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 Comparing the Known Tetration Solutions Gottfried Ultimate Fellow Posts: 758 Threads: 117 Joined: Aug 2007 08/29/2007, 06:19 AM jaydfox Wrote:Using gp, I computed Andrew's solution for base e, using a 50x50 matrix. (Side question: Andrew, how much faster are other libraries at solving these large matrices?)Jay, could you provide me your gp-code for comparision? You may put it here or send me an email. Also I would like to check, whether your last computations can be smoothed by accelerating convergence using Euler-summation of terms. But I've only Pari/GP and maxima(the latter with extremely little experience) and I don't know how complex your computations were and how much work it would be to get it implemented. What do you think? Gottfried Gottfried Helms, Kassel bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/29/2007, 07:48 AM (This post was last modified: 08/29/2007, 07:57 AM by bo198214.) @Jay Wow, this is indeed interesting. I mean theoretically it is clear that $h(x):=f^{-1}(g(x))-x$ must have period 1 for two (strictly increasing continuous) solutions $f$ and $g$ of $\phi(x+1)=F(\phi(x))$. Because $h(x+1)=f^{-1}(g(x+1))-(x+1)=f^{-1}(F(g(x))-(x+1)=f^{-1}(g(x))+1-(x+1)=h(x)$. But to see it as graphs is another thing . And I would think that it is in no way a sinus wave. However the periodic analytic functions can built by Fourier series. andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/29/2007, 08:19 AM Several things. I have never used pari/gp but I have 3 implementations of my super-log code and Carleman-matrix stuff in languages other than Maple/Mathematica: C with GMP (super-logarithm) Perl with BigInt (super-logarithm) Maxima (for Carleman-matrix) However, I'm not sure I know where the first two are, but I just found my maxima code, so I can post that soon. On another note, I like these graphs, although I still don't know how to use Jay's method. I can understand the oscillation, since the further you get away from integers the "less defined" tetration is... so it makes sense to me. I would like to post some graphs of Daniel's and my extensions, and I think I'll stick with the (critical) interval -1

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