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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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

**References**:**Mathematica integration Vs Sympy***From:*Sergio R <sergiorquestion@gmail.com>

**Re: Mathematica integration Vs Sympy***From:*Brentt <brenttnewman@gmail.com>