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 ____________________________________________________________________