[taeric]

And that matters if you are mostly worried about value, to a large extent. If you are evaluating "better" as in "supports more symbolic operations," none of those really enter into it? Right?

This is like opining that the best "car" out there is a gokart you can get complete schematics on, for all of these reasons. I think most of us would accept the argument that the better cars are the ones that pass metrics aimed at cars. In this analogy, the better algebra system is the one that does the most algebra.

[wakawaka28]

If SymPy meets your needs, it is objectively better. Mathematica is expensive and you probably have to pay for licenses on a continuous basis for every instance you use. Many benchmarks are stress tests and not representative of common work.

[taeric]

This is kind of silly, though? Yes, if you do not need a full car, a bike may fit your needs. The bike is still not a better car, though.

You can try to broaden it to saying it is a better vehicle for you. And, sure, for a lot of folks the cost will be important there. As a CAS, though, Mathematica is tough to beat.

[wakawaka28]

No it's not silly. A Lamborghini might be a better performing vehicle that could solve problems I didn't even know I had, but if I don't have the money for it and/or a Ford Pinto covers 99% of the cases I need, the Pinto is better.

I'm not arguing that SymPy is going to beat Mathematica on benchmarks. But if both of them meet your needs, and you like having money and/or control of the code, SymPy wins.

[taeric]

So, in this we don't really disagree. But, I would only agree that it is an objectively better choice for you. It is not an objectively better CAS. Demonstrably so, per that benchmark.

Similarly, a lamborghini is almost certainly an objectively faster car. Such that if you were discussing fast vehicles and someone pointed out that their ebike was good enough for them, it would be a statement out of nowhere that is not using the rubric for ordering that was being discussed. Are they wrong that the ebike is a better choice for them? Almost certainly not. Would it be valid to say that it is the best fast vehicle because of that? (I say this as someone that loves bikes and is fairly anti car...)

And there would be other rubrics that would shine light in either direction regarding python. Arguably, the stewardship of the language lost a lot of trust with people in the hilariously bad 2->3 migration. More so in how bad dependency management has become. Yes, you can roll your own, but people with large support contracts can almost certainly offload a lot of that to the team on Mathematica, if that is truly a concern.

(I could similarly cast shade on Mathematica, but I think my point is made. Yes, you can have a rubric that changes which is the better choice for a situation. No, there is no total ordering of correct choices.)

[wakawaka28]

We are essentially in agreement. I just don't think Mathematica is worth the money unless you need it for something specific like solving tricky problems. As much shade as you can throw on Python, there are lots more possibilities to use Python with SymPy than to use Mathematica. Unfortunately, the cutting edge FOSS math scene will always lag behind the commercial tools, as it is incredibly hard for them to get donations. I remember hearing a story about the developer of Octave (the most popular Matlab clone). He had worked on it for years and hardly got any donations, despite probably having hundreds of thousands of downloads and constant feature requests.

[taeric]

Indeed, I think we are fairly aligned.

I also think the math systems will lag for more than just donations. The work to make a good CAS is pretty intense. A lot like a good SAT system. Or really anything that is deep in the weeds of computer science. A lot of us are so far removed from the math that they focus on, that it can be mind bending to try and get back into it. (Indeed, for a lot like me, we were probably never really great at it, in the first place.)

Mathematica and Matlab are interesting to consider, as they are likely very well integrated into older workflow systems from the mainframe era. In particular, I'd expect the high end simulations for car and vehicle designs are much more integrated with those than anything open source. And a lot of that is largely availability of what they are integrating with. Most of us do not have the science labs and all of the equipment that goes with it.

Which, I think, is a bad feedback loop on this. For folks without those labs, Mathematica/Matlab are prohibitively expensive. For those with the labs, they are probably a rounding error. And there is no real path from the current equilibrium to one that can get it to more people. (The old path was free access in college. But that is becoming less of a thing in modern programming jobs.)

[bmitc]

Objectively better in what sense? There is an objective cost in the initial installation, yes.

Additionally, Mathematica is not really that expensive.

[wakawaka28]

It's not just initial installation. I have not pursued a license lately but these kinds of products cost money for every running instance. Institutions often have license servers on premises that allow a fixed number of people to use the stuff at once. If you use a SDK to build a program with it, that's got a separate license. If you need it for a real product, we are generally talking like thousands of dollars per developer per year in perpetuity, plus god knows whatever you use for SaaS. You might have to negotiate a price for your use case.