Le mardi 6 décembre 2022 à 14:16:56 UTC+1, dim…@gmail.com a écrit :
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) > That wouldn’t explain why the specification included in the lambda expression in the third example isn’t accepted : matplotlib should see the RR values returned by it (which *do* accept the precision specification). > > On Tue, Dec 6, 2022 at 12:53 PM Emmanuel Charpentier < > emanuel.c...@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...@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/d4815776-3bbd-44b1-bc46-cfc423cdedf4n%40googlegroups.com.
