Solvability sensitive to small changes in numerical input

*To*: mathgroup at smc.vnet.net*Subject*: [mg47494] Solvability sensitive to small changes in numerical input*From*: "Gareth J. Russell" <gjr2008 at columbia.edu>*Date*: Wed, 14 Apr 2004 07:16:48 -0400 (EDT)*Organization*: Columbia University*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I have a function that includes the Solve command f[a1_, a2_, b_] := Module[{c}, c = 2*b/(b - 1); Solve[b/(1 + (a1*n)^c) + b/(1 + (a2*n)^c) == 2, n] ] ] but it seems very sensitive to the numerical input. For example, f[2., 0.05, 6.19] and f[2., 0.05, 6.21] Produce the error "The equations appear to involve the variables to be solved for in an essentially non-algebraic way." Whereas f[2., 0.05, 6.20] produces the solutions {{n -> -23.8725 - 13.2503i]}, {n -> -23.8725 + 13.2503i}, { n -> 0.183281 - 0.707873i}, {n -> 0.183281 + 0.707873i]}, {n -> 27. 3032}} Can anyone enlighten me as to what is going on here? Other peoples' work suggests that, given a1 = 2., it should be possible to get numerical solutions for a large range of values of a2 and b. If it makes a differences we make the assumptions a1 > 0, a2 > 0, a2 < a1 and b >= 1. Oh, and v5.0.1.0 on Mac OS X Thanks! Gareth Russell Columbia University

**Follow-Ups**:**Re: Solvability sensitive to small changes in numerical input***From:*Oleksandr Pavlyk <pavlyk@phys.psu.edu>

**Re: Solvability sensitive to small changes in numerical input***From:*Daniel Lichtblau <danl@wolfram.com>