Re: help on Rewrite rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg50897] Re: help on Rewrite rules*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Sun, 26 Sep 2004 05:32:19 -0400 (EDT)*References*: <cj320m$53t$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here is how you do it: r = y^2 -> 1 - x^2; Simplify[3*x^2 + 2*y^2 /. r] 2 + x^2 Simplify[(x^2 + y^2)^(1/2) /. r] 1 Your more general case gets rid of only the y^2 that lead to a simplification. You need to use the TransformationFunctions option of Simplify to do this sort of thing. I have defined a transformation function f below to deal with cases slightly more general than your own (i.e. it uses a pattern that matches expressions of the form f[a+ b y^2]). f[(a_) + ((b_.)*1)*y^2] := a + b*(1 - x^2); Simplify[A[x^2] + B[y^2] + C[x^2 + y^2], TransformationFunctions -> f] A[x^2] + B[y^2] + C[1] Steve Luttrell "Jon Palmer" <Jonathan.palmer at new.ox.ac.uk> wrote in message news:cj320m$53t$1 at smc.vnet.net... >I am having trouble simplifying expressions in mathematica. My epxerissions > involve two parameters x & y that parameterise a unit circle so that > > x^2 + y^2 =1 > > Without chosing a particular parameterization for x and y I want to > simplify > epxpertions of the form: > > > 3x^2 + 2y^2 -----> 2 + x^2 > or > (x^2 + y^2)^(1/2) -----> 1 > > and more importantly for should perform the simplification > > A[x^2] + B [y^2] + C[x^2+y^2] -----> A[ x^2] + B[ y^2] + C[1] > > where A,B&C are functions. > > I assume that this can me achieved with a relatively simple rewrite rule > but > I have had very limited success making this work. Can anyone suggest a > solution, > > Many thanks > Jon Palmer > > P.S. I also want to expand the problem to that of three variables x,y&z > parameterizing a unit sphere but I suspect that this will be obvious form > the solution of the unit circle problem. > > >