Re: A Problem with Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg87536] Re: A Problem with Simplify*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Sat, 12 Apr 2008 07:00:47 -0400 (EDT)*References*: <200804100612.CAA10423@smc.vnet.net> <4CB3309B-D747-450B-B790-C4784DD5719F@mimuw.edu.pl> <47FE0418.2000403@umbc.edu> <ftncra$8bc$1@smc.vnet.net>

Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > I am not convinced (by the way, this very question with the same > example was discussed here quite recently). > > The usual argument is that Mathematica adopts a "generic" approach, > whatever that means. I don't much like this way of thinking because > such a concept of "genericity" is hard to formalize. Instead I have my > own way of thinking about this, which at least satisfies me on this > score. Essentially, I think of all Mathematica expressions as > belonging to some formal algebraic system, a "partial algebra" (you > can formally add and multiply most expressions although not quite all, > and you can even multiply then by "scalars"). There are certain "built > in" relations that hold between certain expressions in the algebra and > other relations can be introduced by the user. Any two different > symbols are always different, unless there is a built in relationship > or a user defined relationship that says otherwise. Hence the answer > returned by > > Assuming[Element[m | n, Integers], > Simplify[Integrate[Sin[(m*Pi*x)/L]*Sin[(n*Pi*x)/L], {x, 0, L}]]] > > 0 > > is completely correct in my interpretation and not just "generically > correct" because in my interpretation m and n are not equal simply by > virtue of being different Mathematica expressions. On the other hand: > > Assuming[Element[m | n, Integers] && m == n, > Simplify[Integrate[Sin[(m*Pi*x)/L]*Sin[(n*Pi*x)/L], {x, 0, L}]]] > L/2 > > is also O.K. because we performed the simplification with the user > introduced relation m==n. That's not the reason. Rather, it's because we performed the _integration_ with the assumption that m==n. (Note that if the integration had been done without that assumption and then that result had been simplified with the assumption, we would have gotten Indeterminate.) > So, with my interpretation (different symbols are always different > quantities unless stated otherwise) all is well. Not in my opinion. If both m and n are 0, then obviously the value of the integral must be 0, rather than L/2. (BTW, I had not noted that fact in my previous response to Kevin.) In my previous post, I gave a result which is valid for all real values of the parameters: L/2 (Sinc[(m - n) Pi] - Sinc[(m + n) Pi]) David W. Cantrell

**References**:**A Problem with Simplify***From:*"Kevin J. McCann" <Kevin.McCann@umbc.edu>

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**Re: A Problem with Simplify**

**Re: A Problem with Simplify**