A nice one, indeed. Here, Sage seems to use Maxima’s integrator :
sage: table([[u,(f(x)-g(x)).integrate(x,algorithm=u)] for u in ["maxima", "sympy", "giac", "fricas", "mathematica_free"]], header_row=["Algorithm", "Indefinite integral"]) Algorithm Indefinite integral +------------------+--------------------------------------------------------------------------------------------------------------------------------------+ maxima -1/9*(-3*I*x - 1)*cos(3*x) - 1/9*(3*I*x + 1)*e^(-3*I*x) + 1/9*(3*x - I)*sin(3*x) - 1/12*cos(6*x) + 1/12*e^(-6*I*x) + 1/12*I*sin(6*x) sympy 0 giac 0 fricas 0 mathematica_free 0 Note that : sage: (f(x)-g(x)).integrate(x).simplify() -1/9*(-3*I*x - 1)*cos(3*x) - 1/9*(3*I*x + 1)*e^(-3*I*x) + 1/9*(3*x - I)*sin(3*x) - 1/12*cos(6*x) + 1/12*e^(-6*I*x) + 1/12*I*sin(6*x) but : sage: (f(x)-g(x)).integrate(x).simplify_full() 0 and : sage: (f(x)-g(x)).expand() 0 There are already some reports of incorrect/surprising Maxima definite and indefinite integral errors, often related to choice of branchs or branch cuts not accounted for. Would you care to check them and file a ticket if yours isn’t already known? Le mercredi 15 décembre 2021 à 20:43:07 UTC+1, juanlui...@gmail.com a écrit : > See this example: > > f(x)=(x+sin(3*x))*exp(-3*x*I) > g(x)=f(x).expand() > integral(f(x)-g(x),(x,0,2*pi)) > > The answer is I*pi, but it should be 0. > > Many other examples (related to Fourier coefficients) give similar errors. > For instance: > > f(x)=(x+cos(x))*exp(-x*I) > g(x)=f(x).expand() > integral(f(x)-g(x),(x,0,2*pi)) > > The answer is -pi, and it should be 0. > > It can be easily with sagemath 9.4 in https://sagecell.sagemath.org > > Thanks in advance, > > Yours, > > Juan Luis Varona > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/ec5574d3-21c4-41d2-b6d7-83c8a2189d41n%40googlegroups.com.
