> > We are just trying to bring the CAS to masses, if I can use > > this expression. :) > > No, I doubt very much if this is possible, at least not any > more than it is possible to bring advanced abstract mathematics > to the masses. It takes years to appreciate the value of doing > certain things certain ways and at least part of this is based > on often unstated cultural and historical biases.
I think the idea of "general consumption" computer algebra systems might be more usefully viewed as domain specific computation. If you think about the mathematical abilities that are required for applied mathematics, they typically consist of a fairly small subset of theoretical mathematics. Within those subsets there are still many difficult problems, but I think the reason calculations work in such systems is that there are many "hidden" assumptions that result in operations not possible or useful in general applying for all cases of interest to a given problem domain. This might also explain why so many people have tried to create "variables with types" in Axiom. I think what at least some people are actually trying to do there is to restrict Axiom to a domain of computation where some of the behaviors they are used to in mathematical calculation from either their other training or other CAS systems can be applied. In theory, this might actually be possible. What would result, in such a scenario, would be "personalities" on top of the rigorous Axiom core. The mathematics at all levels would still be backed by the correctness of the Axiom system, but (say) a physics professor or student could define or use a pre-existing set of assumptions that would result in a mathematical environment that is familiar and more practical. This is not a new idea, but the details of implementing it are not at all simple. Indefinite Types, "provisos", and other such mechanisms would be necessary, as well as a system wide awareness of those mechanisms. I personally think this is very much worth doing, but such large scale projects must wait on more mundane and practical matters. Either an open source Aldor or a more well defined, rigorous and extended SPAD would be needed for any project of that magnitude, and while progress is being made it will be a while. It's a pity there doesn't seem to be much institutional support for research into these matters. IIRC the NSF doesn't fund work in areas where there is commercial activity, but it's rather difficult to argue that the commercial systems are likely to head in this direction - there are few immediate commercial incentives to do so. Anyway, I'm hopeful that someday "CAS for the masses" will consist of not a whole new simplified system but of defining in Axiom or something like it a set of assumptions and constraints that creates the simplified environment. To me that makes the most sense for both correctness and "expandibility" - as people need new ideas they can incrementally add them, examining the consequences of each (for example, expanding the domain of numbers under consideration from Reals to Reals+Imaginary). There's no particular reason I can see to abandon rigor for simplicity - if the mathematics is valid it should be just a question of defining the assumptions made to "simplify" the notation for new users. Cheers, CY ____________________________________________________________________________________ Be a PS3 game guru. Get your game face on with the latest PS3 news and previews at Yahoo! Games. http://videogames.yahoo.com/platform?platform=120121 _______________________________________________ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
