[fddr]

As a former physicist that used Mathematica heavily not that long ago, I have to disagree. It would be great if there were open source alternatives that were "superior in every way" but that is just not the case.

For some use cases at least, Mathematica is clearly better than anything else I have tried.

I feel like something like ipython notebooks with the right combination of libraries might eventually get there, but that is unfortunately still years away.

[monochr]

As another physicist who used mathematica what you mean is that you were too lazy to think about what assumptions were made implicitly in the calculations you were performing and liked mathematica because it did them automagically for you.

This is shown no where better in the paper than when they try to calculate Integrate[Exp[-pt](Sinh[t])ˆ3, {t, 0, Infinity}]. In a good cas, such as maxima, you will get no result and a ton of errors. Which is what you should get without specifying what sort of variable p is, is it a matrix, polynomial, group of some sort? That it's implicitly assumed to be a real number that might turn out to be complex under some circumstances isn't a feature, it's a bug.

[fddr]

I am genuinely surprise at how confidently you (quite wrongly) diagnosed my problem.

What I did mean, was that for my use cases, I found Mathematica was superior to the alternatives. You are welcome to think this was because I was lazy or misguided, but it was definitely not because I liked not having to specify domains for my variables (and I do remember having to write Assuming[p>0 && x \in Reals, ...] and the like often, it definitely does not assume everything is a positive real).

One thing I used Mathematica a lot for was numerical integration of ODEs (that had been derived using the CAS part of Mathematica and had some pretty nasty coefficients). NDSolve in my experience was just better than competition. You can definitely get nonsense out of it, but with a modicum of care it works incredibly well.