# Uncertain behaviour when using FullSimplify

While doing some (symbolic) calculations with Mathematica, I encountered a small problem with the FullSimpilify function that hopefully someone here might explain to me. More specifically, I fear that Mathematica oversimplified my equations (due to the arguments that I gave) and I wonder if there is a different way to parse my commands to get an output more to my liking.

Essentially, my Problem lies with the following two expressions:

1. FullSimplify[ Sin[n a \[Pi]]/n , Assumptions -> {n, a} \[Element] Integers] and
2. Limit[ Sin[n a \[Pi]]/n , n -> 0]

In another longer expression, I have several terms similar to (1) which are all simplified to "= 0" yet for n=0, I would at least like to get a warning that something strange is happening (because of n in the denominator). In the (continuous) Limit the expression does not equal 0. To avoid any confusion: the "n" parameter in my calculations is no Integer, but I want to check how the expression simplifies if n is at least close to an integer value. There are multiple terms like (1) with different factors (besides n, there is stuff like (n-2), (n+1), etc. ) in my longer expression so I would prefer to avoid going over them all by hand and check each case individually.

Is there a way to redo expression (1) but avoid mathematica so evaluate the Sin[n a \[Pi]] with the assumptions first? Such that a warning is returned for the case that the denominator also goes to 0 ?

I'm somewhat new to mathematica so there might be some more fundamental issues on how to use the software that I don't know yet. Any recommendations are highly appreciated.

• I think that this is a know problem with Mathematica. I don't know of any general workaround. I would be happy to be proven wrong. – Somos Oct 28 at 12:39