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Re: A Problem with Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg87643] Re: A Problem with Simplify
• From: Alexey Popkov <popkov at gmail.com>
• Date: Tue, 15 Apr 2008 05:47:46 -0400 (EDT)
• References: <200804100612.CAA10423@smc.vnet.net> <ftmu6f$50v$1@smc.vnet.net>

On Apr 11, 9:50 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
> Simplify does not return conditional answers (in the form If[..]) and  
> I don't think it would be reasonable to expect it to do so.

The problem statement was initially wrong. The problem not in Simplify
but in Integrate!

Integrate may and MUST return conditions as it do it in other cases:
In[1]:= Integrate[Exp[-a x^2], {x, 0, Infinity}]
Out[1]= If[Re[a] > 0, Sqrt[Pi]/(2*Sqrt[a]), Integrate[E^(-(a*x^2)),
{x, 0, Infinity},
  Assumptions -> Re[a] <= 0]]

But it does not do it in many other cases loosing some answers:

On Apr 14, 1:43 pm, Alexey Popkov <pop... at gmail.com> wrote:
> On Apr 10, 10:14 am, "Kevin J. McCann" <Kevin.McC... at umbc.edu> wrote:
>
> Try the following:
> Integrate[Exp[(a - 1)*x], x] /. a -> 1
> Integrate[Cos[(a - 1)*x], x] /. a -> 1
> Integrate[(a - 1)^x, {x, -1, 0}] /. a -> 1
> Integrate[Cos[a x]/Sin[x], x] /. a -> 1
>
> There is the ONE underlying BUG! In some complicated cases this bug
> may result in random partial answers.

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