Axiom vs other CASes
Here I have in front of me a dead tree copy of a document comparing the abilities of several of the more well known CASes: Axiom, Derive, MuPad, Mathematica, Maple, Macsyma, and Reduce. You can find it, and a ton of more detailed information, at http://www.math.unm.edu/~wester/cas_review.html.
I’m very disappointed in Axiom’s perfomance. From what I’ve read in the Axiom book, I got the impression that it would outperform all comers with ease. The only consolation I have is that the tests were performed with the 1993 release of Axiom. Hopefully things have gotten better since. If a quick scan of the table can be considered sufficiently convincing, it seems that Macsyma is the best CAS, according to the criteria he used, which seem reasonable. So now I have to go learn yet another CAS! Hmmm… I just did a quick search on Macsyma, to see if there’s a free version available, which turned up this most interesting bit of propaganda on their website: referring to the same study that I’m reading, they have the number (out of 131) of problems each CAS found a correct solution:
| Axiom 1.2 | Derive 3.0 | Macsyma 420 | Maple V.3 | Mathematica 2.2 | MuPad 1.2.1a | Reduce 3.5 |
| 59.5 | 73.5 | 108 | 90.5 | 88 | 24.5 | 50 |
Of course, I don’t know how reliable this particular study can be considered: Mathematica is now 3 versions up to v5., Maple is 6 versions up to v.9, MuPad is a version up to 2.5, Reduce is up to version 3.7, and Axiom is now an Open Source software project, so I have no idea what version to consider it at. I doubt that Axiom has improved too much in the interim, considering its comparatively rocky history. What a disappointment. Some One™, needs to start a serious open source project to tackle the need for a full powered, extensible, and fast CAS. I would so like to be that someone, but I don’t have the time (or rather, won’t make the sacrifices in my other interests, necessary to gain the time) to learn the level of first mathematics, then computer science, to be a serious consideration for that role. So, I’ll just mope around, until my savior comes along. In the meantime, I’ll keep busy with learning Scheme, and other languages that might be of some use in hacking on a CAS.
Hmmm… Today has been interesting. From the CAS thing, I did a search on LISP, which drew me into a wonderfully hyperlinked world. I didn’t know there was such a well-organized LISP community out there. Now, I’ve added learning CLISP to my list of things to do.