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:
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<x<0 since its the most well-behaved, and use the close-to-zero plots for \( {}^{x}b - (x+1) \) and \( slog_b(x) - (x-1) \) so that any oscillation is immediately obvious. My next post should have them, but I need more time to make the graphs.
Andrew Robbins
PS. That was a beautiful derivation Henryk
- 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<x<0 since its the most well-behaved, and use the close-to-zero plots for \( {}^{x}b - (x+1) \) and \( slog_b(x) - (x-1) \) so that any oscillation is immediately obvious. My next post should have them, but I need more time to make the graphs.
Andrew Robbins
PS. That was a beautiful derivation Henryk