Re: Problem with Simplify and Assumptions
- To: mathgroup at smc.vnet.net
- Subject: [mg119259] Re: Problem with Simplify and Assumptions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 27 May 2011 06:13:16 -0400 (EDT)
On 26 May 2011, at 01:32, ADL wrote:
> On 25 Mag, 11:57, Cisco Lane <travl... at yahoo.com> 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.
>
> To look around Andrzej Kozlowski's suggestions, I observe that Reduce
> seems to be insensitive to $Assumptions or Assuming, which is strange
> (to me) and not mentioned in the help.
>
> In any case,
>
> In[]:= Reduce[m>=1 && s>0 && Exp[(1-2*m)*s]<1]
> Out[]= m>=1 && s>0
>
> which is a rather unusual way to express that the condition on Exp is
> redundant (and thus disappeared).
>
> In fact:
>
> In[]:= Reduce[m >= 1 && s > 0 && Exp[(1 - 2*m)*s] >= 1]
> Out[]= False
>
> So, it seems to be easier to get a False than to get a True.
>
> ADL
>
Reduce is indeed insensitive to $Assumptions, but that is reasonable because you can include them in the expression you wish to reduce. Also remember that Reduce does just what its name suggests - it reduces. The reason why you do not get the answer True in the first case but get False in the second is that the second expression can't be reduced to anything else that would suffice to make the expression that is being reduced True. The first case can.
If you want the answer True using Reduce you have to express what you want to reduce in terms of quantifiers. For example,
Reduce[ForAll[{m, s}, m >= 1 && s > 0, Exp[(1 - 2*m)*s] < 1]]
True
Andrzej Kozlowski