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 Can we get the holomorphic super-root and super-logarithm function? Ember Edison Junior Fellow Posts: 38 Threads: 5 Joined: May 2019 06/08/2019, 05:22 AM (This post was last modified: 06/08/2019, 02:14 PM by Ember Edison.) (06/02/2019, 07:51 AM)sheldonison Wrote: (06/01/2019, 03:59 PM)Ember Edison Wrote: Ps: How to get the photo like you in pari/gp? I need some plot code.  https://math.eretrandre.org/tetrationforum/showthread.php?tid=1017 ok, i see MakeGraph().But why i use write() nothing in my test file? Ps2:How far are we get a perfect code to evaluate super-roots if we get the perfect tetration code? Thanks for the links.  I had seen Paulson's javascript code before, when I exchanged emails with the author last May. I'm assuming you got MakeGraph to generate plots;   This MakeGraph example takes 20minutes??? sexpinit(exp(1)); fmode=3; /* f(z) is used by MakeGraph; fmode=3 sets f(z) to safesexp(z) */ MakeGraph(1080,540,-3,3,9,-3,"sexp_e.ppm",1); /* from -3 to +9 at real axis, -3 to +3 imaginary */ write ("foo.txt","hello"); pari-gp is really slow writing one pixel at a time; attached is a faster version of MakeGraph; I also have faster sexp inversion code, but the faster sexp code has bugs with some complex bases, so I didn't include it.    I think one needs to start by understanding the inverse of super-root before one can understand super-root since you need to take the inverse of sexp_b(n) for some particular value of n for which the super-root is interested in, so I would think you want to understand how sexp_b(1+0.5*I) behaves for example, for the variable b.  What if n is between 0 and 1?  Is sexp_b(0.5) bounded as base(b) changes?  I have no idea.  So obviously, I don't understand the inverse of the function, much less have a perfect code ...  My suggestion is to start with Newton's method and iterate on finding approximations for the inverse, but Newton's method relies on a guess being close enough to the correct answer to converge.  For some particular value of n, I think I might know how to numerically compute the Taylor series for the function given some starting point since I had done something like that earlier to show complex tetration is analytic in the base.This sound like research the tetration can not get key helpful for super-root. This is too regrettable, the all inverse function for tetration just has super-root was non-Complex. Ps:the Tetration Wiki not have any super-root information. It's too carzy. Ps2:If i just need 6 decimal digits for precision, can you speed up the code? You know, the human's eye can not get too high precision for color. Ps3:How to recode the sexp and slog to catch Underflow and Overflow? Yon know, underflow will become overflow in pari/gp. « Next Oldest | Next Newest »

 Messages In This Thread Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 05/28/2019, 02:53 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by sheldonison - 05/29/2019, 03:49 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 05/30/2019, 09:16 AM RE: Can we get the holomorphic super-root and super-logarithm function? - by sheldonison - 05/30/2019, 11:33 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 06/01/2019, 03:59 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by sheldonison - 06/02/2019, 07:51 AM RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 06/08/2019, 05:22 AM RE: Can we get the holomorphic super-root and super-logarithm function? - by sheldonison - 06/09/2019, 12:24 AM RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 06/09/2019, 04:03 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by sheldonison - 06/09/2019, 04:31 PM RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 06/10/2019, 04:29 AM

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