Being open source is definitely a plus for SymPy here. The authors
could have stepped through SymPy with a debugger to help figure out
their problem, and submitted a pull request for a fix once they found
it.

It's not always possible, or obvious, but it's best to verify your
results somehow. A good way is to compute the same thing, but in a
different way (doing a random numerical check counts as this). The
likelihood of a bug manifesting itself in exactly the same way in two
completely different algorithms is very low.

But you are right that all software has bugs. I would consider this
paper to be rather low quality, especially for the ACM. It reads more
like a ranty comment from an idiot on Hacker News than an academic
paper. Even so, others reading it may have the same mindset that they
did, that black box software written by others always works, and it's
good to remove that illusion.

Aaron Meurer

On Tue, Oct 28, 2014 at 6:38 AM, Joachim Durchholz <[email protected]> wrote:
> http://www.ams.org/notices/201410/rnoti-p1249.pdf
>
> It's hammering Mathematica, but of course bugs like that can happen with any
> symbolic math software.
> Still, SymPy might be able to milk arguments from it. Such as: being open
> source, it's easier to find and fix the source of miscalculations like the
> one reported in that paper.
>
> (I find it also remarkable that Wolfram let a known problem lie dormant for
> so long. That paper is going to hurt their name, badly.)
>
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