The AMS Notices has a column about using computers to do math, dwelling
on some problems they had with Mathematica:
http://www.ams.org/notices/201410/rnoti-p1249.pdf
The HackerNews discussion immediately brings up Sage, of course:
https://news.ycombinator.com/item?id=8505665
Funny quote (that I don't necessarily agree with): "This resembles the
well- known Pentium division bug discovered by Thomas Nicely in 1994,
which only affected certain kinds of numbers. But it seems Mathematica
is a black box even darker that the internals of a microprocessor, so it
is difficult to try to understand what kinds of numbers are affected by
the Mathematica bug that we are describing."
Interestingly, throughout the article, they emphasize what a hard time
they had when the found MMA and Maple conflicting, and the problems with
having MMA be closed-source. You'd think they'd end with a resounding
recommendation to use open-source software whereever possible, and fund
and motivate it's development. However, their final recommendation
backpedals quite a bit and is just "However, for the time being, when
dealing with a problem whose answer cannot be easily verified without a
computer, it is highly advisable to perform the computations with at
least two computer algebra systems."
Thanks,
Jason
P.S. It would be interesting to see if Sage can do the calculation they
identified as buggy in mathematica. That would make for a cool
follow-up editorial.
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