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  • $\begingroup$ Thanks for the help. For point 2, I mean that mathematically these two operation should commute so I think there should be an explanation why they don't here unless it is a bug. For point 3, I noted these in case I am not aware of a particular refinement. For point 4 I expect to get x^a+x^b: I don't want Mathematica to drop symbolic terms relative to each other. However, it can and should drop if I have a term x^(a+1) or x^(b+1) which multiplying with (1+O[x]) does. For point 5, even though it is indeed a good check, it is not feasible (or practical) to do that in general. $\endgroup$ Commented Mar 9, 2018 at 8:56