Re: how to explain this weird effect? Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg46290] Re: how to explain this weird effect? Integrate*From*: nma124 at hotmail.com (steve_H)*Date*: Fri, 13 Feb 2004 21:56:55 -0500 (EST)*References*: <200402121216.HAA12039@smc.vnet.net> <c0hhvb$lgl$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message news:<c0hhvb$lgl$1 at smc.vnet.net>... > It's not hard to explain if you actually look at the output you get > before substituting values for n and m. > hi; I think you missed my point. As I said , I do see why Mathematica complained. It is clear from the ouput. and I know that taking the limit will give the correct result I wanted to see. But this is not the point. My point is that mathematically speaking, it should not make a difference when one does the substitution. But using a computer algebra package, it made a difference. I am not looking for a way around this, I wanted to talk about the user not having to work around these limitations. So, the question is that, why did not Mathematica perform the Limit operation itself to give the correct answer? Look at this example: r = 1/a r /. a -> 0 Here Mathematica complains becuase of 1/0 problem, but still returns ComplexInfinity as the correct answer. Now when I type Limit[r, a -> 0] no complaint is given, and infinity is the answer again. mathematically speaking, 1/a when a=0, is the same as Limit[1/a , a->0] So, the final answer should not be different. But when I typed r = Integrate[Sin[m x] Sin[n x], {x, 0, 2 Pi}] r /. {n -> 2, m -> 2} Mathematica complained about 1/0 output, BUT also did NOT give the answer. So, here we have 2 examples, both have 1/0 problem, in both cases Mathematica complained about 1/0, but in one case it still gave the final answer, and in the second case it did not. to conclude, Mathematica should do one of 2 things: 1. complain about 1/0, but internally apply the Limit to see if it can obtain an answer. 2. not complain about 1/0 if applying the Limit will resolve it, else only then complain about 1/0 and give no answer. thanks, Steve

**Follow-Ups**:**Re: Re: how to explain this weird effect? Integrate***From:*Daniel Lichtblau <danl@wolfram.com>

**Re: Re: how to explain this weird effect? Integrate***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

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**Re: how to explain this weird effect? Integrate**

**Re: Re: how to explain this weird effect? Integrate**