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Yacas -- A symbolic computation engine similar to Mathematica or Maple. It has a Lisp core, with plenty of syntactic sugar. Released under the GPL.

Octave -- A damn fine piece of work for numerical computation. IMO, it beats MatLab any day. Released under the GPL.

Maxima -- a descendant of Macsyma, which all True Math Geeks remember. It's a symbolic computation engine with a Lisp core, like Yacas. Released under the GPL.

JACAL -- another symbolic computation engine with a Lisp core. Released under the GPL.

GAP -- a system for doing abstract algebra and combinatorics. This is really only of interest to a limited subset of mathematicians. However, it is incredibly good at doing what it does. GAP is under its own license, which I'm fairly certain would classify as free to RMS.

There are many others, but these are the most mature that I've dealt with. If you're looking for a pretty front-end, Maxima has one, there's one for Octave called G-Octave (uses Gnome), and there's one for GAP called XGAP. None of them match the purtiness of Mathematica or Maple, though. There is TeXmacs, a rather impressive TeX-ish WYSIWYG. With some effort, you can make it serve as an input/output mechanism for any CAS. However, I recommend against using it for its intended purpose as, although its rendering is very impressive, it is a big step backwards for structured documents.

There are certainly times when one would want a non-CLI interface even if one were blind - for example, when using programs that are not (and should not) be for the console, such as word processors.

You mean the WYSIWYG (What You See Is What You Get) word processors? (I hope it's not some stupid joke.) "The best output a blind person using WYSIWYG software can hope for is getting no output at all" as the anonymous geek quoted on BLinux FAQ has said. There are typesetting (or "word processing") tools working perfectly well in any text editor you have. I personally use Donald Knuth's TeX and Leslie Lamport's LaTeX extention because they are more powerful than any WYSIWYG tool I've ever used (including TeXmacs), while also giving me much better looking results. They're not only more powerful for people with good sight like myself, they can also be used from any text editor a blind person can use, like the Emacspeak for example. That's if a blind person ever needs such a tool, like for writing a book or printed article. Because using word processors for communication (like most of people use Microsoft Word these days) instead of plain text email is stupid at least.

PDF is swell as a format to print from. Or squint at on the screen, but it doesn't exactly edit nicely. I don't know what the answer is for editable collaboration between word-users and the TeX-users. Part of the problem is that all of the conversions are (as you note) rather lossy. People who use TeX tend to care. People who use Word or WP for documents with any math in them by definition don't care what they look like :-) Depending on the politics of the situation, it may be feasible for the one person to use LyX (or perhaps TeXmacs) and the other to edit TeX. This gets over (more or less) the "TeX is hard" objection, but it does require a pretty big hassle for Windows users (Install an X server? Is that for Pr0n?).

For anyone interested in free computer algebra systems, I would like to point to GNU TeXmacs, whose version 1.0 has just been released. This program can be used as a frontend for most free computer algebra systems. Please contact us if you want to help us supporting other systems or improving the current interfaces (or adding interfaces to other scientific computation systems).

I am no LyX user. Actually, I tried it once but I found it so ugly that I came right back to AUC-TeX.

TeXmacs on the other hand is a constant aesthetic pleasure. I know that structured documents are not about good looking screens, but I really think that a beautiful tool is WAY more pleasurable to use than a ugly one.

However, I cannot see why you think that TeXmacs is only a tool for maths. if you look at the screenshots on the LyX site, what will you see? Math formulas.

Just have a look at these documents if you want to see how TeXmacs can be be used to typeset source code documentation.

Take a look at GNU TeXmacs, maybe you will like it. I've never used it myself, but if it works half as good as it looks it would be pretty damned nifty.

GNU TeXmacs is a free scientific text editor, which was both inspired by TeX and GNU Emacs. The editor allows you to write structured documents via a wysiwyg (what-you-see-is-what-you-get) and user friendly interface. New styles may be created by the user. The program implements high-quality typesetting algorithms and TeX fonts, which help you to produce professionally looking documents.

I know engineering students who find that very useful for school work.

And engineering students make up "most users"? Methinks not.

For math-heavy texts, one would probably better off with a tool devoted to such things - like maybe TeXmacs.

Most people want a simple, WYSWIG, omnipurpose tool

No, people want a tool that lets them do the things they need to do in a simple manner. Omnipurpose means 99% useless. For the "average" user, complexity and price are stronger negatives than lack of features that they never use.

Well, Lisp isn't really based of anything, at least, not off of any other programming langauges. It is based on the concept of the Lambda Calculus, which is something of a way to describe programs in a mathematical way. Or, something like that. <g> Honestly, I've never gotten a great definition of lambda calculus, but I'm content that Lisp is cool. ;-)

Now, as to why you haven't heard of it before, my guess is because you are either not a University Computer Science graduate, or you haven't branched into functional programming. Most universities will cover it at least very briefly in some sort of programming languages class, though rarely do they do it justice.

As for functional programming, it's a programming paradigm, like imperative or object oriented programming. It tends to be very powerful, often makes use of constructs which are terse (fewer lines of code to do the the same thing than required in other langauges) and generally makes extensive use of recursion.

Lisp is very interesting, however. Even though it is usually thought of as a functional language, it actually provides excellent support for functional, imperative, and object oriented programming. In fact, many people think the Common Lisp Object System (CLOS) is one of the best Object Oriented Programming implementations available. It was also the first object oriented langauge that was standardized (by ANSI or ISO, I don't remember for sure which one).

It's also been around for a while. In fact, Lisp is one of the oldest programming langauges still in somewhat common use today. (The only older language being Fortran, which predates it by about 5 years, as I recall.)

If you've never had any experience with functional programming, I strongly encourage you to investigate and study[1] it a little, even if you never really use it, because you will learn a great deal about programming in general for your time invested.

Now, as for what applications have been written in it, the canonical example is GNU Emacs. At it's core, Emacs is basically a lisp interpreter, and most of the editor is then written in Lisp.

While applications that are written entirely in Lisp are perhaps not as well known, one of the most common places to find Lisp is as an extension language for other programs. Here are a handfull that make impressive use of Lisp:

The GIMP uses Scheme, a dialect of Lisp for it's Script-Fu, which can be used to programatically execute anything that can be done by hand.

Autodesk, the makers of the industry leading CAD software AutoCAD use their own dialect of Lisp, called AutoLISP, for programming and customising the AutoCAD software.

Siag Office is a free small, Open Source, and very impressive, Office Suite making extensive use of Scheme. (SIAG == Scheme In A Grid). It includes a very cool Spreadsheet program, as well as others, and is highly customisable.

GnuCash makes use of the Guile library to provide Scheme as an extension and scripting language for the application.

Speaking of Guile, Guile is the official extension language library of the GNU project. Using Guile to provide Scheme scripting, you can add support for scripting and extensibility to any application. Guile is used in many applications including GnuCash (mentioned above), the SCWM Window Manager, the TeXmacs editor (integrating Tex support into an Emacs like editor), and many others.

One last example is the Sawfish Window Manager, which seems to be among the most popular Window Managers around these days. It makes use of an Emacs-ish philosophy, having a very small core program, including a lisp interpreter, and implementing most of its feature set on top of that with lisp.

This is, of course, not an exhaustive list of applications written in, or making use of, Lisp, however I think everyone here will prolly recognise a few names there. ;-)

[1] If you're interested in learning more about Lisp, I strong suggest you take a look the book Structure and Interpretation of Computer Programs. The full text is available online at the link here, and it is one of the best books ever written about Computer Science. It's also used as an early CS text book at MIT.