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Comment by pfortuny | Hacker News Reader

I use this frequently for plotting planar vector fields: it is much better than Mathematica’s StreamPlot (which I am forced to use from time to time).

Also another colleague found out the hard way that maxima can happen to solve symbolic/arithmetic linear equations much faster (2 orders of magnitude) than Mathematica.

A great tool. A pity it is underestimated.

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As a physics student, I often used maxima for assignments, because while I did have access to Mathematica on lab computers, having a CAS on my laptop was often more convenient. In general, it was able to do what I needed just as well as Mathematica, though with different syntax.

Ironic, considering that Stephen Wolfram insisted in the 80s that Lisp was 100x slower than C, and so a fast mathematics package could not be written in it.

He was wrong then and now, but the crucial speedup of Mathematica vs Maxima was difference in modeling of data and how Mathematica could piggy back on fortran libraries for numerical solving, while Maxima focused on symbolic solving.

This meant that for many cases where numerical method was beneficial, Mathematica easily won on speed.

That's hilarious, because the Wolfram Language is actually quite lispy. Or, at least you can write it in a very lispy style.

Greenspun strikes again[1].

[1] https://en.wikipedia.org/wiki/Greenspun's_tenth_rule

Id say it is lisp, with a slight syntax difference

It kind of literally is lisp. It's about the only implementation of M-expressions instead of S-expressions.

https://en.wikipedia.org/wiki/M-expression#Implementations

The way the whole language is implemented in terms of pattern matching and term rewriting is unlike any other language that I’ve seen. It does not seem quite like Lisp in that way.

Transforming patterns into other patterns is kind of Stephen Wolfram's _thing_. See his long term interest in cellular automata, and now even an attempt to discover the secrets of the universe through a theory of physics based (as far as I can tell from what I've read of it) entirely on pattern matching and rewriting: https://www.wolframphysics.org/.

Now Wolfram Language uses LLVM framework for compilation. SBCL-compiled Maxima is also quite fast .

That's probably because Stephen Wolfram in the 80s knew little about Lisp. Chances are he still knows little about it today!

The predecessor of Mathematica, Wolfram and Cole's SMP, was 10-100x faster than the best Lisp based symbolic math programs at the time on what Wolfram and Cole considered to be small to medium research physics problems. On large problems they were unable to compare because the Lisp based programs needed more memory than the VAX 11/780 at Caltech High Energy Physics had.

Which command do you use, and could you link an example?

No examples (home). Maxima: plotdf, Mathematica: Streamplot.

Sorry.

Thanks, that is enough info for me to proceed.

can you give an example instance? I'll test on both.

For the vector fields just anyone with a couple of singularities would work. The moment you set unequal axes Mathematica blows up.

Sorry but am home. If you mail me during the week I shall find examples for you.

The matrix was something I saw happen, I do not have the example handy, sorry.

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