Internal variable in Sum inside a function

Asked Nov 05 '22 at 09:29

Active Nov 05 '22 at 13:05

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I am writing a simple function which performs a sum, but run into an unexpected answer.

f[n_]:=Sum[n-m, {m, 1, 10}]
f[1] (* gives -45 *)
f[m] (* gives 0; didn't expect this *)

It appears that when fed an unassigned m, m coincides with the iteration variable m, which if of course is undesired. I can change the iteration variable to something like $m. But is there better practice to force the iteration variable to be completely local? Perhaps I should use Module or Block?

(Module seems to do the job)

edited Nov 05 '22 at 13:05

user64494

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asked Nov 05 '22 at 09:29

Lelouch

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This is documented, see "Details and Options": The iteration variable is effectively localized using Block, which leads to the behavior that you describe. Yes, you can use f[n_]:=Module[{m},Sum[n-m,{m,1,10}]]. You write that the default behavior "of course is undesired" but if you think about it... there are cases where this is exactly the behavior that some users expect. See this for example. – user293787 Nov 05 '22 at 09:47
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Does this answer your question? Unexpected result with sums in set delayed functions – user64494 Nov 05 '22 at 13:04
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There is a metaphor from physics to understand the scoping of Module (With) vs. Block: Module localizes variables in a spatial way while Block in a temporal way. – Lacia Nov 05 '22 at 19:11
@user64494 Yes it does. Thanks! – Lelouch Nov 06 '22 at 02:51

Internal variable in Sum inside a function

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