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Re: Error in FractionalPart?

• To: mathgroup at smc.vnet.net
• Subject: [mg102440] Re: [mg102411] Error in FractionalPart?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 9 Aug 2009 06:07:07 -0400 (EDT)
• Reply-to: hanlonr at cox.net

I don't see the problem on my system

$Version

7.0 for Mac OS X x86 (64-bit) (February 19, 2009)

F[x_] := 2 Pi * FractionalPart[x/(2 Pi)]

H[x_] := 2 Pi * FractionalPart[-x/(2 Pi)] + 2 Pi

FullSimplify[(F[x]^2) (H[x]^2)]

16*Pi^4*(FractionalPart[x/(2*Pi)] - 1)^2*
   FractionalPart[x/(2*Pi)]^2


Bob Hanlon

---- Filippo Miatto <miatto at gmail.com> wrote: 

=============
Dear all,
I have a little issue while fullsimplifying an apparently simple expression.
After defining the functions

F[x_] := 2 \[Pi] FractionalPart[x/(2 \[Pi])]
H[x_] := 2 \[Pi] FractionalPart[-x/(2 \[Pi])] + 2 \[Pi]

I plot the function (F[x]^2)(H[x]^2) between 0 and 4pi and i get
something like a double 'gaussian' bell (it's not gaussian, it is just
to picture it).
Then I enter

FullSimplify[(F[x]^2)(H[x]^2)]

and I get as a result

16 \[Pi]^4 FractionalPart[x/(2 \[Pi])]^4

which when plotted does not give the same plot, actually it's very different.
What am I (or is mathematica) doing wrong?

Thank you in advance,
Filippo