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MathGroup Archive 2007

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Re: our good (?!) friend RootSum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75048] Re: our good (?!) friend RootSum
  • From: "Michael Weyrauch" <michael.weyrauch at gmx.de>
  • Date: Sun, 15 Apr 2007 05:11:40 -0400 (EDT)
  • References: <evpoas$698$1@smc.vnet.net>

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 series 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 antiderivative 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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