[goldenkey]

Mathematica is functional. So..you can but you can't. Expressiveness..its a virtue, and Mathematica offers it through being a pattern matched, lazy binding, functional language, with both lexical and block scope, with amazing operators built in for the basic data types.

Shameless plug: https://scrollto.com/the-generalized-mean-an-algorithmic-app...

The code could maybe be written in another language but the fact that Mathematica allows for unbound variables and has beautiful functional library calls like Fold, make it very elegant to write once and work with almost any arguments. Wolfram Cloud is free and Mathematica has a trial, if you did want to fool around.

Mathematica is written in C++, it would be nice to see Wolfram head in the direction of having it produce binaries. It could become a major language of general development if that ever became the case. But Wolfram has always been very "particular" with his goals. One can dream...

[eggy]

I love Mathematica too, so I bought the Home edition. I play in a lot, but at work and home I keep J open [1]. It has a shell and an IDE of sorts if you want it. Something like the geometric mean in your article is:

#%:/

define it as gm =: # %: /

# is tally or number of terms

%: is root

* multiply

/ apply over or map

gm 1 100

10

It also has plot libraries, graphics and is very fast for an interpreted language. Perfect for math and statistics. I do like the curated data available to Mathematica, and WL or Wolfram Language is able to be coded functionally, imperatively, or any way you might want.

  [1] jsoftware.com

[goldenkey]

The main point of the code was to create new means and show derivation of known means. It's easy to write a geometric mean in any language. Having the solve function in Mathematica makes it possible to do dynamically generated means that wouldn't be possible in languages without a strong CAS library.

Also, will J error out on gm a b ? or gm a 100? The beauty of Mathematica is that I can still get results results in algebraic form, when I leave variables unset.

In:= GeneralizedMean[{x, y, z, t}, (#*#2) &]

Out= (t x y z)^(1/4)

[eggy]

The article was great, and I get your point. I was not presenting J as comparable to Mathematica as CAS or WL vs. J, but only showing its expressiveness. You are correct in that it will error out with your examples without writing catch code. I too dream WL goes native. Until then, I will stick with other PLs. How do you like Clojure for mathematics?

I still use Maxima on my Android phone along with J. Wolfram Alpha is nice to have too on it!

Also my example was missing the * even though it was explained below. It should be: gm =: #%:*/

[goldenkey]

Thank you - I hope to eventually produce a paper about alternative continuous and discrete means/norms. Kolmogorov went 5/10 the way, I think I brought his line of questioning to its rightful conclusion. Theres a lot of research to still be done however - only certain forms have easy closed forms when taken on continuous spaces. You might enjoy Part 2: https://scrollto.com/means-of-infinite-sets-and-more/

I actually have never used J, have only minor experience with Clojure in a startup codebase I once worked on, and never heard of Maxima. You have invited me to explore J and Maxima and I thank you for that. So far, I have used solely Mathematica for mathematics. I've tried python with pandas and other libraries but the syntax always seemed obtuse for me. Python's C call interop is why its so library friendly - but the actual language makes these libraries seem bolted on, less integrated than preferable. There are so many languages to try: Haskell, Rust and Julia are on my bucket list. I've mostly conceded to just learning languages when I need to - for an open source codebase or new job. To me, coding is a means to an end of production of tools, apps, deliverables.. Curiosity can deliver one into an abyss of stasis - where one learns all the most amazing expressiveness tools and techniques but never builds anything with them. All a balance..right. Godspeed :-)