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. > >