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Re: Limit, Series and O


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


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