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 : (sqrt(x
On Sat, 7 Sep 2013 15:25:26 +0300
Georgi Guninski wrote:
> 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:
http://trac.sagem
>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 s
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:
'sage.rings.complex_interval.ComplexI
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]
https://groups.google.com/d/msg/sc
