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MathGroup Archive 2000

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Another Simplify Idiosyncrasy

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26458] Another Simplify Idiosyncrasy
  • From: "A. E. Siegman" <siegman at stanford.edu>
  • Date: Thu, 21 Dec 2000 01:51:59 -0500 (EST)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

The following sum (which arises in working with Discrete Fourier 
Transforms)

   uc[M_] := (1/M) Sum[  a[n] b[m] Exp[I (n k - m k + k) 2 Pi/M ], 
                    {n, 0, M - 1}, {m, 0,  M - 1}, {k, 0, M - 1}]  

should Simplify to the general form

   a[M] b[0] + a[0] b[1] + a[1] b[2] + . . .  + a[M-1] b[M]

That's what happens with M = 1, 2, 3, 4, 6, 8, 9 and 12 --

--but with M = 5, 7, 10 and 11 the factors that are equally spaced 
around the unit circle in the complex plane don't simplify out and one 
gets pages of terms with factors of (-1)^(n/m).  Apparently Mathematica can find 
these roots for some rational fractions n/m but not others.

(Not a complaint, just noting the point; I understand that Simplify'ing 
is a complex and not always universally successful process.)


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