Open Source Computer Algebra Systems

timdaly writes "A while back Slashdot had an article decrying the lack of a good open source computer algebra system. That is changing. There is a conference scheduled for the end of May to define the development model and strategy for future work. Students of math, science and engineering will find this valuable. If you're tired of hacking open source editors and want something with a real technical challenge this is the area for you."

Comments

Bad Idea

[cperciva]

A computer algebra system which is built in a bazaar is a Bad Idea.

With an operating system, it isn't all that critical if it crashes occasionally. Ok, it's a nuisance... but it won't go unnoticed, and someone will track down why it's crashing, and it will get fixed.

Computer algebra systems are rather more prone to undiscovered errors. It's very easy, for example, to write a long integer multiplication routine which works perfectly for integers less than 2^20 digits long, but starts to fail (deterministically, but without obvious pattern) for very rare inputs above that size. In a bazaar, where code is accepted from anyone, you're very likely to see this sort of buggy code get introduced.

With a closed (commercial) or pseudo-closed (not necessarily commercial, but within a university where everyone has scrutinized each other's credentials) environment, such errors are far less likely to exist. Computational mathematicians are paranoid about such errors; computational mathematicians will not introduce a piece of code unless they can *prove* that it will work.

Given enough eyes, all detected bugs will be fixed; but actually detecting those bugs in the first place is far from certain.

Re:Bad Idea

[swillden]

Computer algebra systems are rather more prone to undiscovered errors. [...] In a bazaar, where code is accepted from anyone, you're very likely to see this sort of buggy code get introduced.

With a closed (commercial) or pseudo-closed (not necessarily commercial, but within a university where everyone has scrutinized each other's credentials) environment, such errors are far less likely to exist. [...] computational mathematicians will not introduce a piece of code unless they can *prove* that it will work.

Given enough eyes, all detected bugs will be fixed; but actually detecting those bugs in the first place is far from certain.

No offense, but you don't understand the open source process. I know of no open source project anywhere in which "code is accepted from anyone". Patches can be offered by anyone, but there are gatekeepers that decide what is and is not allowed into the source tree. For a project like this, I would expect the gatekeepers to be computational mathematicians and I would expect that they would reject out of hand any non-trivial submission that isn't accompanied by a formal proof of correctness.

Further, it wouldn't surprise me if *this* project used some extensive and formal peer review process, so that before (or maybe after) the gatekeeper accepts a submission there's oversight from a group of other mathematicians.

I think open source is *perfect* for this sort of application. It's certainly much more likely to produce correct code than a closed source shop where only a small number of people can review the code and there are marketing people trying to push the product out the door.

Re:Bad Idea

[cperciva]

I think open source is *perfect* for this sort of application. It's certainly much more likely to produce correct code than a closed source shop where only a small number of people can review the code and there are marketing people trying to push the product out the door.

True, but the scenario you describe is quite unlike what actually happens. In MAPLE, for example, almost all functions can be inspected by anyone. There is a small kernel of builtin functions which are opaque, but the vast majority of code is written in MAPLE's internal programming language, and distributed as source. Anyone (out of the few dozen with sufficient background in the field) can look at the algorithms and verify that they work; but the people who are writing most of this code are doing so because they are getting paid.

Re:Bad Idea

[swillden]

Most of my experience with such software is with Mathematica (which is really closer to what this project wants to do, if I read it correctly. Maple is more focused on computation, but the project we're discussing is intended to be a symbolic algebra package). And almost none of the source is available. Sure it comes with a large selection of packages in source form (Mathematica notebooks) that define various additional (mostly obscure) structures, but the really important part of the code is all closed.

Re:Bad Idea

[mmusn]

First of all, it is foolish to derive results using any system, or by hand, without being able to check them.

Second, the suggestion that commercial, single-developer computer algebra systems are somehow more reliable than bazaar, open source ones flies in the face of reality. For years, Mathematica was released with really serious and subtle bugs, for example in its polynomial code; it would compute results that simply didn't survive even the simplest checks. And Wolfram Research didn't bother fixing them for a long time (for all I know they may still be there). The equivalent code in Macsyma, which was a bazaar-like effort and is now open source, worked just fine.

RPMS (redhat 7.2) of mathematics packages

[rdieter]

I have a collection of self-built RPMS for mathematics packages to try out if you like. Included are: drgenius, gap, geomview, gtkmathview, Macaulay2, maxima (a minor pain 'cause it depends on lisp), and others available at http://www.math.unl.edu/~rdieter. Enjoy.

Re:GiNaC, C++ and Aldor

[timdaly]

I read the GiNac paper posted at the link.
Aldor (www.aldor.org) is a language that goes
well beyond the GiNaC language. It offers Types
as first-class objects (you can store them and
manipulate them), symbolic as well as numeric
evaluation, interpretation and compilation.
Frankly, though I'm certain to be flamed for this,
I find that doing computer algebra in C++ about
like doing division in roman numerals. It is
possible to do but it is the wrong notation and
notation is vital to thinking correctly (and
programming correctly). The closer a language's
syntax and semantics approaches to the problem
domain the fewer chances there are of mistakes.

Re:what will it include?

[njdj]

I understood it to be a symbolic algebra package, somewhat like Maxima. (which is derived, I believe, from a version of Macsyma). Maxima is open-source but presumably the organisers of the conference consider it "not good enough" in some way.

Re:Development model

[joto]

Well let's hope otherwise. There already exists several good open source systems for various sub-fields, but we also need an uber-system that does everything (albeit not necessarily as good as the specialized systems), but is friendly enough to be used by people who could never write it themselves (i.e: mathematica, maple, derive, mathcad, etc).

Today we have muPAD (generally the smartest, pretty friendly, but only somewhat free), maxima (which is usable, but hardly polished), yacas (which I know nothing about), and emacs calc (which is very user-friendly but also the dumbest). None of them (well, maybe muPAD) are close to becoming rivals to the above-mentioned systems in terms of either user-friendlyness or features.

(Of course, this is not special for computer algebra systems. We also need better DMBS (and related tools, such as form-generators, report-generators, etc...), office productivity apps, cad, gis, groupware, financial stuff, graphics, dtp, music, etc...)

Mathemagix

[Joris van der Hoeven]

We plan to write a compiler for a new computer algebra system called mathemagix. We are searching potential contributors or people who would just like to give us some useful suggestions; the development is still in a very early stage due to my work on TeXmacs.

Maxima

[mmusn]

Let me put in another word for Maxima. It is based on Macsyma, and it is very powerful.

Still, people have learned quite a bit about algorithms, software engineering, and software reuse since Macsyma, Maple, and Mathematica were originally implemented, and it might well be worth thinking about having another go at a modern computer algebra system. I suspect that implementing it in something like ML or Haskell might help a lot with correctness and extensibility.