[qsort]

Stephen Wolfram notwithstanding, Mathematica is still far ahead of most alternatives as a CAS. Maple is good on some integrals.

Their downsides are that their languages are not very well suited as general purpose languages, many times the algebraic manipulations you have to perform aren't that complicated and you'd rather work in a "real" language.

Yet another case where python isn't the best in class but still workable and able to benefit from its vast general-purpose ecosystem.

[llm_trw]

Sagemath is a python library that has more capabilities than Mathematica. If you want to do real symbolic computation in python Sagemath is the only way to do it.

That said sympy is quite a cool little library for learning.

[qsort]

Sagemath isn't a python library, it's a collection of packages (of which sympy is one) under a common interface. It is indeed what you would use if you wanted to do real symbolic computation in python, but it's not at the level of Mathematica or Maple.

Look, we all love open source, but we aren't doing anybody any favors by pretending the open source alternative is better when it isn't. I would encourage anyone whose needs are satisfied by sympy/sagemath to opt for the open alternative, but the question was whether or not Mathematica as of now, early 2024, is better. The unfortunate reality is that it is.

[williamstein]

Sagemath is a Python library (and a rather large one at that). It's vastly superior to Mathematica and Maple at some things (e.g., number theory and algebraic combinatorics) and inferior at other things (e.g., symbolic integration).

[llm_trw]

I'm old enough to have had people tell me the same thing about the Linux kernel vs the Windows kernel.

I can do an import sage as the top of any python script.

It's a library.

And since I get all of python for free it's better than Mathematica.

[7thaccount]

Your definition of "better" may be wildly different than many. Mathematica is much better in many cases... especially tasks where Mathematica has a built-in function call for something that would be an absolute pain in Python, but worse with respect to price and licensing. I use Python a lot more than Mathematica, but sometimes Mathematica is the best solution.

Your windows/Linux analogy is also not very relevant here. Both are popular in different areas.

[jfoutz]

I think the windows linux analogy is pretty apt. especially around the win95/98 days.

Getting some random laptop and figuring out what kernel mods to enable and hope that the specific chipset revision was supported, or maybe a patch available that might work was, in fact, a lot of bullshit to put up with to get, say, sound.

sympy will do a lot. but you're probably going to have to reach for a big book of integrals, or find a friendly mathematician to identify the equation and possible approaches. Mathematica as a paid product has a lot of time and effort spent avoiding resorting to asking for help. Much much more built in.

As an undergrad or a hobbyist you probably want to stay "lower" and slog through the calculations when you're stuck. This is part of the process of understanding. But as a professional, or a more advanced user, screwing around for a week looking for a solution is a waste of time and expertise. Spring the cash, and move forward immediately.

I'm not trying to put words in your mouth, but I think there is some nuance that this maybe helps people understand your point.

"Better" really really depends on where you are and what you're trying to do.

[7thaccount]

I don't think many question that open source won't eventually be equivalent or better than Mathematica for computational work. It just isn't for a lot of things in 2024. It might be fully reversed in another 5 years. Agreed everyone's view of "best" is different as I said above.

I will say a really nice thing about Mathematica is consistency.

[behnamoh]

"Python isn't the best tool for anything, but it's the second best tool for most things."

[alexdoesstuff]

I thought the role of "second best tool for most things" belonged to Excel

[StableAlkyne]

Excel is the most popular GUI framework and programming language in existence. And it underpins accounting divisions around the world!

[llm_trw]

No, excel is the worst tool for anything.

[QuadmasterXLII]

"but you have heard of me"