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) ===================================================================== I'm searching for myself... If I get back before I return, please make sure I stay here. =====================================================================