo) == pi/2
assert atan(x).diff(x) == 1/(1+x**2)
assert atan(r).is_real == True
assert atan(-2*I) == -I*atanh(2)
开发者ID:haz，项目名称:sympy，代码行数:19，代码来源:test_trigonometric.py
示例17: test_atan
def test_atan():
assert atan(nan) == nan
assert atan.nargs == FiniteSet(1)
assert atan(oo) == pi/2
assert atan(-oo) == -pi/2
assert atan(0) == 0
assert atan(1) == pi/4
assert atan(sqrt(3)) == pi/3
assert atan(oo) == pi/2
assert atan(x).diff(x) == 1/(1 + x**2)
assert atan(r).is_real is True
assert atan(-2*I) == -I*atanh(2)
assert atan(p).is_positive is True
assert atan(n).is_positive is False
assert atan(x).is_positive is None
开发者ID:AdrianPotter，项目名称:sympy，代码行数:19，代码来源:test_trigonometric.py
示例18: test_conv12
def test_conv12():
x = Symbol("x")
y = Symbol("y")
assert sinh(x/3) == sinh(sympy.Symbol("x") / 3)
assert cosh(x/3) == cosh(sympy.Symbol("x") / 3)
assert tanh(x/3) == tanh(sympy.Symbol("x") / 3)
assert coth(x/3) == coth(sympy.Symbol("x") / 3)
assert asinh(x/3) == asinh(sympy.Symbol("x") / 3)
assert acosh(x/3) == acosh(sympy.Symbol("x") / 3)
assert atanh(x/3) == atanh(sympy.Symbol("x") / 3)
assert acoth(x/3) == acoth(sympy.Symbol("x") / 3)
assert sinh(x/3)._sympy_() == sympy.sinh(sympy.Symbol("x") / 3)
assert cosh(x/3)._sympy_() == sympy.cosh(sympy.Symbol("x") / 3)
assert tanh(x/3)._sympy_() == sympy.tanh(sympy.Symbol("x") / 3)
assert coth(x/3)._sympy_() == sympy.coth(sympy.Symbol("x") / 3)
assert asinh(x/3)._sympy_() == sympy.asinh(sympy.Symbol("x") / 3)
assert acosh(x/3)._sympy_() == sympy.acosh(sympy.Symbol("x") / 3)
assert atanh(x/3)._sympy_() == sympy.atanh(sympy.Symbol("x") / 3)
assert acoth(x/3)._sympy_() == sympy.acoth(sympy.Symbol("x") / 3)
开发者ID:cbehan，项目名称:symengine.py，代码行数:20，代码来源:test_sympy_conv.py
示例19: test_issue_6746
def test_issue_6746():
y = Symbol('y')
n = Symbol('n')
assert manualintegrate(y**x, x) == Piecewise(
(y**x/log(y), Ne(log(y), 0)), (x, True))
assert manualintegrate(y**(n*x), x) == Piecewise(
(Piecewise(
(y**(n*x)/log(y), Ne(log(y), 0)),
(n*x, True)
)/n, Ne(n, 0)),
(x, True))
assert manualintegrate(exp(n*x), x) == Piecewise(
(exp(n*x)/n, Ne(n, 0)), (x, True))
y = Symbol('y', positive=True)
assert manualintegrate((y + 1)**x, x) == (y + 1)**x/log(y + 1)
y = Symbol('y', zero=True)
assert manualintegrate((y + 1)**x, x) == x
y = Symbol('y')
n = Symbol('n', nonzero=True)
assert manualintegrate(y**(n*x), x) == Piecewise(
(y**(n*x)/log(y), Ne(log(y), 0)), (n*x, True))/n
y = Symbol('y', positive=True)
assert manualintegrate((y + 1)**(n*x), x) == \
(y + 1)**(n*x)/(n*log(y + 1))
a = Symbol('a', negative=True)
b = Symbol('b')
assert manualintegrate(1/(a + b*x**2), x) == \
Piecewise((atan(x/sqrt(a/b))/(b*sqrt(a/b)), a/b > 0), \
(-acoth(x/sqrt(-a/b))/(b*sqrt(-a/b)), And(a/b < 0, x**2 > -a/b)), \
(-atanh(x/sqrt(-a/b))/(b*sqrt(-a/b)), And(a/b < 0, x**2 < -a/b)))
b = Symbol('b', negative=True)
assert manualintegrate(1/(a + b*x**2), x) == \
atan(x/(sqrt(-a)*sqrt(-1/b)))/(b*sqrt(-a)*sqrt(-1/b))
assert manualintegrate(1/((x**a + y**b + 4)*sqrt(a*x**2 + 1)), x) == \
y**(-b)*Integral(x**(-a)/(y**(-b)*sqrt(a*x**2 + 1) +
x**(-a)*sqrt(a*x**2 + 1) + 4*x**(-a)*y**(-b)*sqrt(a*x**2 + 1)), x)
assert manualintegrate(1/((x**2 + 4)*sqrt(4*x**2 + 1)), x) == \
Integral(1/((x**2 + 4)*sqrt(4*x**2 + 1)), x)
assert manualintegrate(1/(x - a**x + x*b**2), x) == \
Integral(1/(-a**x + b**2*x + x), x)
开发者ID:gamechanger98，项目名称:sympy，代码行数:41，代码来源:test_manual.py
示例20: test_bng_printer
def test_bng_printer():
# Constants
assert _bng_print(sympy.pi) == '_pi'
assert _bng_print(sympy.E) == '_e'
x, y = sympy.symbols('x y')
# Binary functions
assert _bng_print(sympy.sympify('x & y')) == 'x && y'
assert _bng_print(sympy.sympify('x | y')) == 'x || y'
# Trig functions
assert _bng_print(sympy.sin(x)) == 'sin(x)'
assert _bng_print(sympy.cos(x)) == 'cos(x)'
assert _bng_print(sympy.tan(x)) == 'tan(x)'
assert _bng_print(sympy.asin(x)) == 'asin(x)'
assert _bng_print(sympy.acos(x)) == 'acos(x)'
assert _bng_print(sympy.atan(x)) == 'atan(x)'
assert _bng_print(sympy.sinh(x)) == 'sinh(x)'
assert _bng_print(sympy.cosh(x)) == 'cosh(x)'
assert _bng_print(sympy.tanh(x)) == 'tanh(x)'
assert _bng_print(sympy.asinh(x)) == 'asinh(x)'
assert _bng_print(sympy.acosh(x)) == 'acosh(x)'
assert _bng_print(sympy.atanh(x)) == 'atanh(x)'
# Logs and powers
assert _bng_print(sympy.log(x)) == 'ln(x)'
assert _bng_print(sympy.exp(x)) == 'exp(x)'
assert _bng_print(sympy.sqrt(x)) == 'sqrt(x)'
# Rounding
assert _bng_print(sympy.Abs(x)) == 'abs(x)'
assert _bng_print(sympy.floor(x)) == 'rint(x - 0.5)'
assert _bng_print(sympy.ceiling(x)) == '(rint(x + 1) - 1)'
# Min/max
assert _bng_print(sympy.Min(x, y)) == 'min(x, y)'
assert _bng_print(sympy.Max(x, y)) == 'max(x, y)'
开发者ID:LoLab-VU，项目名称:pysb，代码行数:38，代码来源:test_bng.py
注：本文中的sympy.atanh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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