1from sympy import (Symbol, exp, log, sqrt, O, oo, sin, cos, PoleError)
2from sympy.abc import x
3
4from sympy.testing.pytest import raises
5
6def test_simple():
7    # Gruntz' theses pp. 91 to 96
8    # 6.6
9    e = sin(1/x + exp(-x)) - sin(1/x)
10    assert e.aseries(x) == (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)
11
12    e = exp(x) * (exp(1/x + exp(-x)) - exp(1/x))
13    assert e.aseries(x, n=4) == 1/(6*x**3) + 1/(2*x**2) + 1/x + 1 + O(x**(-4), (x, oo))
14
15    e = exp(exp(x) / (1 - 1/x))
16    assert e.aseries(x) == exp(exp(x) / (1 - 1/x))
17
18    # The implementation of bound in aseries is incorrect currently. This test
19    # should be commented out when that is fixed.
20    # assert e.aseries(x, bound=3) == exp(exp(x) / x**2)*exp(exp(x) / x)*exp(-exp(x) + exp(x)/(1 - 1/x) - \
21    #         exp(x) / x - exp(x) / x**2) * exp(exp(x))
22
23    e = exp(sin(1/x + exp(-exp(x)))) - exp(sin(1/x))
24    assert e.aseries(x, n=4) == (-1/(2*x**3) + 1/x + 1 + O(x**(-4), (x, oo)))*exp(-exp(x))
25
26    e = exp(exp(x)) * (exp(sin(1/x + 1/exp(exp(x)))) - exp(sin(1/x)))
27    assert e.aseries(x, n=4) == -1/(2*x**3) + 1/x + 1 + O(x**(-4), (x, oo))
28
29    n = Symbol('n', integer=True)
30    e = (sqrt(n)*log(n)**2*exp(sqrt(log(n))*log(log(n))**2*exp(sqrt(log(log(n)))*log(log(log(n)))**3)))/n
31    assert e.aseries(n) == \
32            exp(exp(sqrt(log(log(n)))*log(log(log(n)))**3)*sqrt(log(n))*log(log(n))**2)*log(n)**2/sqrt(n)
33
34
35def test_hierarchical():
36    e = sin(1/x + exp(-x))
37    assert e.aseries(x, n=3, hir=True) == -exp(-2*x)*sin(1/x)/2 + \
38            exp(-x)*cos(1/x) + sin(1/x) + O(exp(-3*x), (x, oo))
39
40    e = sin(x) * cos(exp(-x))
41    assert e.aseries(x, hir=True) == exp(-4*x)*sin(x)/24 - \
42            exp(-2*x)*sin(x)/2 + sin(x) + O(exp(-6*x), (x, oo))
43    raises(PoleError, lambda: e.aseries(x))
44