Hi Martin, an old email from Waldek on this subject: -------- Forwarded Message -------- Subject: Re: [fricas-devel] interesting error in integration Date: Tue, 24 Jul 2018 00:12:30 +0200 (CEST) From: Waldek Hebisch <[email protected]> Reply-To: [email protected] To: [email protected]
Martin R wrote: > > Nasser found the following interesting bug at > https://trac.sagemath.org/ticket/25905: > > (1) -> f := (I*a*tan(d*x + c) + a)^3*tan(d*x + c) > > (1) > 3 3 4 2 3 3 3 2 > I a tan(d x + c) + 3 I a tan(d x + c) + 3 I a tan(d x + c) > + > 3 > a tan(d x + c) > Type: > Expression(Integer) > (2) -> F := integrate(f, x) > > (2) > 2 3 1 3 3 3 > (9 I - 3)a log(-----------------) + 2 I a tan(d x + c) > 2 > tan(d x + c) + 1 > + > 2 3 2 3 3 3 3 > 9 I a tan(d x + c) + (- 6 I + 18 I)a tan(d x + c) + (6 I - 18 I)a > d x > / > 6 d > Type: > Union(Expression(Integer),...) > (3) -> D(eval(F, I =%i), x)-eval(f, I=%i) > > (3) 0 > Type: > Expression(Complex(Integer)) > (4) -> F := integrate(eval(f, I=%i), x) > > >> System error: > arithmetic error DIVISION-BY-ZERO signalled > Operation was (/ -2 0). > > Any ideas? This is old confusion between real and complex. We create Complex(Complex(Integer)) and loose. It would be good to clean this up. AFAICS proper fix should not require much code, but it is going to touch several domains and packages. Basically, old code assumed that functions are real and allowed complex functions only as a hack. Current 'FunctionSpaceComplexIntegration' integrates _real_ function by passage to complex variables. We need a function to integrate _complex_ functions. -- Waldek Hebisch -- On 11/3/19 2:55 AM, 'Martin R' via FriCAS - computer algebra system wrote: > Dear all, > > maintaining the sage-FriCAS interface, I recently ran into the problem > of converting expressions that contain the complex unit into FriCAS > expressions. > > I vaguely recall that EXPR INT contains the complex numbers, by using > sqrt(-1), but I am not sure anymore. Hence: > > 1) What is the difference between EXPR INT and EXPR Complex INT > mathematically speaking? > 2) Is it "correct" to use sqrt(-1) for the complex unit? > > Thanks, > > Martin > > -- > You received this message because you are subscribed to the Google > Groups "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/fricas-devel/41025454-9c01-4490-9002-56d424960ea9%40googlegroups.com > <https://groups.google.com/d/msgid/fricas-devel/41025454-9c01-4490-9002-56d424960ea9%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/481cb793-6143-1ebd-edfb-492a8d03cdf2%40gmail.com.
