[adamnemecek]

Unfortunately this is incorrect. Those minima are not the same. Remember that dual points have a real part and a dual part that indicates the rate of change at that point. The real part is the same but the dual is different.

[wenc]

My point is it’s not possible to uniquely reconstruct an arbitrary polynomial by just knowing the extrema because there may be information loss in the general case. I will stop here.

[adamnemecek]

It is possible if you know the rate of change which you do with dual points. Like you don’t interpolate just position but also the dual parts I.e. rate of change.