Designing a Tetration Library

[andydude]

So I wrote a few more files. To start, I implemented a simple version of the right hyper operations, which can be found in "hyper/hyper.py", and to test these you can try this:

Code:

sage: from hyper.all import *
sage: hyper(3)(3, 2)
9
sage: hyper(4)(3, 2)
27
sage: hyper(5)(3, 2)
7625597484987
sage: plot(lambda x: hyper(4)(e.n(20), x), -1.9, 2.1)

You get the idea.

I have also implemented a wrapper around Jay Fox's infinitely iterated exponential (what he calls 'FindFixed', I renamed it to KnoebelH), and copied the Wikipedia implementation of LambertW, which does not work very well below -1/e, so I hope to improve upon this using the research of Corless et.al. so, for now, we can use it for simple things like:

Code:

sage: LambertW(1)
0.567143290409784
sage: KnoebelH(e)
0.318131505204764 + 1.33723570143069*I
sage: KnoebelH(e^(pi/2))
1.49809129296906e-13 + 1.00000000000024*I

Well, almost...