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Re: Limit, Series and O
*To*: mathgroup at smc.vnet.net
*Subject*: [mg14612] Re: Limit, Series and O
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Wed, 4 Nov 1998 13:46:44 -0500
*Organization*: University of Western Australia
*References*: <71bkon$pua@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
RENZONI_FERRUCCIO wrote:
> I work in the complex plane, but all my variable are real. It has soon
> become clear that the answer I get running the commands Limit, Series
> and O[x]^k are not correct because I can't define reality and
> (sometimes) positivity of my variables. So for example if I have "a"
> positive and I have as a result of a computation
>
> x / ( a - Sqrt[a^2] + x) + O[x]^2
>
> and I ask to Simplify, I don't get the result I want.
The result you "want" is, of course
In[1]:= (x / ( a - Sqrt[a^2] + x)//PowerExpand) + O[x]^2
Out[1]=
2
1 + O[x]
and, as you've observed, you don't get what you want if you change the
evaluation order:
In[2]:= x / ( a - Sqrt[a^2] + x) + O[x]^2//PowerExpand
Out[2]=
2
ComplexInfinity x + O[x]
So, the moral of this story is that you must algebraically simplify your
expression before you compute the series. Basically, the series
expansion and simplification do not commute.
> So I am trying to "redefine" the various commands "Sqrt,Log,Power..."
I cannot see how this will resolve your problem. I understand that you
want these simplifications to take place automatically, but in general
(for many variables), I don't think this is possible.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
____________________________________________________________________
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