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Would be nice if dragging the coefficients would also change the roots.

Yeah. I think I punted on that because, although it's easy for degrees <= 4 (since those have general formulas!), I'd have to implement some root-finding method for degrees >= 5, and somehow preserve the orderings of the roots. Not insurmountable problems -- I might go back and do that someday!

I was just pondering about this. I imagine that moving a coefficient a small amount (and so long as the roots are not too close) that Newton-Raphson, initialized with a previously-known root, would converge very quickly to the new root while preserving the order.

If there truly are roots of multiplicity >= 2, then preserving the order of the multiple roots doesn't matter. Another issue is that Newton-Raphson might fail if the roots are too close.

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