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