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 computations, we should have
gder(x)=g'(x)=f(x) (*) According to sage, gder is the constant $1$ and (*) fails. sage session: === f=2^(x - 1/2*I*log(-e^(-2*I*pi*x))/pi - 1/2) g=integrate(f,x);gder=g.derivative(x) g #1/2*sqrt(2)*(-1)^(-1/2*I*log(2)/pi)*x gder #1/2*sqrt(2)*(-1)^(-1/2*I*log(2)/pi) CC(gder) #1.00000000000000 x0=5;CC((f-gder)(x=x0)) #31.0000000000000 === Some questions: 1. What other CASes say about g(x)? 2. Why the derivative test fails? 3. Besides the jumps at integer, do branches of log() give instability? Some comments suggest discontinuous functions cause integral problems. There are built-in discontinuous functions like tan() which are widely used. 4. Why tan() integrals are used without problems (?) when this fails the derivative check? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD-E3tab-kwWUPAZQkJLzWOOYOLPLRZoe4VuqMU8znqR7A%40mail.gmail.com.
