On Thu, May 1, 2008 at 1:19 PM, Bill Hart <[EMAIL PROTECTED]> wrote: > > William Stein wrote: > > > > I 100% totally and absolutely agree with Tim Daly that computer > > > algebra is at the handwaving stage. > > > As a mathematician concerned with > > > rigour, I am interested to know what SAGE hopes to do about it. > > > > Nothing. This is certainly not one of my goals of Sage; it's not > > needed to create a viable alternative to the MA*'s, since they are also > > at the handwaving stage. > > I believe we can do a *lot* better than that.
So do I. However, that is definitely not my goal. > As I want to actually *use* SAGE for research, I need to know I can > trust the output to a relatively high degree, just as I trust results > from other people's papers. So, the upshot is that you can expect the > parts of SAGE that I end up using to be pretty well tested - by me. > The reason is simply that it is a lot less work to test SAGE properly > and visually check the code than it is to develop it all over again > myself. But be prepared for the onslaught! Excellent! The more bugs we know about the better. Thanks. I know the Magma group greatly appreciates your bug reports, and so will I. > I also think that people from other projects who start to worry about > the threat SAGE poses and read that comment are not going to sit back > and let SAGE become a viable alternative. > Especially the Magma group > are going to think, OK, to make SAGE irrelevant, we need to do much > better testing, formalise things better and write better documentation > (oh and they should open source it as well, though there are other > options they don't seem to have thought of). Maybe all mathematical software will improve even more in overall quality as a result. That would make the world a better place. > Magma is not a stationary > target. To be a viable alternative, you need to aim ahead of them. This makes the game sound one dimensional, but it isn't. Things are more complicated than your analogy about moving targets might suggest. Features, speed, usability, books, user communities, cost, the user programming language, support, etc., are all important factors that people consider when deciding which products to use in a free marketplace. When I say making Sage a viable alternative this is what I'm talking about it. My impression talking to a lot of users over the last few years is that most people who currently use Sage do so for the simple reason that it has enough functionality and they like Python a lot more than the custom programming languages in the other math software systems. For these people "Python" of course means the whole ecosystem of Python, which includes the millions of users, the thousands of third party packages, the books, classes, and other resources, etc. They might not like the Python language that much, but it's at least usable, has a good ecosystem around it, extremely good financial support, and a clear path forward. > Anyway, it proves Tim Daly's thesis that SAGE has done nothing new if > we only aim to emulate roughly what has already been done by the > Ma*'s. I'm not entirely sure I completely agree with that thesis, I do > see new things in SAGE, but it does start to sound like he has a > point. I don't care whether Sage does anything new or not in the above "computer algebra researcher" sense. My humble goal is simply to give people (starting with me) a viable open source free mathematical software choice like how the generous folks who work on Firefox (and Inkscape, OpenOffice, Linux, etc.), give people a choice so they don't have to use Internet Explorer (and Illustrator, Word, Windows Vista, etc.). > I also recall Roman Pearce recently getting upset about developers not > wishing to do the hard work to tackle some of the big algorithms and > just imagining that wrapping the right functionality in another > package will deal with those. Off list he made the point to me that he > doesn't even consider Magma worth competing with. He is thinking so > far ahead of Magma that it is not even relevant to him. Getting within > a factor of two of what Magma already does is not a worthy aim. As a > general principle, that is a good way to think. We need to aim past > Magma to become a viable alternative to them, and the big problems > with Magma are bugs, documentation and closed codebase. They have > speed for the most part and they have coverage. The main advantage we > have at present is an open code base. The above thinking is typical from people doing research in the computer algebra community. And there is nothing wrong with it at all. It just has nothing to do with what the Sage project is about. Sage is a just a good old-fashioned open source software engineering project aimed at normal everyday people who like using computation to enrich their enjoyment of mathematics. That's it. Sage is supposed to solve an immediate need today of everyday working mathematicians like me and my students. "Nobody should start to undertake a large project. You start with a small _trivial_ project, and you should never expect it to get large. If you do, you'll just overdesign and generally think it is more important than it likely is at that stage. Or worse, you might be scared away by the sheer size of the work you envision. So start small, and think about the details. Don't think about some big picture and fancy design. If it doesn't solve some fairly immediate need, it's almost certainly over-designed. And don't expect people to jump in and help you. That's not how these things work. You need to get something half-way _useful_ first, and then others will say "hey, that _almost_ works for me", and they'll get involved in the project." -- Linus Torvalds. "Your job is being a professor and researcher: That's one hell of a good excuse for some of the brain-damages of Minix." -- Linus Torvalds For example, I think Sage will be very useful in the large "database of modular forms" project I sure as heck have to finish in the next 3 years (since it's funded by a specific grant). If I had Roman's perspective on Sage where do you honestly think I would be with regard to that project in 3 years? I'm going to succeed at the modular forms database project by combining lots of 10-year old ideas with a bit of old fashioned ingenuity, any new ideas that turn out to be *needed* to make it happen. That's it. What I care about is that I get a lot of useful data out, and that the resulting data leads me or others to make new conjectures, and some of those conjectures get proved. I've been through the above cycle many times before, just as the generations of math researchers before me have (e.g., Birch and Swinnerton-Dyer, Barry Mazur, etc.). It's nothing new. -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
