> Are these "numerical approximation methods" pythonically possible?
>

Yes and that's how they are normally found - not necessarily with
Python,
but by applying computer simulations of the equations. Generally you
calculate values in ever decreasing increments until you get enough
accuracy. eg you discover a zero crossingh between 3 and 4, then
between 3.3 and 3.4 then between 3.36 and 3.37 and so on...

Caveat:
You also need to look out for double crossings within a single step
change, so don't make the steps too big. And check the number of
roots you expect versus the number you get as an error detection
scheme.

Alan G.

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