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MathGroup Archive 2002

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RE: RE: Re: Q: Simplify with "muchless"assumptions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35682] RE: [mg35657] RE: [mg35622] Re: [mg35600] Q: Simplify with "muchless"assumptions
  • From: "DrBob" <majort at cox-internet.com>
  • Date: Thu, 25 Jul 2002 04:46:38 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

OK, if "x is much less than y" means x/y->0, then let r be that ratio
and the original function transforms into 

F[x , y, w, z]==F[r y, y, w, z]

If r->0 in this expression, that's

Limit[F[r y, y, w, z], r->0]

If x=0 is a non-removable singularity of F, the Limit as r->0 will
depend on y (if it exists).

If F is continuous at x=0 it's just F[0, y, w, z].

If F has a removable singularity there, it's Limit[F[x, y, w, z], x->0].

Bobby

-----Original Message-----
From: Eric L. Strobel [mailto:fyzycyst at comcast.net] 
To: mathgroup at smc.vnet.net
Subject: [mg35682] Re: [mg35657] RE: [mg35622] Re: [mg35600] Q: Simplify with
"muchless"assumptions

on 7/24/02 2:06 AM, DrBob at majort at cox-internet.com wrote:

> When you say, "x is much less than y", do you mean close to 0?  Or
close
> to -Infinity?  In either case, there's no good definition of
"simplify"
> unless you mean to take the Limit, and that only works if the function
> has a limit at 0 or -Infinity.  You can use Limit or you can simply
> substitute x->0.
> 
> Be clear on what you want, and I think the solution will become
obvious.
> 
> Bobby
> 
> -----Original Message-----
> From: Xuguang(Heather) Zhang [mailto:xuguang_zhang at hotmail.com]
To: mathgroup at smc.vnet.net
> Subject: [mg35682] [mg35657] [mg35622] Re: [mg35600] Q: Simplify with "much
less"
> assumptions
> 
> 
> AW: [mg35600] Q: Simplify with "much less" assumptionsThank you, bode.
> Maybe the last example I gave is too simplified. In fact, the problem
I
> always meet with is as follows:
> F(x,y,w,z) is a function of x,y,w and z where x,y,w and z are greater
> than zero. I want to simplify F(x,y,w,z) under the assumption that x
is
> much less than y.
> Can you please tell me how to do that? Thank you.
> 
> ----- Original Message -----
> From: Matthias.Bode at oppenheim.de
To: mathgroup at smc.vnet.net
> Sent: Monday, July 22, 2002 8:48 AM
> Subject: [mg35682] [mg35657] [mg35622] AW: [mg35600] Q: Simplify with "much
less"
> assumptions
> 
> 
> Hello Heather,
> 
> try:
> 
> 1 + x^2 /. {x -> 0}
> 
> It will give you the 1 you wish.
> 
> Best regards,
> Matthias Bode.
> 
> Von: Xuguang(Heather) Zhang [mailto:xuguang_zhang at hotmail.com]
> Gesendet: Montag, 22. Juli 2002 08:11
> An: mathgroup at smc.vnet.net
> Betreff: [mg35600] Q: Simplify with "much less" assumptions
> 
> 
> 
> 
> Hello, everybody,
> 
> I have one question regarding simplify answer with assumptions. For
> example, I have "1+x^2". The assumptions is  x is much much less than
> 1.
> Therefore x^2 can be neglected under the above assumption. What I get
> after simplification should be "1" only. Can anybody tell me how do
> this
> in Mathematica? It seems there is no "much less" or "much greater"
> symbol in Mathematica. Thank you all.
> 
> Heather
> 

I think, from the general usage of the term "much less than", at least
as
far as my experience, that the correct interpretation is:

x/y -> 0

This, of course, also suggests a way to handle the problem.  If Heather
can
recast the problem from F(x,y,w,z) to F(x/y,w,z), and then evaluate the
desired expression with the limit ( desiredExpression /. {x/y -> 0} ),
then
the problem should be solved.  Or did I miss something?

- Eric.

-- 

Eric Strobel (fyzycyst at NOSPAM^mailaps.org)

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