本文整理汇总了Python中sympy.atan函数的典型用法代码示例。如果您正苦于以下问题：Python atan函数的具体用法？Python atan怎么用？Python atan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atan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: log_to_atan
def log_to_atan(f, g):
"""Convert complex logarithms to real arctangents.
Given a real field K and polynomials f and g in K[x], with g != 0,
returns a sum h of arctangents of polynomials in K[x], such that:
df d f + I g
-- = -- I log( ------- )
dx dx f - I g
"""
if f.degree() < g.degree():
f, g = -g, f
f = f.to_field()
g = g.to_field()
p, q = f.div(g)
if q.is_zero:
return 2*atan(p.as_expr())
else:
s, t, h = g.gcdex(-f)
u = (f*s+g*t).quo(h)
A = 2*atan(u.as_expr())
return A + log_to_atan(s, t)
开发者ID:101man，项目名称:sympy，代码行数:27，代码来源:rationaltools.py
示例2: test_nsimplify
def test_nsimplify():
x = Symbol("x")
assert nsimplify(0) == 0
assert nsimplify(-1) == -1
assert nsimplify(1) == 1
assert nsimplify(1+x) == 1+x
assert nsimplify(2.7) == Rational(27, 10)
assert nsimplify(1-GoldenRatio) == (1-sqrt(5))/2
assert nsimplify((1+sqrt(5))/4, [GoldenRatio]) == GoldenRatio/2
assert nsimplify(2/GoldenRatio, [GoldenRatio]) == 2*GoldenRatio - 2
assert nsimplify(exp(5*pi*I/3, evaluate=False)) == sympify('1/2 - sqrt(3)*I/2')
assert nsimplify(sin(3*pi/5, evaluate=False)) == sympify('sqrt(sqrt(5)/8 + 5/8)')
assert nsimplify(sqrt(atan('1', evaluate=False))*(2+I), [pi]) == sqrt(pi) + sqrt(pi)/2*I
assert nsimplify(2 + exp(2*atan('1/4')*I)) == sympify('49/17 + 8*I/17')
assert nsimplify(pi, tolerance=0.01) == Rational(22, 7)
assert nsimplify(pi, tolerance=0.001) == Rational(355, 113)
assert nsimplify(0.33333, tolerance=1e-4) == Rational(1, 3)
assert nsimplify(2.0**(1/3.), tolerance=0.001) == Rational(635, 504)
assert nsimplify(2.0**(1/3.), tolerance=0.001, full=True) == 2**Rational(1, 3)
assert nsimplify(x + .5, rational=True) == Rational(1, 2) + x
assert nsimplify(1/.3 + x, rational=True) == Rational(10, 3) + x
assert nsimplify(log(3).n(), rational=True) == \
sympify('109861228866811/100000000000000')
assert nsimplify(Float(0.272198261287950), [pi,log(2)]) == pi*log(2)/8
assert nsimplify(Float(0.272198261287950).n(3), [pi,log(2)]) == \
-pi/4 - log(2) + S(7)/4
assert nsimplify(x/7.0) == x/7
assert nsimplify(pi/1e2) == pi/100
assert nsimplify(pi/1e2, rational=False) == pi/100.0
assert nsimplify(pi/1e-7) == 10000000*pi
开发者ID:ness01，项目名称:sympy，代码行数:30，代码来源:test_simplify.py
示例3: _expr_big_minus
def _expr_big_minus(cls, x, n):
from sympy import atan, sqrt, pi
if n.is_even:
return atan(sqrt(x)) / sqrt(x)
else:
return (atan(sqrt(x)) - pi) / sqrt(x)
开发者ID:ness01，项目名称:sympy，代码行数:7，代码来源:hyper.py
示例4: _expr_big_minus
def _expr_big_minus(cls, a, z, n):
from sympy import I, pi, exp, sqrt, atan, sin
if n.is_even:
return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z)*sin(2*a*atan(sqrt(z)))
else:
return (1 + z)**a*exp(2*pi*I*n*a)*sqrt(z) \
*sin(2*a*atan(sqrt(z)) - 2*pi*a)
开发者ID:ALGHeArT，项目名称:sympy，代码行数:7，代码来源:hyper.py
示例5: test_heurisch_trigonometric
def test_heurisch_trigonometric():
assert heurisch(sin(x), x) == -cos(x)
assert heurisch(pi*sin(x) + 1, x) == x - pi*cos(x)
assert heurisch(cos(x), x) == sin(x)
assert heurisch(tan(x), x) in [
log(1 + tan(x)**2)/2,
log(tan(x) + I) + I*x,
log(tan(x) - I) - I*x,
]
assert heurisch(sin(x)*sin(y), x) == -cos(x)*sin(y)
assert heurisch(sin(x)*sin(y), y) == -cos(y)*sin(x)
# gives sin(x) in answer when run via setup.py and cos(x) when run via py.test
assert heurisch(sin(x)*cos(x), x) in [sin(x)**2 / 2, -cos(x)**2 / 2]
assert heurisch(cos(x)/sin(x), x) == log(sin(x))
assert heurisch(x*sin(7*x), x) == sin(7*x) / 49 - x*cos(7*x) / 7
assert heurisch(1/pi/4 * x**2*cos(x), x) == 1/pi/4*(x**2*sin(x) -
2*sin(x) + 2*x*cos(x))
assert heurisch(acos(x/4) * asin(x/4), x) == 2*x - (sqrt(16 - x**2))*asin(x/4) \
+ (sqrt(16 - x**2))*acos(x/4) + x*asin(x/4)*acos(x/4)
assert heurisch(sin(x)/(cos(x)**2+1), x) == -atan(cos(x)) #fixes issue 13723
assert heurisch(1/(cos(x)+2), x) == 2*sqrt(3)*atan(sqrt(3)*tan(x/2)/3)/3
assert heurisch(2*sin(x)*cos(x)/(sin(x)**4 + 1), x) == atan(sqrt(2)*sin(x)
- 1) - atan(sqrt(2)*sin(x) + 1)
assert heurisch(1/cosh(x), x) == 2*atan(tanh(x/2))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:31，代码来源:test_heurisch.py
示例6: test_solve_sqrt_3
def test_solve_sqrt_3():
R = Symbol("R")
eq = sqrt(2) * R * sqrt(1 / (R + 1)) + (R + 1) * (sqrt(2) * sqrt(1 / (R + 1)) - 1)
sol = solveset_complex(eq, R)
assert sol == FiniteSet(
*[
S(5) / 3 + 4 * sqrt(10) * cos(atan(3 * sqrt(111) / 251) / 3) / 3,
-sqrt(10) * cos(atan(3 * sqrt(111) / 251) / 3) / 3
+ 40 * re(1 / ((-S(1) / 2 - sqrt(3) * I / 2) * (S(251) / 27 + sqrt(111) * I / 9) ** (S(1) / 3))) / 9
+ sqrt(30) * sin(atan(3 * sqrt(111) / 251) / 3) / 3
+ S(5) / 3
+ I
* (
-sqrt(30) * cos(atan(3 * sqrt(111) / 251) / 3) / 3
- sqrt(10) * sin(atan(3 * sqrt(111) / 251) / 3) / 3
+ 40 * im(1 / ((-S(1) / 2 - sqrt(3) * I / 2) * (S(251) / 27 + sqrt(111) * I / 9) ** (S(1) / 3))) / 9
),
]
)
# the number of real roots will depend on the value of m: for m=1 there are 4
# and for m=-1 there are none.
eq = -sqrt((m - q) ** 2 + (-m / (2 * q) + S(1) / 2) ** 2) + sqrt(
(-m ** 2 / 2 - sqrt(4 * m ** 4 - 4 * m ** 2 + 8 * m + 1) / 4 - S(1) / 4) ** 2
+ (m ** 2 / 2 - m - sqrt(4 * m ** 4 - 4 * m ** 2 + 8 * m + 1) / 4 - S(1) / 4) ** 2
)
raises(NotImplementedError, lambda: solveset_real(eq, q))
开发者ID:LuckyStrikes1090，项目名称:sympy，代码行数:28，代码来源:test_solveset.py
示例7: test_evalf_integrals
def test_evalf_integrals():
assert NS(Integral(x, (x, 2, 5)), 15) == '10.5000000000000'
gauss = Integral(exp(-x**2), (x, -oo, oo))
assert NS(gauss, 15) == '1.77245385090552'
assert NS(gauss**2 - pi + E*Rational(1,10**20), 15) in ('2.71828182845904e-20', '2.71828182845905e-20')
# A monster of an integral from http://mathworld.wolfram.com/DefiniteIntegral.html
t = Symbol('t')
a = 8*sqrt(3)/(1+3*t**2)
b = 16*sqrt(2)*(3*t+1)*(4*t**2+t+1)**Rational(3,2)
c = (3*t**2+1)*(11*t**2+2*t+3)**2
d = sqrt(2)*(249*t**2+54*t+65)/(11*t**2+2*t+3)**2
f = a - b/c - d
assert NS(Integral(f, (t, 0, 1)), 50) == NS((3*sqrt(2)-49*pi+162*atan(sqrt(2)))/12,50)
# http://mathworld.wolfram.com/VardisIntegral.html
assert NS(Integral(log(log(1/x))/(1+x+x**2), (x, 0, 1)), 15) == NS('pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))', 15)
# http://mathworld.wolfram.com/AhmedsIntegral.html
assert NS(Integral(atan(sqrt(x**2+2))/(sqrt(x**2+2)*(x**2+1)), (x, 0, 1)), 15) == NS(5*pi**2/96, 15)
# http://mathworld.wolfram.com/AbelsIntegral.html
assert NS(Integral(x/((exp(pi*x)-exp(-pi*x))*(x**2+1)), (x, 0, oo)), 15) == NS('log(2)/2-1/4',15)
# Complex part trimming
# http://mathworld.wolfram.com/VardisIntegral.html
assert NS(Integral(log(log(sin(x)/cos(x))), (x, pi/4, pi/2)), 15, chop=True) == \
NS('pi/4*log(4*pi**3/gamma(1/4)**4)', 15)
#
# Endpoints causing trouble (rounding error in integration points -> complex log)
assert NS(2+Integral(log(2*cos(x/2)), (x, -pi, pi)), 17, chop=True) == NS(2, 17)
assert NS(2+Integral(log(2*cos(x/2)), (x, -pi, pi)), 20, chop=True) == NS(2, 20)
assert NS(2+Integral(log(2*cos(x/2)), (x, -pi, pi)), 22, chop=True) == NS(2, 22)
# Needs zero handling
assert NS(pi - 4*Integral('sqrt(1-x**2)', (x, 0, 1)), 15, maxn=30, chop=True) in ('0.0', '0')
# Oscillatory quadrature
a = Integral(sin(x)/x**2, (x, 1, oo)).evalf(maxn=15)
assert 0.49 < a < 0.51
assert NS(Integral(sin(x)/x**2, (x, 1, oo)), quad='osc') == '0.504067061906928'
assert NS(Integral(cos(pi*x+1)/x, (x, -oo, -1)), quad='osc') == '0.276374705640365'
开发者ID:wxgeo，项目名称:sympy，代码行数:35，代码来源:test_integrals.py
示例8: eval
def eval(cls, arg):
from sympy import atan
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Infinity
elif arg is S.NegativeOne:
return S.NegativeInfinity
elif arg is S.Infinity:
return -S.ImaginaryUnit * atan(arg)
elif arg is S.NegativeInfinity:
return S.ImaginaryUnit * atan(-arg)
elif arg.is_negative:
return -cls(-arg)
else:
if arg is S.ComplexInfinity:
from sympy.calculus.util import AccumBounds
return S.ImaginaryUnit*AccumBounds(-S.Pi/2, S.Pi/2)
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return S.ImaginaryUnit * atan(i_coeff)
else:
if _coeff_isneg(arg):
return -cls(-arg)
开发者ID:moorepants，项目名称:sympy，代码行数:31，代码来源:hyperbolic.py
示例9: test_issue_2850
def test_issue_2850():
assert manualintegrate(asin(x)*log(x), x) == -x*asin(x) - sqrt(-x**2 + 1) \
+ (x*asin(x) + sqrt(-x**2 + 1))*log(x) - Integral(sqrt(-x**2 + 1)/x, x)
assert manualintegrate(acos(x)*log(x), x) == -x*acos(x) + sqrt(-x**2 + 1) + \
(x*acos(x) - sqrt(-x**2 + 1))*log(x) + Integral(sqrt(-x**2 + 1)/x, x)
assert manualintegrate(atan(x)*log(x), x) == -x*atan(x) + (x*atan(x) - \
log(x**2 + 1)/2)*log(x) + log(x**2 + 1)/2 + Integral(log(x**2 + 1)/x, x)/2
开发者ID:gamechanger98，项目名称:sympy，代码行数:7，代码来源:test_manual.py
示例10: test_atan2_expansion
def test_atan2_expansion():
assert cancel(atan2(x ** 2, x + 1).diff(x) - atan(x ** 2 / (x + 1)).diff(x)) == 0
assert cancel(atan(y / x).series(y, 0, 5) - atan2(y, x).series(y, 0, 5) + atan2(0, x) - atan(0)) == O(y ** 5)
assert cancel(atan(y / x).series(x, 1, 4) - atan2(y, x).series(x, 1, 4) + atan2(y, 1) - atan(y)) == O(x ** 4)
assert cancel(
atan((y + x) / x).series(x, 1, 3) - atan2(y + x, x).series(x, 1, 3) + atan2(1 + y, 1) - atan(1 + y)
) == O(x ** 3)
assert Matrix([atan2(y, x)]).jacobian([y, x]) == Matrix([[x / (y ** 2 + x ** 2), -y / (y ** 2 + x ** 2)]])
开发者ID:rpmuller，项目名称:sympy，代码行数:8，代码来源:test_trigonometric.py
示例11: test_atan2_expansion
def test_atan2_expansion():
assert cancel(atan2(x + 1, x ** 2).diff(x) - atan((x + 1) / x ** 2).diff(x)) == 0
assert cancel(atan(x / y).series(x, 0, 5) - atan2(x, y).series(x, 0, 5) + atan2(0, y) - atan(0)) == O(x ** 5)
assert cancel(atan(x / y).series(y, 1, 4) - atan2(x, y).series(y, 1, 4) + atan2(x, 1) - atan(x)) == O(y ** 4)
assert cancel(
atan((x + y) / y).series(y, 1, 3) - atan2(x + y, y).series(y, 1, 3) + atan2(1 + x, 1) - atan(1 + x)
) == O(y ** 3)
assert Matrix([atan2(x, y)]).jacobian([x, y]) == Matrix([[y / (x ** 2 + y ** 2), -x / (x ** 2 + y ** 2)]])
开发者ID:Maihj，项目名称:sympy，代码行数:8，代码来源:test_trigonometric.py
示例12: test_atan2
def test_atan2():
assert refine(atan2(y, x), Q.real(y) & Q.positive(x)) == atan(y/x)
assert refine(atan2(y, x), Q.negative(y) & Q.positive(x)) == atan(y/x)
assert refine(atan2(y, x), Q.negative(y) & Q.negative(x)) == atan(y/x) - pi
assert refine(atan2(y, x), Q.positive(y) & Q.negative(x)) == atan(y/x) + pi
assert refine(atan2(y, x), Q.zero(y) & Q.negative(x)) == pi
assert refine(atan2(y, x), Q.positive(y) & Q.zero(x)) == pi/2
assert refine(atan2(y, x), Q.negative(y) & Q.zero(x)) == -pi/2
assert refine(atan2(y, x), Q.zero(y) & Q.zero(x)) == nan
开发者ID:preetskhalsa97，项目名称:sympy，代码行数:9，代码来源:test_refine.py
示例13: test_atan2
def test_atan2():
assert atan2.nargs == FiniteSet(2)
assert atan2(0, 0) == S.NaN
assert atan2(0, 1) == 0
assert atan2(1, 1) == pi/4
assert atan2(1, 0) == pi/2
assert atan2(1, -1) == 3*pi/4
assert atan2(0, -1) == pi
assert atan2(-1, -1) == -3*pi/4
assert atan2(-1, 0) == -pi/2
assert atan2(-1, 1) == -pi/4
i = symbols('i', imaginary=True)
r = symbols('r', real=True)
eq = atan2(r, i)
ans = -I*log((i + I*r)/sqrt(i**2 + r**2))
reps = ((r, 2), (i, I))
assert eq.subs(reps) == ans.subs(reps)
x = Symbol('x', negative=True)
y = Symbol('y', negative=True)
assert atan2(y, x) == atan(y/x) - pi
y = Symbol('y', nonnegative=True)
assert atan2(y, x) == atan(y/x) + pi
y = Symbol('y')
assert atan2(y, x) == atan2(y, x, evaluate=False)
u = Symbol("u", positive=True)
assert atan2(0, u) == 0
u = Symbol("u", negative=True)
assert atan2(0, u) == pi
assert atan2(y, oo) == 0
assert atan2(y, -oo)== 2*pi*Heaviside(re(y)) - pi
assert atan2(y, x).rewrite(log) == -I*log((x + I*y)/sqrt(x**2 + y**2))
assert atan2(y, x).rewrite(atan) == 2*atan(y/(x + sqrt(x**2 + y**2)))
ex = atan2(y, x) - arg(x + I*y)
assert ex.subs({x:2, y:3}).rewrite(arg) == 0
assert ex.subs({x:2, y:3*I}).rewrite(arg) == -pi - I*log(sqrt(5)*I/5)
assert ex.subs({x:2*I, y:3}).rewrite(arg) == -pi/2 - I*log(sqrt(5)*I)
assert ex.subs({x:2*I, y:3*I}).rewrite(arg) == -pi + atan(2/S(3)) + atan(3/S(2))
i = symbols('i', imaginary=True)
r = symbols('r', real=True)
e = atan2(i, r)
rewrite = e.rewrite(arg)
reps = {i: I, r: -2}
assert rewrite == -I*log(abs(I*i + r)/sqrt(abs(i**2 + r**2))) + arg((I*i + r)/sqrt(i**2 + r**2))
assert (e - rewrite).subs(reps).equals(0)
assert conjugate(atan2(x, y)) == atan2(conjugate(x), conjugate(y))
assert diff(atan2(y, x), x) == -y/(x**2 + y**2)
assert diff(atan2(y, x), y) == x/(x**2 + y**2)
assert simplify(diff(atan2(y, x).rewrite(log), x)) == -y/(x**2 + y**2)
assert simplify(diff(atan2(y, x).rewrite(log), y)) == x/(x**2 + y**2)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:57，代码来源:test_trigonometric.py
示例14: test_manualintegrate_parts
def test_manualintegrate_parts():
assert manualintegrate(exp(x) * sin(x), x) == \
(exp(x) * sin(x)) / 2 - (exp(x) * cos(x)) / 2
assert manualintegrate(2*x*cos(x), x) == 2*x*sin(x) + 2*cos(x)
assert manualintegrate(x * log(x), x) == x**2*log(x)/2 - x**2/4
assert manualintegrate(log(x), x) == x * log(x) - x
assert manualintegrate((3*x**2 + 5) * exp(x), x) == \
-6*x*exp(x) + (3*x**2 + 5)*exp(x) + 6*exp(x)
assert manualintegrate(atan(x), x) == x*atan(x) - log(x**2 + 1)/2
开发者ID:cstrobach83，项目名称:sympy，代码行数:9，代码来源:test_manual.py
示例15: test_invert_real
def test_invert_real():
x = Symbol('x', real=True)
x = Dummy(real=True)
n = Symbol('n')
d = Dummy()
assert solveset(abs(x) - n, x) == solveset(abs(x) - d, x) == EmptySet()
n = Symbol('n', real=True)
assert invert_real(x + 3, y, x) == (x, FiniteSet(y - 3))
assert invert_real(x*3, y, x) == (x, FiniteSet(y / 3))
assert invert_real(exp(x), y, x) == (x, FiniteSet(log(y)))
assert invert_real(exp(3*x), y, x) == (x, FiniteSet(log(y) / 3))
assert invert_real(exp(x + 3), y, x) == (x, FiniteSet(log(y) - 3))
assert invert_real(exp(x) + 3, y, x) == (x, FiniteSet(log(y - 3)))
assert invert_real(exp(x)*3, y, x) == (x, FiniteSet(log(y / 3)))
assert invert_real(log(x), y, x) == (x, FiniteSet(exp(y)))
assert invert_real(log(3*x), y, x) == (x, FiniteSet(exp(y) / 3))
assert invert_real(log(x + 3), y, x) == (x, FiniteSet(exp(y) - 3))
assert invert_real(Abs(x), y, x) == (x, FiniteSet(-y, y))
assert invert_real(2**x, y, x) == (x, FiniteSet(log(y)/log(2)))
assert invert_real(2**exp(x), y, x) == (x, FiniteSet(log(log(y)/log(2))))
assert invert_real(x**2, y, x) == (x, FiniteSet(sqrt(y), -sqrt(y)))
assert invert_real(x**Rational(1, 2), y, x) == (x, FiniteSet(y**2))
raises(ValueError, lambda: invert_real(x, x, x))
raises(ValueError, lambda: invert_real(x**pi, y, x))
raises(ValueError, lambda: invert_real(S.One, y, x))
assert invert_real(x**31 + x, y, x) == (x**31 + x, FiniteSet(y))
assert invert_real(Abs(x**31 + x + 1), y, x) == (x**31 + x,
FiniteSet(-y - 1, y - 1))
assert invert_real(tan(x), y, x) == \
(x, imageset(Lambda(n, n*pi + atan(y)), S.Integers))
assert invert_real(tan(exp(x)), y, x) == \
(x, imageset(Lambda(n, log(n*pi + atan(y))), S.Integers))
assert invert_real(cot(x), y, x) == \
(x, imageset(Lambda(n, n*pi + acot(y)), S.Integers))
assert invert_real(cot(exp(x)), y, x) == \
(x, imageset(Lambda(n, log(n*pi + acot(y))), S.Integers))
assert invert_real(tan(tan(x)), y, x) == \
(tan(x), imageset(Lambda(n, n*pi + atan(y)), S.Integers))
x = Symbol('x', positive=True)
assert invert_real(x**pi, y, x) == (x, FiniteSet(y**(1/pi)))
开发者ID:ChaliZhg，项目名称:sympy，代码行数:55，代码来源:test_solveset.py
示例16: test_nsimplify
def test_nsimplify():
x = Symbol("x")
assert nsimplify(0) == 0
assert nsimplify(-1) == -1
assert nsimplify(1) == 1
assert nsimplify(1 + x) == 1 + x
assert nsimplify(2.7) == Rational(27, 10)
assert nsimplify(1 - GoldenRatio) == (1 - sqrt(5)) / 2
assert nsimplify((1 + sqrt(5)) / 4, [GoldenRatio]) == GoldenRatio / 2
assert nsimplify(2 / GoldenRatio, [GoldenRatio]) == 2 * GoldenRatio - 2
assert nsimplify(exp(5 * pi * I / 3, evaluate=False)) == sympify("1/2 - sqrt(3)*I/2")
assert nsimplify(sin(3 * pi / 5, evaluate=False)) == sympify("sqrt(sqrt(5)/8 + 5/8)")
assert nsimplify(sqrt(atan("1", evaluate=False)) * (2 + I), [pi]) == sqrt(pi) + sqrt(pi) / 2 * I
assert nsimplify(2 + exp(2 * atan("1/4") * I)) == sympify("49/17 + 8*I/17")
assert nsimplify(pi, tolerance=0.01) == Rational(22, 7)
assert nsimplify(pi, tolerance=0.001) == Rational(355, 113)
assert nsimplify(0.33333, tolerance=1e-4) == Rational(1, 3)
assert nsimplify(2.0 ** (1 / 3.0), tolerance=0.001) == Rational(635, 504)
assert nsimplify(2.0 ** (1 / 3.0), tolerance=0.001, full=True) == 2 ** Rational(1, 3)
assert nsimplify(x + 0.5, rational=True) == Rational(1, 2) + x
assert nsimplify(1 / 0.3 + x, rational=True) == Rational(10, 3) + x
assert nsimplify(log(3).n(), rational=True) == sympify("109861228866811/100000000000000")
assert nsimplify(Float(0.272198261287950), [pi, log(2)]) == pi * log(2) / 8
assert nsimplify(Float(0.272198261287950).n(3), [pi, log(2)]) == -pi / 4 - log(2) + S(7) / 4
assert nsimplify(x / 7.0) == x / 7
assert nsimplify(pi / 1e2) == pi / 100
assert nsimplify(pi / 1e2, rational=False) == pi / 100.0
assert nsimplify(pi / 1e-7) == 10000000 * pi
assert not nsimplify(factor(-3.0 * z ** 2 * (z ** 2) ** (-2.5) + 3 * (z ** 2) ** (-1.5))).atoms(Float)
e = x ** 0.0
assert e.is_Pow and nsimplify(x ** 0.0) == 1
assert nsimplify(3.333333, tolerance=0.1, rational=True) == Rational(10, 3)
assert nsimplify(3.333333, tolerance=0.01, rational=True) == Rational(10, 3)
assert nsimplify(3.666666, tolerance=0.1, rational=True) == Rational(11, 3)
assert nsimplify(3.666666, tolerance=0.01, rational=True) == Rational(11, 3)
assert nsimplify(33, tolerance=10, rational=True) == Rational(33)
assert nsimplify(33.33, tolerance=10, rational=True) == Rational(30)
assert nsimplify(37.76, tolerance=10, rational=True) == Rational(40)
assert nsimplify(-203.1) == -S(2031) / 10
assert nsimplify(0.2, tolerance=0) == S.One / 5
assert nsimplify(-0.2, tolerance=0) == -S.One / 5
assert nsimplify(0.2222, tolerance=0) == S(1111) / 5000
assert nsimplify(-0.2222, tolerance=0) == -S(1111) / 5000
# issue 7211, PR 4112
assert nsimplify(S(2e-8)) == S(1) / 50000000
# issue 7322 direct test
assert nsimplify(1e-42, rational=True) != 0
# issue 10336
inf = Float("inf")
infs = (-oo, oo, inf, -inf)
for i in infs:
ans = sign(i) * oo
assert nsimplify(i) == ans
assert nsimplify(i + x) == x + ans
开发者ID:pabloferz，项目名称:sympy，代码行数:54，代码来源:test_simplify.py
示例17: test_manualintegrate_inversetrig
def test_manualintegrate_inversetrig():
# atan
assert manualintegrate(exp(x) / (1 + exp(2*x)), x) == atan(exp(x))
assert manualintegrate(1 / (4 + 9 * x**2), x) == atan(3 * x/2) / 6
assert manualintegrate(1 / (16 + 16 * x**2), x) == atan(x) / 16
assert manualintegrate(1 / (4 + x**2), x) == atan(x / 2) / 2
assert manualintegrate(1 / (1 + 4 * x**2), x) == atan(2*x) / 2
assert manualintegrate(1/(a + b*x**2), x) == \
Piecewise(((sqrt(a/b)*atan(x*sqrt(b/a))/a), And(a > 0, b > 0)))
assert manualintegrate(1/(4 + b*x**2), x) == \
Piecewise((sqrt(1/b)*atan(sqrt(b)*x/2)/2, b > 0))
assert manualintegrate(1/(a + 4*x**2), x) == \
Piecewise((atan(2*x*sqrt(1/a))/(2*sqrt(a)), a > 0))
assert manualintegrate(1/(4 + 4*x**2), x) == atan(x) / 4
# asin
assert manualintegrate(1/sqrt(1-x**2), x) == asin(x)
assert manualintegrate(1/sqrt(4-4*x**2), x) == asin(x)/2
assert manualintegrate(3/sqrt(1-9*x**2), x) == asin(3*x)
assert manualintegrate(1/sqrt(4-9*x**2), x) == asin(3*x/2)/3
# asinh
assert manualintegrate(1/sqrt(x**2 + 1), x) == \
asinh(x)
assert manualintegrate(1/sqrt(x**2 + 4), x) == \
asinh(x/2)
assert manualintegrate(1/sqrt(4*x**2 + 4), x) == \
asinh(x)/2
assert manualintegrate(1/sqrt(4*x**2 + 1), x) == \
asinh(2*x)/2
assert manualintegrate(1/sqrt(a*x**2 + 1), x) == \
Piecewise((sqrt(-1/a)*asin(x*sqrt(-a)), a < 0), (sqrt(1/a)*asinh(sqrt(a)*x), a > 0))
assert manualintegrate(1/sqrt(a + x**2), x) == \
Piecewise((asinh(x*sqrt(1/a)), a > 0), (acosh(x*sqrt(-1/a)), a < 0))
# acosh
assert manualintegrate(1/sqrt(x**2 - 1), x) == \
acosh(x)
assert manualintegrate(1/sqrt(x**2 - 4), x) == \
acosh(x/2)
assert manualintegrate(1/sqrt(4*x**2 - 4), x) == \
acosh(x)/2
assert manualintegrate(1/sqrt(9*x**2 - 1), x) == \
acosh(3*x)/3
assert manualintegrate(1/sqrt(a*x**2 - 4), x) == \
Piecewise((sqrt(1/a)*acosh(sqrt(a)*x/2), a > 0))
assert manualintegrate(1/sqrt(-a + 4*x**2), x) == \
Piecewise((asinh(2*x*sqrt(-1/a))/2, -a > 0), (acosh(2*x*sqrt(1/a))/2, -a < 0))
# piecewise
assert manualintegrate(1/sqrt(a-b*x**2), x) == \
Piecewise((sqrt(a/b)*asin(x*sqrt(b/a))/sqrt(a), And(-b < 0, a > 0)),
(sqrt(-a/b)*asinh(x*sqrt(-b/a))/sqrt(a), And(-b > 0, a > 0)),
(sqrt(a/b)*acosh(x*sqrt(b/a))/sqrt(-a), And(-b > 0, a < 0)))
assert manualintegrate(1/sqrt(a + b*x**2), x) == \
Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), And(a > 0, b < 0)),
(sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), And(a > 0, b > 0)),
(sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), And(a < 0, b > 0)))
开发者ID:A-turing-machine，项目名称:sympy，代码行数:58，代码来源:test_manual.py
示例18: test_main_trig_functions_numeric
def test_main_trig_functions_numeric(self):
print "\n\n\n" + " Test if sin, cos and tan and inverses Work Numerically ".center(75, "#")
from sympy import symbols, sin, cos, tan, asin, acos, atan
x, y = symbols('x,y')
test_expr = sin(x) + cos(x) + tan(x) + asin(y) + acos(y) + atan(y)
target_expr = sin(x) + cos(x) + tan(x) + asin(y) + acos(y) + atan(y)
print "Target expression: '%s'" % target_expr
print "Test expression: '%s'" % test_expr
equal = api.numeric_equality(test_expr, target_expr)
self.assertTrue(equal, "Expected expressions to be found numerically equal!")
print " PASS ".center(75, "#")
开发者ID:ucam-cl-dtg，项目名称:equality-checker，代码行数:13，代码来源:unittests.py
示例19: test_rational_algorithm
def test_rational_algorithm():
f = 1 / ((x - 1) ** 2 * (x - 2))
assert rational_algorithm(f, x, k) == (-2 ** (-k - 1) + 1 - (factorial(k + 1) / factorial(k)), 0, 0)
f = (1 + x + x ** 2 + x ** 3) / ((x - 1) * (x - 2))
assert rational_algorithm(f, x, k) == (-15 * 2 ** (-k - 1) + 4, x + 4, 0)
f = z / (y * m - m * x - y * x + x ** 2)
assert rational_algorithm(f, x, k) == (((-y ** (-k - 1) * z) / (y - m)) + ((m ** (-k - 1) * z) / (y - m)), 0, 0)
f = x / (1 - x - x ** 2)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == (
((-Rational(1, 2) + sqrt(5) / 2) ** (-k - 1) * (-sqrt(5) / 10 + Rational(1, 2)))
+ ((-sqrt(5) / 2 - Rational(1, 2)) ** (-k - 1) * (sqrt(5) / 10 + Rational(1, 2))),
0,
0,
)
f = 1 / (x ** 2 + 2 * x + 2)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == (
(I * (-1 + I) ** (-k - 1)) / 2 - (I * (-1 - I) ** (-k - 1)) / 2,
0,
0,
)
f = log(1 + x)
assert rational_algorithm(f, x, k) == (-(-1) ** (-k) / k, 0, 1)
f = atan(x)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == (((I * I ** (-k)) / 2 - (I * (-I) ** (-k)) / 2) / k, 0, 1)
f = x * atan(x) - log(1 + x ** 2) / 2
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == (
((I * I ** (-k + 1)) / 2 - (I * (-I) ** (-k + 1)) / 2) / (k * (k - 1)),
0,
2,
)
f = log((1 + x) / (1 - x)) / 2 - atan(x)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == (
(-(-1) ** (-k) / 2 - (I * I ** (-k)) / 2 + (I * (-I) ** (-k)) / 2 + Rational(1, 2)) / k,
0,
1,
)
assert rational_algorithm(cos(x), x, k) is None
开发者ID:Carreau，项目名称:sympy，代码行数:51，代码来源:test_formal.py
示例20: test_fps__hyper
def test_fps__hyper():
f = sin(x)
assert fps(f, x).truncate() == x - x ** 3 / 6 + x ** 5 / 120 + O(x ** 6)
f = cos(x)
assert fps(f, x).truncate() == 1 - x ** 2 / 2 + x ** 4 / 24 + O(x ** 6)
f = exp(x)
assert fps(f, x).truncate() == 1 + x + x ** 2 / 2 + x ** 3 / 6 + x ** 4 / 24 + x ** 5 / 120 + O(x ** 6)
f = atan(x)
assert fps(f, x).truncate() == x - x ** 3 / 3 + x ** 5 / 5 + O(x ** 6)
f = exp(acos(x))
assert fps(f, x).truncate() == (
exp(pi / 2)
- x * exp(pi / 2)
+ x ** 2 * exp(pi / 2) / 2
- x ** 3 * exp(pi / 2) / 3
+ 5 * x ** 4 * exp(pi / 2) / 24
- x ** 5 * exp(pi / 2) / 6
+ O(x ** 6)
)
f = exp(acosh(x))
assert fps(f, x).truncate() == I + x - I * x ** 2 / 2 - I * x ** 4 / 8 + O(x ** 6)
f = atan(1 / x)
assert fps(f, x).truncate() == pi / 2 - x + x ** 3 / 3 - x ** 5 / 5 + O(x ** 6)
f = x * atan(x) - log(1 + x ** 2) / 2
assert fps(f, x, rational=False).truncate() == x ** 2 / 2 - x ** 4 / 12 + O(x ** 6)
f = log(1 + x)
assert fps(f, x, rational=False).truncate() == x - x ** 2 / 2 + x ** 3 / 3 - x ** 4 / 4 + x ** 5 / 5 + O(x ** 6)
f = airyai(x ** 2)
assert fps(f, x).truncate() == (
3 ** Rational(5, 6) * gamma(Rational(1, 3)) / (6 * pi)
- 3 ** Rational(2, 3) * x ** 2 / (3 * gamma(Rational(1, 3)))
+ O(x ** 6)
)
f = exp(x) * sin(x)
assert fps(f, x).truncate() == x + x ** 2 + x ** 3 / 3 - x ** 5 / 30 + O(x ** 6)
f = exp(x) * sin(x) / x
assert fps(f, x).truncate() == 1 + x + x ** 2 / 3 - x ** 4 / 30 - x ** 5 / 90 + O(x ** 6)
f = sin(x) * cos(x)
assert fps(f, x).truncate() == x - 2 * x ** 3 / 3 + 2 * x ** 5 / 15 + O(x ** 6)
开发者ID:Carreau，项目名称:sympy，代码行数:51，代码来源:test_formal.py
注：本文中的sympy.atan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。 |
客服电话
APP下载
官方微信
请发表评论