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 new fatou.gp program JmsNxn Ultimate Fellow Posts: 977 Threads: 114 Joined: Dec 2010 07/07/2022, 01:09 AM Hmm, Okay That's something I've never seen before. You are right, Catullus, I've made a mistake somewhere in my observations. From here, I don't have an answer to your question. I am not familiar enough with the fatou.gp program. I thought it'd run the Schroder for $$i$$, didn't realize it ran the kneser algorithm. I guess the best statement that I have is that for $$1 < b < \eta$$ Sheldon's algorithm runs a kneser algorithm which roughly approximates the Schroder iteration. But for complex values it runs the Kneser iteration, as an analytic continuation. I'm still wary though of this solution. I apologize, my mistake. Catullus Fellow Posts: 210 Threads: 46 Joined: Jun 2022   07/09/2022, 06:55 AM (This post was last modified: 07/09/2022, 06:58 AM by Catullus.) Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Please remember to stay hydrated. Sincerely: Catullus JmsNxn Ultimate Fellow Posts: 977 Threads: 114 Joined: Dec 2010 07/10/2022, 01:51 AM (07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise. Catullus Fellow Posts: 210 Threads: 46 Joined: Jun 2022 07/10/2022, 02:23 AM (07/10/2022, 01:51 AM)JmsNxn Wrote: (07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise.What about using tetcomplex.gp? ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Please remember to stay hydrated. Sincerely: Catullus « Next Oldest | Next Newest »

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