I have now identified where the problem is in the plotting of unduloids using elliptic functions. There seem to be some singularities arising in Maple 10 that were not there in earlier Maple versions. I noticed also that, on the functionadvisor help page for EllipticE, the branch points are listed differently. Maple 9.5 has ... k, 1/k and Maple 10 has ... -1/k,1/k ... Is this a misprint or the source of the trouble. At any rate, for those who want to see what is happening, try the following in Maple 9.5 and in Maple 10:

>

Once again Maple has screwed things up in a new version. The material in my book, Differential Geometry and its Applications, on unduloids using elliptic functions doesn't give the correct pictures in Maple 10. Maple 9.5 worked fine. Also, something has been done to the simplification routines. In Maple 9.5, the metric and second fundamental form for unduloids are simplified to a point where they can be easily identified. In Maple 10, all that you get is a huge mess. At the Maple Workshop in 2002, I asked about these issues that have cropped up before (the worst being the transition from the wonderful Maple 4 to the horrendous Maple 5).