       RE: finding independent variable groups

• To: mathgroup at smc.vnet.net
• Subject: [mg32439] RE: [mg32406] finding independent variable groups
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 20 Jan 2002 04:28:17 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Ioan,

Seeing Allan's reply reminded me about a package at my web site which Ted
Ersek helped me write and which also contains ideas contributed to
MathGroup, some by Allan.

The package, among other things, allows you to find and use what I call
extended positions. An extended position is a set of level parts in a
containing subexpression. The package has routines for finding extended
positions and using them. I made your example a little more complicated to
illustrate the use.

Needs["Algebra`ExpressionManipulation`"]

expr = x w/y E^(x z/y);

pos = ExtendedPosition[expr, x/y];
{eP[{1, 2}, {1, 2}], eP[{}, {3, 4}]}

Extended positions are wrapped in eP and interpreted as eP[containing part,
level subparts]. We can then use these positions. For example,

ReplacePart[expr, q, pos]
E^(q*z)*q*w

David Park

> From: Ioan Alexandre Romoscanu [mailto:romoscanu at imes.mavt.ethz.ch]
To: mathgroup at smc.vnet.net
>
>
> I wonder if it is possible to do the following formula manipulation
>
> Suppose you have a function of 3 variables [x,y,z], where only the
> ratio x/y occurs. Example
>
> f[x_,y_,z_]=(x/y) Exp[z]
>
> If now you have a large formula of more than 3 variables, where
> however certain variables always occur grouped together, in the same
> pattern (like x and y above).
>
> Is there a way to make Mathematica find out such groups of variables
> in a larger expression?
>
> Thank you for any help
>
> A.I.R.
>

```

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