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Limit, Series and O

• To: mathgroup at smc.vnet.net
• Subject: [mg14569] Limit, Series and O
• From: RENZONI_FERRUCCIO <RENZONI at physnet.uni-hamburg.de>
• Date: Fri, 30 Oct 1998 03:07:39 -0500
• Sender: owner-wri-mathgroup at wolfram.com

Dear All,

I am recently programming using many times functions as  Limit, Series
and the "big O" O[x]^k expression.

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. So I am trying to
"redefine" the various commands "Sqrt,Log,Power..." and so on in  order
that if I define 

Sign[a] ^= 1

this really affects the result (it is in fact clear that in a long 
calculation simply writing /. Sqrt[a^2] -> a will not solve the
problem).

The question is: did some of you already tried (and maybe succeeded) in
redefine the various funtions in the way to make them usable in the
real domain? I already wrote a first draft of package (obviously
Mathematica gets really slow) and I would like discuss with somebody
with some experience.

Please e-mail me.

Thanks a lot,

Ferruccio