Re: Limit, Series and O

*To*: mathgroup at smc.vnet.net*Subject*: [mg14604] Re: [mg14569] Limit, Series and O*From*: BobHanlon at aol.com*Date*: Mon, 2 Nov 1998 01:51:11 -0500*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 10/30/98 6:49:21 AM, RENZONI at physnet.uni-hamburg.de writes: >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. > {Sqrt[a^2], Sqrt[b^2]^n, Log[c^2]} {Sqrt[a^2], (b^2)^(n/2), Log[c^2]} If you know that the variables are all positive real numbers, then just use PowerExpand: % // PowerExpand {a, b^n, 2*Log[c]} Bob Hanlon