even more fun can be had by trying to plot the symbolic derivative of the function at hand. It's just making no sense at all what I see...
On Tue, Dec 6, 2022 at 1:41 PM Dima Pasechnik <dimp...@gmail.com> wrote: > I can only say that the precision settings are ignored somewhere, so you > get e.g. with digits=20, not 30, the following: > sage: sage: def foo(x): > ....: ....: return RR(N(-1/2*pi*(tan(1/2*pi*tanh(x))^2 + 1)*(tanh(x)^2 > - 1)/tan(1/2*pi*tanh(x)), digits > ....: =20)) > ....: > sage: [foo(t) for t in [1..30]] > [1.93774723784661, > 1.96821438642349, > 1.99513501225342, > 1.99933077915401, > 1.99990923138260, > 1.99998771214757, > 1.99999833695304, > 1.99999977492984, > 1.99999996954002, > 1.99999999587773, > 1.99999999944087, > 1.99999999992499, > 1.99999999996552, > 2.00000000042880, > 1.99999999864906, > 1.99999996835578, > 1.99999995885087, > 2.00000113072913, > 2.00001042817460, > 2.00003433318607, > 1.99883239681839, > 1.99062668609516, > 1.94465796436172, > 2.14811194088516, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000] > > or wihout digits set: > sage: [foo(t) for t in [1..30]] > [1.93774723784661, > 1.96821438642349, > 1.99513501225340, > 1.99933077915395, > 1.99990923138165, > 1.99998771213936, > 1.99999833692570, > 1.99999977472377, > 1.99999996716508, > 1.99999996314183, > 1.99999991577607, > 1.99999955972581, > 1.99998381431810, > 1.99992717313233, > 1.99985733718347, > 1.99771319132044, > 2.00589700214384, > 1.91808127189615, > 1.23125745353424, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000, > -0.000000000000000] > > if it were able to use the 30 digits, we would not have seen that drop > down of the function graph to 0 somewhere just before 20. > > > On Tue, Dec 6, 2022 at 1:28 PM Emmanuel Charpentier < > emanuel.charpent...@gmail.com> wrote: > >> The same thing happens after : >> >> sage: def foo(x): >> ....: return RR(N(-1/2*pi*(tan(1/2*pi*tanh(x))^2 + 1)*(tanh(x)^2 - >> 1)/tan(1/2*pi*tanh(x)), digits=30)) >> ....: >> sage: foo >> <function foo at 0x7fe472aab250> >> sage: plot(foo, (1, 30)) >> Launched png viewer for Graphics object consisting of 1 graphics primitive >> >> >> >> >> Le mardi 6 décembre 2022 à 14:23:48 UTC+1, Emmanuel Charpentier a écrit : >> >>> 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/de783db9-35b4-47a4-88ba-064a1f67f532n%40googlegroups.com >> <https://groups.google.com/d/msgid/sage-support/de783db9-35b4-47a4-88ba-064a1f67f532n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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