So friday afternoon I wanted to test for existence of a certain mapping that takes one surface to another surface. Everything is algebraic so one might assume if a mapping exist it might actually be polynomial and since everything is of low degree, the mapping might be as well. So I just set up brute force equations and tried an arbitrary degree 2 mapping. After a second or two, maxima returned no solutions to the resulting system. OK, so how about plugging in degree 3. It turns out I don’t need to test the linear terms, and there are 3 variables so 16 variables per component so I get an algebraic system in 48 variables. Sounds bad, but lot of the equations become something of the form “x=0”. So I looked at a subset of the system. Already the generating of the equations took a few seconds. So I thought, this will take a few minutes. So I started “algsys” on the equations. Well, that was wednesday afternoon. It is Sunday and the thing is still running. Unfortunately it just says “Maxima is calculating” in the wxMaxima window, so one has no clue if it will take another day or so, another year or so, or if the sun will implode first. I sort of have the feeling it is doing something stupid. Once I get more time for math on monday, I’ll probably try to simplify the equations by hand first. I could also try for the solution (or lack thereof) numerically. In the meantime I’ll let it run. This is on my laptop which is surely not meant as a computation machine. It’s only running on one core so it’s not heating up too badly. When I was running some computations for days in the summer on all four cores you could almost cook eggs on the keyboard.
On a related front, I decided that my work computer is sitting too idly so I started the degree 19 calculation that we never did with Danny on our paper . In 2008 we thought it would take at least half a year. Presumably the computers have gotten a tad quicker in the meantime (and since I’m running it on 4 cores), so perhaps the result will come in sooner. Still the progress seems slow from the output so far. It is a bit difficult to judge, I’ll try to estimate time left more precisely later on, but just as first guess from looking at the output I don’t think this will be done before christmas.
There is something magical about pressing ENTER to start the computation you know will take months to complete. It is one of the few places where you really use the fact that you have a fast computer. Most computer power is totally wasted. So for example in somewhat similar time frame Firefox managed to get 70 minutes of CPU time (maxima is up to 5208 now). Now that’s with only very occasional short browsing over the last few days. It seems mostly it’s the tabs being open that eat up time, run the CPU and heat our house. Come to think of that my office will be quite warm I bet once I get there on monday, I don’t think the heating runs on the room termostat, as the swich on that thing is in “off” position and it still heats the room. So with the added heating from 4 cores running at top speed and it being a small room, it should get toasty.
Update (monday morning): Actually my office was not much warmer. The computer case is actually quite cold and I don’t feel a huge difference in temperature of the air output. I don’t know why I never ran anything on this computer and always used my laptop so far for longer computations. I think I’ll abuse it more from now on.
 Jiří Lebl and Daniel Lichtblau, Uniqueness of certain polynomials constant on a line, Linear Algebra and its Applications, 433 (2010), no. 4, 824-837, arXiv:0808.0284.