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Re: Problem with Simplify and Assumptions

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  Re: Problem with Simplify and Assumptions Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-05-25 10:59 +0000

#2706 — Re: Problem with Simplify and Assumptions

On 25 May 2011, at 11:57, Cisco Lane wrote:

> I am wondering how to get the last line to say "True"
>
> In[1]:= $Assumptions = {m >= 1, s > 0}
>
> Out[1]= {m >= 1, s > 0}
>
> In[3]:= Simplify[(1 - 2*m)*s < 0]
>
> Out[3]= True
>
> In[4]:= Simplify[Exp[(1 - 2*m)*s] < 1]
>
> Out[4]= E^s < E^(2 m s)
>
> Thanks,
> Frank L.

I don't think you can because Simplify (and FullSimplify) does not (at present, anyway) use algorithms that can solve inequalities involving exponentials. This particular case is, of course, very easy to do by hand, but more general ones are not and the algorithms needed (when available) are quite complicated. Still, Reduce can solve this (and many much more complicated cases too):

Reduce[Exp[(1 - 2*m)*s] < 1, {m, s}, Reals]

(m < 1/2 && s < 0) || (m > 1/2 && s > 0)

so it would be possible in principle for Simplify to perform this simplification. The fact that it does not to so is probably due to the slowness of these methods in more difficult cases (although that does not seem to be reason applicable to FullSimplify).

Andrzej Kozlowski

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