Question already asked on |`ask.sagemath.org`](https://ask.sagemath.org/question/64934/plotting-ill-conditionned-function/), where it didn't attract a lot of attention...
Let ``` sage: f(x)=log(tan(pi/2*tanh(x))).diff(x) ; f x |--> -1/2*pi*(tan(1/2*pi*tanh(x))^2 + 1)*(tanh(x)^2 - 1)/tan(1/2*pi*tanh(x)) ``` It can be shown (see Juanjo's answer [here](https://ask.sagemath.org/question/64794/inconsistentincorrect-value-of-limit-involving-tan-and-tanh/)) that this finction's limit at `x=oo` is 2. A couple CASes are wrong about it : ``` sage: f(x).limit(x=oo) 0 sage: f(x).limit(x=oo, algorithm="maxima") 0 ``` A couple get it right : ``` sage: f(x).limit(x=oo, algorithm="giac") 2 sage: f(x).limit(x=oo, algorithm="mathematica_free") 2 ``` And Sympy currently never returns. A "naïve" way to explore this is to assess the situation is to look for numerical values : ``` plot(f, (1, 30)) ``` [image: tmp_bnpx6r7n.png] This plot hints at ill-conditionong of the epression of the function. And it turns out that this ill-conditioning can be overcome by specifying an "absurd" precision : ``` sage: f(30).n() -0.000000000000000 sage: f(30).n(digits=30) 1.99999483984586167962667231030 ``` But `plot` seems to *ignore* this specification : ``` sage: plot(lambda u:f(u).n(digits=30), (1, 30)) ``` [image: tmp_jeq3c8ko.png] We can try to "isolate" the precision specification in a Python function, which seems to work : ``` sage: def foo(x): return RR(f(x).n(digits=30)) sage: foo(30) 1.99999483984586 ``` but is still defeated byr the inner gears of `plot` : ``` sage: plot(foo, (1, 30)) ``` [image: tmp_dg2gelpc.png] Why, Ô why ??? -- 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/db271244-0ad7-4484-8a46-bdc4b1edd0f0n%40googlegroups.com.
