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Error in FractionalPart?

• To: mathgroup at smc.vnet.net
• Subject: [mg102411] Error in FractionalPart?
• From: Filippo Miatto <miatto at gmail.com>
• Date: Sat, 8 Aug 2009 04:39:18 -0400 (EDT)

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

• Follow-Ups:
  • Re: Error in FractionalPart?
    • From: DrMajorBob <btreat1@austin.rr.com>