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MathGroup Archive 2005

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Re: Re: limit problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58953] Re: [mg58944] Re: limit problem
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Mon, 25 Jul 2005 01:12:09 -0400 (EDT)
  • References: <dbt3lm$sk4$1@smc.vnet.net> <42E2A56C.3050808@gmail.com> <200507240522.BAA14483@smc.vnet.net> <EA846B97-7BC1-4A29-935A-061C72C8ABC7@mimuw.edu.pl>
  • Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

The following is a guess:

Andrzej Kozlowski, I think you have found a reason why Simplify and
FullSimplify do not "pass assumptions". Since they do not hold their
arguments, passing assumptions would cause a "double evaluation".
(Always or usually) Returning conditional results means Limit may not
be as fast as it could be if it were specifically told which
conditions applied before it's called. Not wanting FullSimplify and
Simplify to Hold their arguments, WRI created Assuming, which has the
attribute HoldRest.

So Assuming allows for passing of assumptions & for Limit to "keep its speed".

On 7/24/05, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> I do not think there is any need for this. If Limit returned a
> conditional answer in the manner of Integrate with symbolic
> integration limits, then this problem would not arise. As it is,
> since Simplify and FullSimplify  evaluate their arguments what you
> would get with your suggested approach is a double attempted
> evaluation of Limit, first without the assumptions of Simplify and
> then again with the assumptions: hardly the most efficient way to go
> about this.
> 
> Since Integrate already returns conditional solutions applying
> Simplify will normally work the way you expect:
> 
> 
> 
> Simplify[Integrate[1/x, {x, a, b}], 0 < a < b]
> 
> Log[b/a]
> 
> There was no "passing of assumptions" involved and none is needed.
> 
> 
> 
> Andrzej Kozlowski
> 
> On 24 Jul 2005, at 07:22, Chris Chiasson wrote:
> 
> > As others have kindly demonstrated, Assuming is able to pass its
> > assumptions to Limit. I know that the second argument of Simplify and
> > FullSimplify is for assumptions. For this reason, I think WRI should
> > update FullSimplify and Simplify to pass their assumptions to Limit
> > and Integrate, etc. Is there a reason why they should not do so?
> >
> > On 7/23/05, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> >
> >> Chris Chiasson wrote:
> >>
> >>> Dear MathGroup,
> >>> Honestly, I see no reason why this should return "unevaluated"
> >>> instead of zero.
> >>>
> >>> FullSimplify[Limit[E^(-R t),t\[Rule]
> >>> Infinity],Infinity>R>0&&Element[R,Reals]]
> >>>
> >>> 5.2 on windows
> >>>
> >>> Regards,
> >>>
> >> Hi Chris,
> >>
> >> The following works:
> >>
> >> In[1]:=
> >> Limit[E^(-t), t -> Infinity]
> >>
> >> Out[1]=
> >> 0
> >>
> >> In[2]:=
> >> Limit[E^((-R)*t), t -> Infinity]
> >>
> >> Out[2]=
> >> Limit[E^((-R)*t), t -> Infinity]
> >>
> >> In[3]:=
> >> Assuming[R > 0, Limit[E^((-R)*t), t -> Infinity]]
> >>
> >> Out[3]=
> >> 0
> >>
> >> Best regards,
> >> /J.M.
> >>
> >>
> >
> >
> > --
> > Chris Chiasson
> > http://chrischiasson.com/
> > 1 (810) 265-3161
> >
> >
> 
> 



-- 
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161


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