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from sympy import (Symbol, exp, log, sqrt, O, oo, sin, cos, PoleError)
from sympy.abc import x

from sympy.testing.pytest import raises

def test_simple():
    # Gruntz' theses pp. 91 to 96
    # 6.6
    e = sin(1/x + exp(-x)) - sin(1/x)
    assert e.aseries(x) == (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)

    e = exp(x) * (exp(1/x + exp(-x)) - exp(1/x))
    assert e.aseries(x, n=4) == 1/(6*x**3) + 1/(2*x**2) + 1/x + 1 + O(x**(-4), (x, oo))

    e = exp(exp(x) / (1 - 1/x))
    assert e.aseries(x) == exp(exp(x) / (1 - 1/x))
    assert e.aseries(x, bound=3) == exp(exp(x) / x**2)*exp(exp(x) / x)*exp(-exp(x) + exp(x)/(1 - 1/x) - \
            exp(x) / x - exp(x) / x**2) * exp(exp(x))

    e = exp(sin(1/x + exp(-exp(x)))) - exp(sin(1/x))
    assert e.aseries(x, n=4) == (-1/(2*x**3) + 1/x + 1 + O(x**(-4), (x, oo)))*exp(-exp(x))

    e = exp(exp(x)) * (exp(sin(1/x + 1/exp(exp(x)))) - exp(sin(1/x)))
    assert e.aseries(x, n=4) == -1/(2*x**3) + 1/x + 1 + O(x**(-4), (x, oo))

    n = Symbol('n', integer=True)
    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
    assert e.aseries(n) == \
            exp(exp(sqrt(log(log(n)))*log(log(log(n)))**3)*sqrt(log(n))*log(log(n))**2)*log(n)**2/sqrt(n)


def test_hierarchical():
    e = sin(1/x + exp(-x))
    assert e.aseries(x, n=3, hir=True) == -exp(-2*x)*sin(1/x)/2 + \
            exp(-x)*cos(1/x) + sin(1/x) + O(exp(-3*x), (x, oo))

    e = sin(x) * cos(exp(-x))
    assert e.aseries(x, hir=True) == exp(-4*x)*sin(x)/24 - \
            exp(-2*x)*sin(x)/2 + sin(x) + O(exp(-6*x), (x, oo))
    raises(PoleError, lambda: e.aseries(x))