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 Rational operators (a {t} b); a,b > e solved JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 06/06/2011, 05:34 AM (This post was last modified: 06/06/2011, 07:08 AM by JmsNxn.) (06/06/2011, 04:39 AM)sheldonison Wrote: mylatest kneser.gp code, which includes $\text{sexp}_\eta(z)$ support. This would also make it easier for other to try it. Code:fatb(a,t,b) = {   if (t>=1, return (cheta(invcheta(b*cheta(invcheta(a)+1-t))+t-1)));   if (t<1,  return (cheta(invcheta( cheta(invcheta(a)-t)+cheta(invcheta(b)-t) )+t))); } Oh that's great! I'd love to see what happens for complex operator values, I'll just modify your code slightly to say real(t) under the if conditions. (06/06/2011, 04:39 AM)sheldonison Wrote: I've gotten as far as quickly verifying that for t=0, we have addition, t=1, we have multiplication, and t=2 is exponentiation. for example, fatb(3,0,4)=7, which is 3+4 fatb(3,1,4)=12, which is 3x4 fatb(3,2,4)=81, which is 3^4 what does it mean that fatb(3,-1,4)=5.429897..? Is there a smooth continuation to a function for t=3, which would be tetration? if ae, and $n \in N$, which would be rational tetration. So actually yes, I can evaluate $4\, \{t\}\, 3$ over domain $t \in (-\infty, 3]$ The formula is given by: $a\, \{2 + q\}\, n = a_1\, \{1+q\}\, (a_2 \,\{1+q\}\, (a_3\,\{1+q\}...a_n$ And lastly, I tried using sexp/slog base $\eta$ for a,b < e and the graph of $a\, \{t\} \,b$ is not smooth and there are two humps at about {0.5} and {1.5} which is very unflattering. I was surprised when the cheta function worked, but it did. I have to give myself time to think about it first, but right now I'm sure the extension for a,b <= e is right infront of our eyes. Edit: I edited your code and tested if fatb(3, i, 3) = fatb(3, i+1, 2), and it does. Ackerman function is entering the complex plane me thinks. Edit again: Quote: if a

 Messages In This Thread Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 02:45 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 04:39 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 05:34 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 06:02 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 07:03 AM RE: Rational operators (a {t} b); a,b > e solved - by nuninho1980 - 06/06/2011, 05:16 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 06:53 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 08:47 AM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 09:23 AM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 06/06/2011, 11:59 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 05:44 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 09:28 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 07:47 PM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 08:43 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/07/2011, 02:45 AM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/07/2011, 06:59 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 04:54 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 07:31 PM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/08/2011, 08:32 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/08/2011, 09:14 PM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 01:50 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 11:47 PM RE: Rational operators (a {t} b); a,b > e solved - by Gottfried - 06/11/2011, 02:33 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/12/2011, 07:55 PM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/21/2016, 06:56 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 08/22/2016, 12:36 AM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/24/2016, 07:24 PM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/29/2016, 02:06 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 09/01/2016, 06:47 PM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 02:04 AM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 02:11 AM

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