It's plotting via matplotlib, perhaps that's why the precision setting is ignored (or pehaps something like RDF is hardcoded in Sage plotting code)
On Tue, Dec 6, 2022 at 12:53 PM Emmanuel Charpentier < emanuel.charpent...@gmail.com> wrote: > 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 > <https://groups.google.com/d/msgid/sage-support/db271244-0ad7-4484-8a46-bdc4b1edd0f0n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAAWYfq2wmF1jUH85LVFzjO33LxBr%2BxvSg4dYJ9mSSxNwXzz4FA%40mail.gmail.com.
