Erik Lane wrote:
That's almost certainly true. In fact, the result printed by the "failure"
is more accurate than the expected value! I tried this in Mathematica:
This might be a trivial question, but how do you know which number is
more accurate than the other, if those results are machine-dependent?
The result I showed, the answer was not computed using a floating point
processor, but by arbitrary precision arithmetic. As such, it should not have
been machine defendant.
Or is the Mathematica answer your gold standard?
I'm not suggesting it is a gold standard, but given the results agreed
reasonably closely with Sage, and were computed to arbitrary precision, then I
had a reasonable degree of confidence in believing the "failure" was not really
a failure at all.
If that is the case I
find it troubling. One of the reasons for Sage, in my mind, is to
avoid Mathematica and its 'black-box' approach. Therefore to trust its
answers over your own program's as the arbiter of accuracy is not a
promising sign.
From a practical point of view, despite the open source nature of Sage and the
closed-source nature of Mathematica, I am *personally* in a no better position
to evaluate Sage's answer than I am to check Mathematica's answer. Since Sage is
not anyone's program really.
If my life depended on that integral, I'd look at other ways of verifying the
result.
I really am not meaning to troll, but that raised a huge red flag in my mind.
It was not meant to.
Thanks,
Erik
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