       Re: RE: RE: Question about Replace

• To: mathgroup at smc.vnet.net
• Subject: [mg35733] Re: [mg35713] RE: [mg35696] RE: [mg35670] Question about Replace
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sun, 28 Jul 2002 03:32:04 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> On Saturday, July 27, 2002, at 07:43  PM, Allan Hayes wrote:
>
> "Xuguang(Heather) Zhang" <xuguang_zhang at hotmail.com> wrote in message
> news:ahr0mf\$l20\$1 at smc.vnet.net...
> Hi, Bob,
>
> I tried ReplaceRepeated, however, I got the following answer:
> x+y+z/(x+y)+e^(x+y)+(w*x)+y//. x+y->x
>
> e^x+x+(w*x)+2y+z/x
>
> In fact, there is still one more (x+y) term if we rewritten the answer.
> That
> is e^x+(x+y)+y+(w*x)+z/x. Do you know how to get rid of it? Thanks.
>
> Heather,
>
> Use Simplify with the assumption x+y=x:
>
>     Simplify[x + y + z/(x + y) + e^(x + y) + w*x + y, {x + y == x}]
>
>         e^x + x + w*x + z/x
>
> In other circumstances we may have to give more help Simplify (or
> FullSimplify).
> Please check possiblities in the Help Browser.
>
>
> Allan
>
> ---------------------
> Allan Hayes
> Mathematica Training and Consulting
> Leicester UK
> www.haystack.demon.co.uk
> hay at haystack.demon.co.uk
> Voice: +44 (0)116 271 4198
> Fax: +44 (0)870 164 0565
>

The problem is that  the assumption {x+y==x} is exactly the same as
{y==0} ,e.g.  :

Simplify[y + z/(x + y) + e^(x + y) + w*x + y, {x + y == x}]

e^x + w*x + z/x

which presumably is not what was wanted (if it was than it is much
simpler just to substitute y -> 0}? Quite frankly, the original request
does not make any mathematical sense at all, at least to me. For a
start, it is hard to imagine under what conditions it is reasonable to
substitute x for x+y if y is not 0! In addition, what does it mean to
say "there is still one more term if we rewrite the answer"? If x+2y
"contains" x+y because it can be rewritten as (x+y) + y than so does
x+1/2 y since that can be re-written as (x+y)-1/2y and so does any
expression. The kind of magic that seems to asked for cannot be achieved
either by syntactic pattern matching (because of the need to interpret
"contains") or by Simplify which uses wll defined mathematical rules
(and in this case the only well defined rule is y==0).

Actually on second thoughts I began to suspect that this question is
related to another one posted by Heather, concerning simplifying
expressions in which x is "much larger than" y. I am not at all sure if
a sensible calculus of this kind can be developed but obviously Simplify
will not do this. Moreover, it seems to me that under any sensible
interpretation of "much larger  than", if x+y is approximately x, then
so is x+2y, and so on. In other words, x is essentially Infinity in
relation to y. If so, there is no reason then why a single y should be
left int the answer and  x+ (any numeric quantity) y ought to be
replaced by just x (without at the same time assuming that y is zero).
This sort of thing may perhaps  be achieved with the following rule:

x + y + z/(x + y) + e^(x + y) + e^y + w*x + y//.
x + (k:(_?NumericQ):1)*y -> x

e^x + e^y + x + w*x + z/x

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

```

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