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

[hermann@stamm-wilbrandt.de]

On 2024-01-29 11:54, Bill Allombert wrote:
> The problem is that the value of q for example is so large it will not 
> fit in
> the memory of your computer...
>
> Cheers,
> Bill
At the end of

"Universal Diophantine Equation", James P. Jones,
The Journal of Symbolic Logic, Vol. 47, No. 3 (Sep., 1982), pp. 549-571

... such that conditions (D1)-(D37) hold. There are 53 variables here. 
We eliminate
17 by simple substitution, viz. A, b, C, D_0, M_1, Q, V, W, N_1, N_2, 
N_3, S_1, S_2, S_3,
T1, T2, T3. Then introducing 22 new variables, to define λB, b^2, 2AB - 
B^2 - 1,
AC_1, c^2, c^4, <, Q^2, Q^3, Q^4, c^4 Q^3, N^2, MU, PK, □, YK, <, AC, 
C^2, AE, F^2 and GH,
allows all of our conditions to be expressed as a system of diophantine 
equations
of degree 2 and hence by a single diophantine equation of degree 4. ...

Unfortunately only instructions on how to create system of Diophantine 
equations
in 58 variables, but with maximal degree 2 is given — but that sounds 
interesting.

Can this set of Diophantine equations can be found somewhere written 
out?


Regards,

Hermann.