Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Can we get the holomorphic super-root and super-logarithm function?
(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.
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???
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.

Messages In This Thread
RE: Can we get the holomorphic super-root and super-logarithm function? - by Ember Edison - 06/08/2019, 05:22 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 1,898 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is bugs or features for super-logarithm? Ember Edison 10 5,891 08/07/2019, 02:44 AM
Last Post: Ember Edison
  Is there a function space for tetration? Chenjesu 0 897 06/23/2019, 08:24 PM
Last Post: Chenjesu
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 8,248 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Degamma function Xorter 0 1,334 10/22/2018, 11:29 AM
Last Post: Xorter
  Inverse super-composition Xorter 11 16,128 05/26/2018, 12:00 AM
Last Post: Xorter
  The super 0th root and a new rule of tetration? Xorter 4 5,263 11/29/2017, 11:53 AM
Last Post: Xorter
  Solving tetration using differintegrals and super-roots JmsNxn 0 2,354 08/22/2016, 10:07 PM
Last Post: JmsNxn
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 19,613 08/22/2016, 12:19 AM
Last Post: JmsNxn
  The super of exp(z)(z^2 + 1) + z. tommy1729 1 3,185 03/15/2016, 01:02 PM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)