> 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? 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 fricas-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/5ae78271-f75f-45b0-99dc-0ec802fc572an%40googlegroups.com.
