Appears to me diffs back: False not necessarily
means wrong result.
For:
[23] diffs back: False
integrand: x*log(x + sqrt(x^2 + 1))*arctan(x)/sqrt(x^2 + 1)
antideriv: sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1))*arctan(x) - x*arctan(x) -
1/2*log(x + sqrt(x^2 + 1))^2 + 1/2*log(x^2 + 1)
maxima :
On Sat, 7 Sep 2013 15:25:26 +0300
Georgi Guninski gunin...@guninski.com wrote:
snip
btw, I get:
'sage.rings.complex_interval.ComplexIntervalFieldElement' object has
no attribute 'cot'
when trying your |check| on this:
-arctan(cot(pi*x))/pi + 1/2 #fractional part of x
This is now #15179:
Interesting experiment.
Your methodology for diffs back assumes
correctly computing the derivative and correctly
comparing symbolic expressions and for the latter
counterexamples are known [1]
bool( sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2) )
True
btw, I get:
Your methodology for diffs back assumes
correctly computing the derivative and correctly
comparing symbolic expressions and for the latter
counterexamples are known
Yes. This is just an indicator of possible problems, nothing more.
diffs back checks f == 0 which is incorrect a priori, it should
Recently two integration test suites were discussed at sci.math.symbolic
[1], [2].
I executed the tests with Sage and put the results on my webpage [3].
Not all results are favorable for Sage. Maybe this is worth to be
noted by some Sage developers.
Peter
[1]
