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.)

```

• Prev by Date: Re: Mathematica - Init Display problem
• Next by Date: Re: Integral involving erfc and j1
• Previous by thread: Re: question
• Next by thread: Re: Another Simplify Idiosyncrasy