3 ms·
The VERY important detail is that the question dealz with randomness. From here the conclussion is more or less reasonable and not surprising (the residur formu
by pfortuny 12y ago
The VERY important detail is that the question dealz with randomness. From here the conclussion is more or less reasonable and not surprising (the residur formula gives most of the information). Essentially a matter of symmetry, I guess.
- deleted 12y ago[deleted]
- retroencabulato 12y agoI'm confused; I don't see how the randomness is really important here. I modified the code such that the expected value of each coefficient is a function of the term's degree: randomPoly[n_, x_] := x^Range[0, n].Table[RandomReal[{1, i}], {i, n + 1}] With this bias (or any of the various of biases I've tried), the result is exactly the same. I guess my observation is 'symmetry' of the coefficients has nothing to do with the 'symmetry' of the roots.
- Sharlin 12y agoI think coefficients that are merely linear (or even polynomial!) functions of the degree are all "almost equal to 1" in this case. As user conistonwater mentions in another comment, "I also think it's important to mention that the roots ax^300-b have magnitude (b/a)^(1/300), which is much closer to 1 than b/a, which is why the magnitudes of a and b don't matter very much."
- pfortuny 12y agoSorry I did not reply sooner. My answer what rather vague. Symmetry meant something related to the disk unit and zero and infinity but in a very very imprecise way...