Re: A Problem with Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg87456] Re: A Problem with Simplify*From*: Alexey Popkov <popkov at gmail.com>*Date*: Fri, 11 Apr 2008 01:42:26 -0400 (EDT)*References*: <ftkb7f$a9m$1@smc.vnet.net>

This seems to be very strange: Mathematica 6.0 for Microsoft Windows (32-bit) Copyright 1988-2008 Wolfram Research, Inc. In[1]:= Imn = Integrate[Sin[(m*Pi*x)/L]*Sin[(n*Pi*x)/L], {x, 0, L}]; In[2]:= Imn // InputForm Out[2]//InputForm= (L*n*Cos[n*Pi]*Sin[m*Pi] - L*m*Cos[m*Pi]*Sin[n*Pi])/ (m^2*Pi - n^2*Pi) In[3]:= Simplify[Imn, Assumptions -> n == m] L n Cos[n Pi] Sin[m Pi] - L m Cos[m Pi] Sin[n Pi] Simplify::infd: Expression ------------------------------------------------- simplified to 2 2 m Pi - n Pi Indeterminate. Out[3]= Indeterminate But: In[4]:= Integrate[Sin[(n*Pi*x)/L]*Sin[(n*Pi*x)/L], {x, 0, L}] // InputForm Out[4]//InputForm= (L*(2 - Sin[2*n*Pi]/(n*Pi)))/4 This is a bug! :( Recently I also have found another strange bug in Simplfy (not so dangerous): FullSimplify[Sin[x]*Cos[x]] gives Sin[x]*Cos[x] instead Sin[2*x]/2. The workaround is FullSimplify[2*Sin[x]*Cos[x]]/2. Kevin J. McCann wrote: > I have the following rather simple integral of two sines, which should > evaluate to zero if m is not equal to n and to L/2 if they are the same. > > The following is just fine > > Imn = Simplify[Integrate[ > Sin[(m*Pi*x)/L]* > Sin[(n*Pi*x)/L], > {x, 0, L}]] > > > However, if I specify that m and n are integers, I only get the > "general" solution of zero, i.e. when m and n are not equal. > > Imn = Simplify[Integrate[ > Sin[(m*Pi*x)/L]* > Sin[(n*Pi*x)/L], > {x, 0, L}], > Element[m, Integers] && > Element[n, Integers]] > > The workaround is obvious in this case, but shouldn't Mathematica give multiple > answers? Perhaps something similar to what it already does with Integrate? > > Kevin > -- > > Kevin J. McCann > Research Associate Professor > JCET/Physics > Physics Building > University of Maryland, Baltimore County > 1000 Hilltop Circle > Baltimore, MD 21250

**Follow-Ups**:**Re: A Problem with Simplify***From:*Alexey Popkov <popkov@gmail.com>

**Re: Re: A Problem with Simplify***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>