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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>