A problem with getting a coefficient

Question

I try

Coefficient[E^(I a (t - b)), E^(I a t)]

and expect the output

E^(-I a b)

but in fact I get 0.

What should be corrected in my code? I cannot solve this problem for a week.

Since the documentation on Coefficient[] speaks of polynomials only, why do you expect anything sensible? — Igor Rivin, Commented Oct 6, 2014 at 17:19
I am sure it is possible, but it may be a little painful, the question is: what is it you are really trying to do? — Igor Rivin, Commented Oct 6, 2014 at 17:22
I need to collect the coefficients of exponents with particular powers e.g. E^(I a t), E^(I b t) and so on. Now I see that it is not a Coefficient[] but any other method. Somehow I did not pay attention that Coefficient[] processes only polynomials. — Vladimir, Commented Oct 6, 2014 at 17:24
Possibly you can get the sort of behavior you want by using TrigExpand[ExpToTrig[expression]] and the trying to extract the coefficients of Cos[a*t] and Sin[a*t]. Another approach would be to recast as an explicit polynomial, by converting Exp[I*a*t] to a "variable" eiat and likewise for Exp[I*a*b]. — Daniel Lichtblau, Commented Oct 6, 2014 at 17:54

RunnyKine · Accepted Answer · 2014-10-06 19:11:52Z

2

Coefficient[E^(I a (t - b)) // ExpandAll, E^(I a t)]

(* Exp[-I a b] *)

RunnyKine

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answered Oct 6, 2014 at 19:10

Fred Simons

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– RunnyKine
Commented Oct 6, 2014 at 19:48

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