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Re: UH oh, integration of rational functions has a bug.

• To: mathgroup at smc.vnet.net
• Subject: [mg41666] Re: [mg41650] UH oh, integration of rational functions has a bug.
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Fri, 30 May 2003 03:56:15 -0400 (EDT)
• Organization: computer science division, UC Berkeley
• References: <200305291214.IAA03988@smc.vnet.net> <3ED6182A.2020809@attbi.com>
• Sender: owner-wri-mathgroup at wolfram.com

Murray Eisenberg wrote:
> I see nothing strange here: you have a fifth degree polynomial in the 
> denominator (when a -> c) whose roots cannot be found in closed form. 
> When a -> 10, they can be, so a partial fraction decomposition can proceed.

The answer for a=c  should be the same except for
c substituted for a.   It isn't.  It has Integrate`V[1][6] in it.

This strange item only appears the second (and later) time, I think,
which is why I gave the sequence of calculations.

As for the answer generically, it would be nice if the result for 
general "a"  also covered the answer for a=10. Mathematica tends to
give answers with a hidden caveat, namely that for some unknown subset
of parameter values the answer is wrong. Sometimes the answer is wrong
for ALL values of the parameter. (Construct an answer false for a>=0 and
another one false for a<0. Add them). It is a thought that in
the constrained circumstances here, something more correct could be
devised.


RJF




> 
> 
> Richard Fateman wrote:
> 
>> Mathematica 4.1
>>
>> In[1]:=  1 + 5*x + a*x^2 + 10*x^3 + 5*x^4 + x^5
>>
>>
>> Integrate[1/%, x]
>>
>> %1 /. a -> 10
>>
>> Integrate[1/%, x]
>>
>> %1 /. a -> c
>>
>> Integrate[1/%, x]
>>
>> InputForm[%]    ===>
>>
>> RootSum[1 + 5*#1 + c*#1^2 + 10*#1^3 + 5*#1^4 + #1^5 & ,
>>    Log[x - #1]/(5 + 30*#1^2 + 20*#1^3 + 5*#1^4 +
>>       2*#1*Integrate`V[1][6]) & ]
>>
>> WHAT is THIS ^^^^^^^^^^^^^^^ ??   and why did it not
>> appear in the identical problem where there was an "a"
>> instead of a "c" ??
>>
>> It is somehow dependent on the sequence of commands.
>>
>>
>>
> 

• References:
  • UH oh, integration of rational functions has a bug.
    • From: Richard Fateman <fateman@cs.berkeley.edu>