Can’t reproduce on Sage 9.5.rc1 running in Debian testing. First thing after session start :
sage: integrate(e^x/(x^2+1), x, -pi, pi)
// Giac share root-directory:/usr/share/giac/
// Giac share root-directory:/usr/share/giac/
Added 0 synonyms
1/2*(imag_part(Ei(pi + I))*tan(1/2)^2 - imag_part(Ei(pi - I))*tan(1/2)^2 + 2*real_part(Ei(pi + I))*tan(1/2) + 2*real_part(Ei(pi - I))*tan(1/2) - imag_part(Ei(pi + I)) + imag_part(Ei(pi - I)))/(tan(1/2)^2 + 1) - 1/2*(imag_part(Ei(-pi + I))*tan(1/2)^2 - imag_part(Ei(-pi - I))*tan(1/2)^2 + 2*real_part(Ei(-pi + I))*tan(1/2) + 2*real_part(Ei(-pi - I))*tan(1/2) - imag_part(Ei(-pi + I)) + imag_part(Ei(-pi - I)))/(tan(1/2)^2 + 1)
BTW:
sage: integrate(e^x/(x^2+1), x).simplify_full()
1/2*(2*I*cos(1/2)^2 + 2*cos(1/2)*sin(1/2) - I)*Ei(x + I) + 1/2*(-2*I*cos(1/2)^2 + 2*cos(1/2)*sin(1/2) + I)*Ei(x - I)
sage: integrate(e^x/(x^2+1), x, algorithm="fricas").simplify_full()
1/2*(-I*Ei(x - I)*e^(2*I) + I*Ei(x + I))*e^(-I)
And these expressions are equal :
sage: integrate(e^x/(x^2+1), x).trig_reduce().exponentialize().factor()
-1/2*I*(Ei(x - I)*e^(2*I) - Ei(x + I))*e^(-I)
sage: integrate(e^x/(x^2+1), x, algorithm="fricas")
-1/2*I*(Ei(x - I)*e^(2*I) - Ei(x + I))*e^(-I)
Mathematica gives the same (mathematical) result (but this can’t be backtranslated to Sage now, for lack of ExpIntegralEi
in the translation dictionary) :
sage: mathematica.Integrate(e^x/(x^2+1), x)
((-I/2)*(E^(2*I)*ExpIntegralEi[-I + x] - ExpIntegralEi[I + x]))/E^I
HTH,
Okay. That’s a nice one…
After upgrading to 9.5.rc5 and disabling system’s pari
and singular
(for other reasons, see there), configure
somehow decided to install the giac
SPKG and not to use system’s giac
.
This triggered the behaviour your reported. Ahiii…
FWIW, system’s giac
version is 1.7.0, Sage’s is 1.6.0.
HTH,
To add insult to injury, trying to re-enable system’s giac
(make giac-clean && configure failed. Somehow,
./configurefinds no *suitable* system
giacversion, and re-builds Sage's giac. It seems that I should also clean
pari` and consorts and re-re-build…
Sigh…
2022-01-30 05:10:25 UTC, Emmanuel Charpentier:
>
> After upgrading to 9.5.rc5 and disabling system’s pari and singularDid you mean "after upgrading to 9.5.rc4"?
FWIW, after rebuilding Sage with system’s giac
:
sage: integrate(e^x/(x^2+1), x, -pi, pi)
1/2*(imag_part(Ei(pi + I))*tan(1/2)^2 - imag_part(Ei(pi - I))*tan(1/2)^2 + 2*real_part(Ei(pi + I))*tan(1/2) + 2*real_part(Ei(pi - I))*tan(1/2) - imag_part(Ei(pi + I)) + imag_part(Ei(pi - I)))/(tan(1/2)^2 + 1) - 1/2*(imag_part(Ei(-pi + I))*tan(1/2)^2 - imag_part(Ei(-pi - I))*tan(1/2)^2 + 2*real_part(Ei(-pi + I))*tan(1/2) + 2*real_part(Ei(-pi - I))*tan(1/2) - imag_part(Ei(-pi + I)) + imag_part(Ei(-pi - I)))/(tan(1/2)^2 + 1)
sage: giac.version()
"giac 1.7.0, (c) B. Parisse and R. De Graeve, Institut Fourier, Universite de Grenoble I"
But now, ptestlong
exhibits new bugs. Sigh (again)…
HTH,