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Re: finding independent variable groups

• To: mathgroup at smc.vnet.net
• Subject: [mg32498] Re: finding independent variable groups
• From: romoscanu at imes.mavt.ethz.ch (Ioan Alexandre Romoscanu)
• Date: Wed, 23 Jan 2002 01:00:28 -0500 (EST)
• References: <a2e2q2$qmp$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Dear David and Allan

Mena thanks for your help. They really improve my Mathematica skills.

However, I was lookign fro smth slightly different, perhaps more
ambitious, although Mathematica can do more complicated things as far
as formula manipulation is concerned.

The formulae I need to manipulate are more complicated, and the goel
is to identify recurrect groups. According to Buckingham's Pi theorem,
a physical value per definition depends on a finite number of
non-dimensional parameters (see this nice page about this:
http://scienceworld.wolfram.com/physics/BuckinghamsPiTheorem.html)

I have a large formula describing a complex material property. It is
really large (well, under 1 page, so to speak), so looking for the
combined non-dimensional group is tedious, if not impossible. I wonder
if this is doable with Mathematica.

In other words, I would like Mathematica to find the (x/y) group in
the example. Simplify does not work, but since I need only a partial
simplification, I wonder if this is not still doable.

Thanks again

Ioan




"David Park" <djmp at earthlink.net> wrote in message news:<a2e2q2$qmp$1 at smc.vnet.net>...
> 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
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
> 
> > 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
> > task with Mathematica.
> >
> > 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.
> >