regular vs intuitive (formerly: natural)

[bo198214]

I'm curious: What programs and methods are you using to compute this? Esp. how do you compute the solution in reasonable time?

You mean the intuitive Abel function via the Abel matrix? Well I use some self written algorithm in Sage. It takes some time to compute the coefficients for a 300 matrix. I get 100x100 in less than a minute. But regardless how long it takes you only need to compute it once (even if it takes 5 days ), save it, and later you can use it anytime. If you need code, just tell me.

But J.D. Fox development much more sophisticated algorithms, giving better precision. I will have a look at it later and improve my own algorithms accordingly.

Also, can you try to expand, say, the \( \exp_{\sqrt{2}}^{1/2}(z) \) generated by this method about the fixed point 2? If it's not the same as the regular iteration then it should fail to be holomorphic there, right? (as that's the thing that characterizes the regular iteration -- that it's differentiable at the fixed point, no?)

yes. I will have a go at it (when I implemented Fox's improvements).