Re: Problem with replacement rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg91993] Re: Problem with replacement rules*From*: magma <maderri2 at gmail.com>*Date*: Tue, 16 Sep 2008 19:24:02 -0400 (EDT)*References*: <ga82r6$re7$1@smc.vnet.net> <gaar52$17m$1@smc.vnet.net>

On Sep 11, 12:16 pm, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de> wrote: > Hi, > > makeFunction[expr_, x_] := Module[{var}, > var = Complement[Variables[expr], {x}]; > Function @@ {var, x /. Solve[expr == 0, x][[1]]} > ] > > and > > f = makeFunction[2 + x - y^2, x]; > > Plot[f[z], {z, -2, 2}] > > ?? > > Regards > Jens This code proposed by Jens-Peer Kuska only works with polynomial equations, because Variables only works correctly with polynomials. For example, makeFunction[Sin[x]-y,x] gives as output: Function[{y, Sin[x]}, ArcSin[y]] which is incorrect and cannot be plotted. A more general code is the following: invFunction[expr_, x_, vars_List] := Function @@ {vars, x /. Solve[expr == 0, x][[1]]} where the argument x is the dependent variable and vars_List is the list of independent variables. Now you have as before: f = invFunction[2 + x - y^2, x, {y}] Plot[f[z], {z, -2, 2}] for your polynomial functions, but also f = invFunction[Sin[x] - y, x, {y}] Plot[f[z], {z, -2, 2}] without a problem. An example with multiple indep. variables: f = invFunction[Sin[x] - y - z, x, {y, z}] Plot3D[f[y, z], {y, -1, 1}, {z, -1, 1}] hth