On Mon, Oct 23, 2023 at 12:35 AM Mild Shock <[email protected]> wrote: > > > There is 'romberg' in NumericalQuadrature package. > > Is this something under the heading "FriCAS API"? > > I have no clue how to load a package, and I even > don't understand how I get into a ")" prompt?
")" is not a prompt, it's part of a command you type at "->" prompt, > > All I see when I start FriCAS is a "->" prompt: > > (1) -> > > > Waldek Hebisch schrieb am Sonntag, 22. Oktober 2023 um 23:20:17 UTC+2: >> >> On Sat, Oct 21, 2023 at 03:49:08PM -0700, Mild Shock wrote: >> > The slope multiplied by the distance would be, >> > using real-valued root (the Wolfram Alpha assumption): >> > >> > integral_0^(2 π) 1/100 (2 + cos(t)) cos(t)^(1/3) dt = 0.0364298 >> > https://www.wolframalpha.com/input?i=integ_0%5E%282*pi%29+cos%28t%29%5E%281%2F3%29+%282%2Bcos%28t%29%29+%2F100+dt&assumption=%22%5E%22+-%3E+%22Real%22 >> > >> > But I am not sure whether the interval - π/2 to π/2, >> > as you suggest, would give me the slope. >> >> I suggested splitting interval into two parts: one where cos is >> positive and one where it is negative. You then need to add >> both parts, taking only one would be wrong. >> >> > The factor >> > cos(t)^(1/3) is indeed positive in this interval, but >> > >> > the integrand itself is not symmetric, for example the >> > range π/2 to π is not a mirror of the range 0 to π/2. Also >> > the smaller interval doesn't improve integrability: >> > >> > (1) -> integrate(cos(t)^(1/3)*(2+cos(t))/100, t = -%pi/2..%pi/2, "noPole") >> > >> > (1) "failed" >> >> Yes, I was illustrating general principle. Above the approach >> breaks down because FriCAS can not compute indefinite integral. >> However, in cases when FriCAS can compute indefinite integral >> you may have trouble due to singularities and choice of >> brnaches. Splitting is a fairly general method to limit >> troubles caused by singularities. >> >> > Maybe there is a function in FriCAS for some >> > numerical integral algorithm? Have to check the FriCAS >> > manual, maybe I find something. >> >> There is 'romberg' in NumericalQuadrature package. >> >> -- >> Waldek Hebisch > > -- > 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/5ae78271-f75f-45b0-99dc-0ec802fc572an%40googlegroups.com. -- 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/CAAWYfq2wpph%3Dtk9_1%2BYmJ7kT%2BpNtoKVDQ6UbaSctirqXECnsuA%40mail.gmail.com.
