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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41680] Re: UH oh, integration of rational functions has a bug.
  • From: carlos at colorado.edu (Carlos Felippa)
  • Date: Fri, 30 May 2003 03:56:25 -0400 (EDT)
  • References: <bb4vr4$491$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Richard Fateman <fateman at cs.berkeley.edu> wrote in message news:<bb4vr4$491$1 at smc.vnet.net>...
> 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.

This might be related to a problem reported in the thread
"Integration Bug" of Dec 2002.  My post in that thread was

=============================================================
The Integrate behavior seems to be connected to lexicographic 
ordering of the variables. For example (from 4.2):

ClearAll[x,z,a,b];
Print[Integrate[Cos[x+z]/(x+z)^2,{x,-Infinity,Infinity}] //InputForm];
Print[Integrate[Cos[x+z]/(x+z)^2,{z,-Infinity,Infinity}] //InputForm];
Print[Integrate[Cos[x+z]/(x+z)^3,{x,-Infinity,Infinity}] //InputForm];
Print[Integrate[Cos[x+z]/(x+z)^3,{z,-Infinity,Infinity}] //InputForm];
Print[Integrate[Sin[x+a+b]/(x+a+b),{x,-Infinity,Infinity}] //InputForm];
Print[Integrate[Sin[x+a+b]/(x+a+b),{a,-Infinity,Infinity}] //InputForm];
Print[Integrate[Sin[x+a+b]/(x+a+b),{b,-Infinity,Infinity}] //InputForm];

-Pi
0

-CosIntegral[-z]/2 + CosIntegral[z]/2
0

0
Pi - SinIntegral[-b - x] - SinIntegral[b + x]
0


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