Re: question on a 3 variable polynomial equation

Hermann:

Thanks for finding the trivial solution... well it IS correct

:-) (guess I asked for it, didn't I ?

Randall

On 6/1/26 16:18, [email protected] wrote:
> 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.