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Le 22/09/2020 à 12:28, Bald Eagle a écrit :
> Cousin Ricky <ric### [at] yahoo com> wrote:
>> I am not convinced that this property is directly relevant to the
>> problem I am trying to solve. I still think the key is in that quartic
>> equation I came up with, which should not require numerical methods
>> (beyond what's implicit in POV-Ray's built-in functions). The problem
>> is that I am not practiced in solving quartic equations.
>
> Dumb question, but is there an online solver?
Sir, Yes Sir !
mathworld wolfram (alpha) has such beast.
It take a bit of learning to get it do what is desired, but there is
some examples along the pages.
You can ask it to refactor, solve (even based on chosen parameters), and
far more.
We are more in algebra than geometry.
https://www.wolframalpha.com/examples/mathematics/algebra/
> A language with the proper symbolic logic?
>
> Cheat and get the right answer first, then use that knowledge as a light to
> guide you along the path of working out the quartic.
>
I think the elliptical torus with a minor radius of 0 should match the
equation of the ellipse.
That's the basic check of any solution: minor radius of 0 would simplify
the equation to an ellipse.
The difficulty is going backward: reintroduce a non-0 minor radius.
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