M. Edward (Ed) Borasky wrote:

Paul L. 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”:

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.