Re: question on a 3 variable polynomial equation

On 2026-06-02 00:32, American Citizen wrote:
> This question is about finding more solutions of a certain 14-degree
> polynomial in 3 variables = 0.
> 
> Let P(a,s,t) = (a^10*s^4 + 2*a^10*s^2*t^2 + a^10*t^4 - a^8*s^6 -
> 3*a^8*s^4*t^2 + 4*a^8*s^4 - 3*a^8*s^2*t^4 + 4*a^8*s^2*t^2 - a^8*t^6 +
> 4*a^8*t^4 - 2*a^6*s^6 - 4*a^6*s^4*t^2 + 6*a^6*s^4 - 6*a^6*s^2*t^4 -
> 4*a^6*t^6 + 6*a^6*t^4 - 2*a^4*s^4*t^2 + 4*a^4*s^4 - 4*a^4*s^2*t^2 -
> 6*a^4*t^6 + 4*a^4*t^4 - a^2*s^8 + 2*a^2*s^6 - 4*a^2*s^4*t^2 + a^2*s^4
> + 6*a^2*s^2*t^4 - 2*a^2*s^2*t^2 - 4*a^2*t^6 + a^2*t^4 + s^6 -
> 3*s^4*t^2 + 3*s^2*t^4 - t^6) = 0
> 
...
> 
> How can more rational solutions be found? Is it possible?
> 
> Randall
> 
I asked gemini, and while one conclusion returned was wrong, this was 
right:
An entire rational line (the a-axis where s=t=0).

? P(a,0,0)
%6 = 0
?

Regards,

Hermann.