Complete SAGE code for tetration

[eyu100]

I want to see the results of the function, how fast it runs, etc., but I can't code. jaydfox definitely has working code; can someone post some here?

[bo198214]

I want to see the results of the function, how fast it runs, etc., but I can't code. jaydfox definitely has working code; can someone post some here?

Of which function? We have 4 approaches to tetration. (Unfortunately I only have Maple code. Jay and Andrew are the Sage masters here )
Btw. welcome on the tetration forum!

[jaydfox]

I can post some code that solves Andrew's slog with my "acceleration" code that I've described. The code is fairly short, but it isn't entirely automated yet, so there are certain steps that I manually run, manually summing partial sums along the way. This is mainly due to the inability to free memory in SAGE (or if there is such a way, I haven't found it). So I have to calculate partial results, save them to disk, and reload for the next set of partial results.

I also have code for my other approach with the change of base formula, but it's also fairly manual for the most part. I haven't abandoned it, because I still consider it an interesting line of work, but I'm much more interested in the slog solution at the moment.

[jaydfox]

For studying tetration in general, I think the best place to start is with base eta, which can be solved using a continuous iteration of \( f(z)=e^z-1 \). Andrew has already posted functional SAGE code for this. I know I had to make a few additions to it, but it wasn't much, so let me know if you need help getting it to work with high precision (you should be able to get decently fast results with hundreds of digits of precision).

For a more complex (no pun intended) solution, consider the case of base e, which I'm confident will serve as a template for all bases greater then eta.

I'm nearly finished putting together a library for my accelerated version of Andrew's slog for base e. I think it'll be the most helpful solution for anyone wanting to study tetration as a newbie, especially complex tetration. Whether you're wanting to study complex tetration or real-valued tetration, Andrew's slog (and its inverse) seems to have several very wonderful properties that make it a strong contender for "the" solution, at least for base e.

I'm hoping to have the code ready to post within the next couple days. I'm automating steps I had been doing by hand, so hopefully this will be helpful for others as well.

[jaydfox]

I've posted some source code here:
http://math.eretrandre.org/tetrationforu...php?tid=74

It's a bit unpolished, but I've tried to make it fairly painless. Future versions will fully automate (hopefully) the process.