M. Edward (Ed) Borasky wrote:

> Paul Lutus wrote:
>> Mathematical notation is extremely strict and slow to change. Apart from
>> some recent window dressing, the last significant change was the adoption
>> of Liebniz' Calculus notation over that used by Newton in the late 17th
>> century.
> 
> Ah, but a variant of Newton's notation is still in wide use for ordinary
> differential equations:
> 
> y'(x) = y(x); y(0) = 1

Interesting. I didn't realize that notation originated with Newton. I find
myself increasingly dependent on that particular notation --

"Modeling Gravity with Ruby":

http://www.arachnoid.com/ruby/gravity/index.html

> 
>> Consequently, mathematical notation has the widest audience of any
>> formal symbolic language. And programs that purport to be able to
>> fluently read and write mathematical notation are in great demand and
>> fetch high prices (Mathematica, Maple, Matlab, IDL).
> 
> I wouldn't call Matlab a "symbolic" language, unless it's changed a lot
> over the years.

I shouldn't have listed it, because I now realize it can't process symbolic
math.

> And concerning the high prices, there are two or three 
> open-source Matlab-like environments, Octave being the most well known.
> For purely numerical computing with an emphasis on statistics, there is,
> of course, R as well.

I hope for an eventual decent open-source symbolic math processor. There was
one (the name of which escapes me at the moment), but it is presently
abandonware.

> 
> In the symbolic realm, there is Axiom and Maxima,

I believe I was thinking of Maxima, or a variant thereof, above. I was able
to make it process some kinds of symbolic constructs, with somewhat more
effort than with Mathematica.

> both open source, in 
> the general-purpose category. In addition, there are a number of
> open-source high-speed special-purpose tools like GiNaC, Pari, GAP, and
> Singular.

I am personally spoiled by Mathematica, and, not being a particularly
skilled mathematician, perhaps to a fault.

> And let's not forget TeX and mathematical typesetting and the notions of
> "literate programming" and "reproducible research". I know there are
> some high-priced commercial tools to do this, but most everybody I know
> uses things like LyX, TeXmacs, noweb and such rather than "the
> high-priced spread". (or Word.) :)
> 
> Finally, I think there's a formal symbolic language with a wider
> audience than mathematics. Can you guess what it is? I'll give you a
> hint -- Google for "lilypond". :)

I wouldn't have guessed musical notation without help, but I agree, it meets
the definition, and, until the invention of the car radio, it was more
widely used than mathematical notation. :)

-- 
Paul Lutus
http://www.arachnoid.com