def test_simpleDE():
# Tests just the first valid DE
for DE in simpleDE(exp(x), x, f):
assert DE == (-f(x) + Derivative(f(x), x), 1)
break
for DE in simpleDE(sin(x), x, f):
assert DE == (f(x) + Derivative(f(x), x, x), 2)
break
for DE in simpleDE(log(1 + x), x, f):
assert DE == ((x + 1) * Derivative(f(x), x, 2) + Derivative(f(x), x),
2)
break
for DE in simpleDE(asin(x), x, f):
assert DE == (x * Derivative(f(x), x) +
(x**2 - 1) * Derivative(f(x), x, x), 2)
break
for DE in simpleDE(exp(x) * sin(x), x, f):
assert DE == (2 * f(x) - 2 * Derivative(f(x)) + Derivative(f(x), x, x),
2)
break
for DE in simpleDE(((1 + x) / (1 - x))**n, x, f):
assert DE == (2 * n * f(x) + (x**2 - 1) * Derivative(f(x), x), 1)
break
for DE in simpleDE(airyai(x), x, f):
assert DE == (-x * f(x) + Derivative(f(x), x, x), 2)
break
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)
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)
def test_airy():
from sympy import airyai, airybi
expr1 = airyai(x)
expr2 = airybi(x)
prntr = SciPyPrinter()
assert prntr.doprint(expr1) == 'scipy.special.airy(x)[0]'
assert prntr.doprint(expr2) == 'scipy.special.airy(x)[2]'
prntr = NumPyPrinter()
assert prntr.doprint(expr1) == ' # Not supported in Python with NumPy:\n # airyai\nairyai(x)'
assert prntr.doprint(expr2) == ' # Not supported in Python with NumPy:\n # airybi\nairybi(x)'
prntr = PythonCodePrinter()
assert prntr.doprint(expr1) == ' # Not supported in Python:\n # airyai\nairyai(x)'
assert prntr.doprint(expr2) == ' # Not supported in Python:\n # airybi\nairybi(x)'
def test_airy():
from sympy import airyai, airybi
expr1 = airyai(x)
expr2 = airybi(x)
prntr = SciPyPrinter()
assert prntr.doprint(expr1) == 'scipy.special.airy(x)[0]'
assert prntr.doprint(expr2) == 'scipy.special.airy(x)[2]'
prntr = NumPyPrinter()
assert "Not supported" in prntr.doprint(expr1)
assert "Not supported" in prntr.doprint(expr2)
prntr = PythonCodePrinter()
assert "Not supported" in prntr.doprint(expr1)
assert "Not supported" in prntr.doprint(expr2)
def test_simpleDE():
# Tests just the first valid DE
for DE in simpleDE(exp(x), x, f):
assert DE == (-f(x) + Derivative(f(x), x), 1)
break
for DE in simpleDE(sin(x), x, f):
assert DE == (f(x) + Derivative(f(x), x, x), 2)
break
for DE in simpleDE(log(1 + x), x, f):
assert DE == ((x + 1) * Derivative(f(x), x, 2) + Derivative(f(x), x), 2)
break
for DE in simpleDE(asin(x), x, f):
assert DE == (x * Derivative(f(x), x) + (x ** 2 - 1) * Derivative(f(x), x, x), 2)
break
for DE in simpleDE(exp(x) * sin(x), x, f):
assert DE == (2 * f(x) - 2 * Derivative(f(x)) + Derivative(f(x), x, x), 2)
break
for DE in simpleDE(((1 + x) / (1 - x)) ** n, x, f):
assert DE == (2 * n * f(x) + (x ** 2 - 1) * Derivative(f(x), x), 1)
break
for DE in simpleDE(airyai(x), x, f):
assert DE == (-x * f(x) + Derivative(f(x), x, x), 2)
break