BTW :
sage: a, b = var("a, b") sage: f(x) = floor(x)^2 sage: f(x).integrate(x, a,
b) // Giac share root-directory:/usr/local/sage-9/local/share/giac/ // Giac
share root-directory:/usr/local/sage-9/local/share/giac/ Added 0 synonyms
No checks were made for singular points of antiderivative
floor(sageVARa)^2*sageVARx for definite integration in [sageVARa,sageVARb]
-a*floor(a)^2 + b*floor(a)^2
Even accepting x*floor(x)^2 as an antiderivative of floor(x), this
*definite* integral is wrong, *wrong*, *wrong*. One could expect :
sage: F(x) = f(x).integrate(x) ; F x |--> x*floor(x)^2 sage: F(b) - F(a)
-a*floor(a)^2 + b*floor(b)^2
Something is amiss in Giac’s definite integration. Is thois already known ?
Le vendredi 20 janvier 2023 à 18:17:52 UTC+1, Georgi Guninski a écrit :
> I have theoretical reasons to doubt the correctness
> of integrals involving `floor`.
>
> The smallest testcases:
>
> sage: integrate(floor(x)^2,x)
> // Giac share root-directory:/usr/share/giac/
> // Giac share root-directory:/usr/share/giac/
> Added 0 synonyms
> x*floor(x)^2
>
> sage: integrate(2**floor(x),x)
> 2^floor(x)*x
>
> Would someone check with another CAS or prove/disprove by hand?
>
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