Status: New
Owner: ----
Labels: Type-Defect Priority-Medium

New issue 1516 by ronan.l...@gmail.com: exp.as_leading_term returns wrong  
results
http://code.google.com/p/sympy/issues/detail?id=1516

as_leading_term is implicitly understood (at least by me) to obey the
following mathematical contract: expr.as_leading_term(x) ~ expr as x -> 0.
However, it fails on the common pitfall that f(x) ~ g(x) doesn't imply
exp(f(x)) ~ exp(g(x)). Concretely, we have:

>>> exp((x+1)/x**2).as_leading_term(x)
exp(x**(-2))

but, of course,

>>> limit(exp((x+1)/x**2)/exp(x**(-2)), x, 0)
oo

Obtaining a correct answer requires performing a full asympotic expansion
to order o(1) which might be outside the scope of this method, so maybe it
should return the expression unchanged unless it can easily get a correct
answer.

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