       Re: Another Simplify Idiosyncrasy

• To: mathgroup at smc.vnet.net
• Subject: [mg26627] Re: Another Simplify Idiosyncrasy
• From: Will Self <wself at msubillings.edu>
• Date: Sat, 13 Jan 2001 22:36:08 -0500 (EST)
• References: <91sbmn\$8k9@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I tried FullSimplify[uc] and it succeeded in giving the appropriate
simplification.  FullSimplify takes considerably more time than
Simplify.

Will Self

In article <91sbmn\$8k9 at smc.vnet.net>,
"A. E. Siegman" <siegman at stanford.edu> wrote:
> 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 + a b + a b + . . .  + 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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```

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