Plotting implicit functions with multiple branches
- To: mathgroup at smc.vnet.net
- Subject: [mg42725] Plotting implicit functions with multiple branches
- From: "Alan" <infoNOSPAM at optioncity.net>
- Date: Wed, 23 Jul 2003 00:25:16 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I have been spending some time assembling a plot of a function y(x) where there are multiple branches to the function. My specific example is where y(x) is defined implicitly as the solution to the equation Sin[y]/y = E^x / ( a - b x) , where a and b are positive constants. For any solution y(x), there is also a solution -y(x), so suppose one just wants to plot solutions y(x) for y >= 0. As it turns out, for x greater than some values, there are an infinity of solutions which could be labeled y(x,k), k = 1, 2 ... For any range (xmin, xmax) and (0, ymax) there are only a finite number of these solution or branches. As x grows large, each branch approache the asymptote y = 2 k Pi from below. My question is whether anyone knows of a general algorithm or package to automate the generation of this type of plot, for say a general implicit equation of the form f(y) = g(x) where the equation has multiple solutions? My current method is quite tedious: identifying branches, creating individual plots, and using Show to combine them. I could live with that and expect to more fully automate this *particular* function. But I have some more complicated functions f(y) = g(x) that I would like to consider and would really like an automated general method, if such exists. Ideally, there would be something like a function ImplicitPlot[ f[y] == g[x], Ranges, Options] Thanks for any advice.