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Re: Mathematica integration Vs Sympy
*To*: mathgroup at smc.vnet.net
*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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*References*: <20130420094229.B63996A64@smc.vnet.net> <20130421091626.26FB96AC3@smc.vnet.net>
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)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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