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MathGroup Archive 2007

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Re: our good (?!) friend RootSum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75078] Re: our good (?!) friend RootSum
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Mon, 16 Apr 2007 20:11:28 -0400 (EDT)
  • References: <evpoas$698$1@smc.vnet.net><evsqoi$119$1@smc.vnet.net>

Thanks a lot for interest.

Faithfully
Dimitris

=CF/=C7 Michael Weyrauch =DD=E3=F1=E1=F8=E5:
> Hello
>
> well, I think, at this stage, we just have to live with the fact that this
> type of integrals is not evaluated correctly by Mathematica, but other CAS
> -- if we like it or not-- do that easily. It 's up to the developers
> to fix that. And I would be surprised if it wasn't fixed in the upcoming =
version.
>
> You my find it interesting to also modify the Series command using
>
> Unprotect[Series];
> Series[a___] := Null /; (Print[series[a]]; False)
>
> and then integrate any of the integrals you discussed recently in your se=
ries of threads on integration (including the one of this
> thread).
> >From the rather lengthy output (in Mathematica 5.2) we see the following:
>
> 1) Series[] is indeed explicitly called along the way expanding the antid=
erivative around Infinity.
>
> 2) The RootSum[] is expanded out and Root objects are inserted explicitly=
. So RootSum isn't the offender.
>
> 3) Internally the results are expressed by a new variable
>
>  Integrate`NLtheoremDump`newx
>
> (Hopefully this is not meant to read as "Dump the Newton-Leibnitz theorem=
" ;=), but at least we are definitly convinced now that the
> NL theorem is used for integration.)
>
> 4) If you calculate the series expansion at Infinity using the output of =
the above modification of Series you see that this also is
> done correctly. If you just replace the variable  Integrate`NLtheoremDump=
`newx with Infinity in this output of Series[ ] the correct
> limit 0 is obtained. So it appears that also Series[] is doing everthing =
just fine.
>
> 5) Why Mathematica then doesn't finally use this easily obtained limit to=
 return the evaluated Integral remains mysterious to me.
>
> I suggest, let's wait and see that these somewhat mysterious effects will=
 disappear...
>
> Regards    Michael



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