Comment #5 on issue 3912 by ronan.l...@gmail.com: Order terms don't cancel correctly
http://code.google.com/p/sympy/issues/detail?id=3912

O(f(x)) - O(f(x)) is the same as O(f(x)) + O(f(x)), because O(f(x)) is a vector space, which implies O(f(x)) = -O(f(x)) (g(x) = O(f(x)) iff -g(x) = O(f(x)) ).

Perhaps you're getting confused by the notation g(x) = O(f(x))? Don't forget that it's an abuse of notation that actually means g(x) ∈ O(f(x)).



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