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Re: Simplify with NestedLessLess?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106543] Re: Simplify with NestedLessLess?
  • From: Albert Retey <awnl at gmx-topmail.de>
  • Date: Fri, 15 Jan 2010 07:00:35 -0500 (EST)
  • References: <himsqd$jd0$1@smc.vnet.net>

Hi,

> Please excuse if this has been answered before, but I can't find it.
> 
> Is there some way to do a Simplify with assumptions using a 
> NestedLessLess or something similar? For example:
> 
> d=a+b
> Simplify[d,NestedLessLess[a,b]]
> 
> Answer is:
> a+b
> 
> Answer should be:
> b
> 

I don't think that Simplify does provide the functionality you are
searching for. It is a combination of replacing and Series that will do:

expr=a+b

Normal[Series[expr /. {a -> b*eps}, {eps, 0, 0}]]

the idea is to first rewrite the expression you want to "simpify" in
terms of the quantity that will be small, that is eps=a/b in this case,
then you can use Series to expand the result.

Using Normal will get rid of the O[eps] term, which you often want to
get rid of. Further simplification with Simplify might then of course
also possible for more complicated cases...

I think that approach should also work with more compicated expressions,
but there are probably limits...

hth,

albert


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