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Comment by hcarvalhoalves | Hacker News Reader

Computer Algebra is criminally underused - it has the potential to make math-heavy critical-path code a lot more clear, testable, observable and bug-free by design.

I feel I need to mention "Structure and Interpretation of Classical Mechanics" by Wisdom and Sussman, and the accompanying "scmutils" library, which first implemented in Scheme many of the same features, although this Julia library seems to be more complete.

There's also a great one-to-one port to Clojure by Colin Smith [2] in case you want to use it on a more production-friendly environment. The Strange Loop talk [3] is a good showcase of the power and simplicity of these kind of systems.

[1] https://groups.csail.mit.edu/mac/users/gjs/6946/

[2] https://github.com/sicmutils/sicmutils

[3] https://www.youtube.com/watch?v=7PoajCqNKpg&ab_channel=Cloju...

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SICMUtils co-author here, if anyone has any questions on the Clojure port.

One beautiful thing about a Clojure computer algebra system is that it can run completely in the browser. This includes automatic differentiation, numerical integration, all of the hardcore Lagrangian and Hamiltonian mechanics work, differential geometry... it is startling stuff.

For example, here's a(n interactive!) derivation of Kepler's Third Law in the browser (thanks to Nextjournal's lovely integration), if anyone wants to play: https://nextjournal.com/try/sicm/ex-1-11

Many more exercises live here: https://nextjournal.com/sicm/

Yes, we found these and this (along with Mathematica) was the impetus for building automated Latexification into Symbolics.jl. Here for example is a teaching notebook used in Alan Edelman's MIT Computational Thinking course where Symbolics.jl is used to visualize the numerical methods as they iterate, and all of the outputs convert to LaTeX:

https://computationalthinking.mit.edu/Spring21/newton_method...

Thanks for the ideas!

Those are gorgeous. How were they done? Using Julia packages?

This is a Pluto notebook over Symbolics.jl and ForwardDiff. All of the packages used are at the top of the page. You can click the edit button on the top right to open it up.

Forgot to mention: Shashi cites SICMUtils as a big influence for the rewrite system SymbolicUtils.jl, which is the rewrite system underneath Symbolics.jl.

https://discourse.julialang.org/t/ann-symbolicutils-jl-groun...

He took Sussman's course and became interested in the field from that! Great work.

Whenever SICM comes up here on HN it receives a lot of admiration. One thought that a lot of people have is whether there would be advantages in trying to do something like that in a statically typed language. Have you thought about types and SICMUtils?

Hey, I have... I'm a co-author of Algebird[0], which has many ideas that I'd pull over.

I'm hoping to introduce Clojure's "spec" or "schema" libraries so that the types at play can at least be inspectable inside the system. In a fully typed language, I'd implement the extensible generics as typeclasses.

I suspect it would make it quite a bit tougher (at least in the approach I'm imagining) for folks to write new generic functions, due to many type constructors...

On the other hand, the complexity is there, even if you don't write it down!

It would be a big project, and a worthy effort, to write down types for everything in SICM.

[0] https://github.com/twitter/algebird

I made a scratch like visual programming system for sicmutils, clj-tiles[0]. Types are inspectable by right-clicking->Inspect on a specific block. Clj-tiles uses Clojure spec under the hood. One note: I am not sure whether a static type system can improve on this for someone who wants to learn Physics. After all, the types of function parameters change during the running program, as the same functions are called several times. But see for yourself:

[0] https://kloimhardt.github.io/cljtiles.html?page=pendulumfina...

I was amazed the first time I used Mathematica. I have used later professionally Maxima to compute some Taylor series and also simpy for some hobby projects. I found simpy less powerful than Maxima (not to mention Mathematica) but the ability to integrate it with the rest of the program is wonderful.

Using Maxima in my day-to-day work has been a complete game changer. I use it via org-mode and use the `tex()` command to have it output TeXified results. These automatically get formatted into beautiful readable equations.

Cool! I managed to do something similar with org-mode + sicmutils, works quite well.

Render (pt_BR): https://github.com/hcarvalhoalves/math-fin-training/blob/mas... Source: https://raw.githubusercontent.com/hcarvalhoalves/math-fin-tr...

I would love to see how you're using org-mode for that if possible :)

> "Structure and Interpretation of Classical Mechanics" by Wisdom and Sussman

I come across this book every so often and find it really tough to read due to the complete lack of "types" in any of the code. Math, especially physics, relies heavily on units and function signatures to be understood.

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