new fatou.gp program

[sheldonison]

I have just downloaded it from somewhere. It includes the following:

\r kneser.gp
/* hyperoperators */
h(a,s,b) = ....

It might be incorrect according to the graph.

This was a reply to me asking, "I'm not familiar with H(x); sorry. How do you define/implement it? What function in fatou.gp are you using?"

First off, this post should never have been posted here in the fatou.gp discussion since Xorter's H function has nothing to do with fatou.gp.  Xorter's H function has two different definitions (ignoring the subtle use of both superfunctions of eta) depending on whether s<2 or s>=2.   Let's focus on only on the 2nd definition for S>=2.  For integer values of S, Xorter's pari-gp code for H(a,s,b) is equivalent to the following equation.

\( H(a,s,b) = \exp^{[\circ(s-2)]}_\eta(b \cdot \log^{[\circ(s-2)]}_{\eta}(a))\;\;\;\eta=\exp(1/e) \)
For s=2, this is just b*a which is as Xorter expected
For s=3, this is \( \eta^{b\cdot\log_{\eta}(a))}\;=\;a^b\; \) so this is as Xorter expected.
So it "works" for integer values of 2,3.  But Xorter "complains" about other values making a funny graph.
For s=4: H(2,4,3) = 11.713
For s=5: H(2,5,3) = 11.103
For s=6: H(2,6,3) = 3.411
So H(2,s,3) is doing exactly what Xorter's equation says it should do, with S extended to non-integer values of S by using the superfunction and the inverse superfunction of eta.  Of course its "incorrect" according to the graph... because H(2,s,3) is only "correct" at s=2 and s=3, but not other integer values of S, where H has nothing to do with the extended hyper operator Xorter claims it should be!