Re: Any chance to compute system of Diophantine exquations in 26 variables in GP?

[hermann@stamm-wilbrandt.de]

On 2024-01-26 20:28, Bill Allombert wrote:
> The issue is that the smallest solution is doubly exponential in k^4,
> so you will probably not be able to compute it.
> ...
> but then
> p=(n+1)^k
> q=(p+1)^n
>
> is going to be too large.
>
> Cheers,
> Bill.
I placed all variables besides k (which I assume constant) into a 
GraphViz graph.
I created edges for 14 formulas a0, a1, ..., a13 each variable is 
contained in.
Some variables have high degree, some only 2 or even 1.

I used GraphViz neato spring embedder with overlap=false to get an 
overview.

The GrahvizFiddle share link created is of length 984 bytes.
In order to prevent link issues, I used my personal website as URL 
shortener  by redirect:
https://stamm-wilbrandt.de/diophantine_26.html

Perhaps some kind of optimized backtracking algorithm (utilizing GP 
where helpful)
will be able to determine variable settings for small k in reasonable 
amount of time?

Interesting is variable o, it appears only in a4 and is the only 
negative (quadratic) term.
Since only positive integers for the variable are searched, these 
negative variables restrict the others.


Regards,

Hermann.