On Sat, Jan 21, 2023 at 8:43 AM Jonathan Thornburg wrote:
>
>
> Maple reports the same result for your first testcase:
>
> But, I think Maple and Sage/Giac are both wrong: consider the *definite*
> integral (latex notation) $I = \int_0^{3/2} \lfloor x \rfloor^2 \, dx$:
>
Lol, a cross-CAS exploit
On Sat, 21 Jan 2023 at 06:43, Jonathan Thornburg wrote:
>
> On Fri, Jan 20, 2023 at 07:16:14PM +0200, Georgi Guninski wrote:
> > I have theoretical reasons to doubt the correctness
> > of integrals involving `floor`.
> >
> > The smallest testcases:
> >
> > sage: integrate(floor(x)^2,x)
> > // Giac
I got an integral, which fails the derivative check.
For real positive x, define
f(x)=2^(x - 1/2*I*log(-e^(-2*I*pi*x))/pi - 1/2)
f(x) is just an obfuscation of 2^floor(x) and
for all positive x, f(x) is integer.
Let g(x) be the indefinite integral of f(x)
and let gder(x)=g'(x).
Assuming correct co
