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Re: Mathematica integration Vs Sympy

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  • Subject: [mg130568] Re: [mg130564] Mathematica integration Vs Sympy
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 22 Apr 2013 03:10:28 -0400 (EDT)
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Mathematica certainly seems to be assuming a != 1, since of course the displayed output is undefined when a = 1.

However:

   1/(x*(1 - a*(1 - x))) /. a -> 1
1/x^2
   Integrate[%, x]
-1/x

which is correct. And:

   Limit[(Log[1 + a (-1 + x)] - Log[x])/(-1 + a), a -> 1]
(-1 + x)/x

which differs from -1/x by a constant.

The real question should be, I think: why does Mathematica generate conditions on parameters for some integrals but not others?


On Apr 21, 2013, at 5:16 AM, Brentt <brenttnewman at gmail.com> wrote:

> The result:
>
> In[0]: Integrate[1/(x*(1 - a*(1 - x))), x]
> Out[0]: (Log[1 + a (-1 + x)] - Log[x])/(-1 + a)
>
> Seems to be true for all complex a and x . Why do you think it assumes a>1?
>
>
> On Sat, Apr 20, 2013 at 2:42 AM, Sergio R <sergiorquestion at gmail.com> wrote:
>
>> Hello all,
>>
>>   Just for fun a put an integral I was doing via mathematica
>> WolframAlpha
>> [
>> =
http://www.wolframalpha.com/input/?i=Integrate[1%2F%28x*%281-a*%281-x%29%29%29%2Cx]
>> ]
>> into the online sympy [ http://live.sympy.org/ ] console
>> the following:
>>
>> a = Symbol('a'); g = 1/(x*(1-a*(1-x))) ; u=simplify(integrate(g,x))
>>
>> Then, to display the result, at the sympy ">>>" prompt, type u
>> and hit return.
>>
>>  To my surprise,  sympy seems to give the right result without any
>> assumption, while mathematica's result seems to assume a>1, which is
>> not specified. Also for this case (a>1) sympy gives an extra constant
>> which is not present in the mathematica result.
>>
>> Is there a way to make mathematica to output a general result like
>> sympy
>> in this case?

---
Murray Eisenberg                                    murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
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