I am interested in determining the most probable maximum values of the real roots of polynomials of form $P(x)=\sum_{k=0}^n a_{k} x^k$ where the degree $n$ will have a defined value (say 3,4,5...) and $a_k$ are chosen from the set $\{-1,1\}$ with equal probability. Previously I had considered the maximum possible root for a set degree (see my previous question).
So in this case, I'm more looking to:
Enumerate all possible polynomials for a given degree $n$ (e.g.
Tuples[{-1, 1}, {4}].{1, x, x^2, x^3}
for $n=3$)For each possible enumerated polynomial $P(x)$ for a given degree, find the maximum $|root|$.
- Plot a (bar?) graph of the maximum $|root|$ values and their occurrences. (For a set degree)
So, in this case, rather than finding the maximum possible root a polynomial could have for a set degree $n$, I'd like to graphically see the most probable largest roots of $P(x)$ for $n$ fixed.
Any suggestions/help with this issue is immensely appreciated. Thank You!
n
that you describe grows as2^n
. The problem very quickly becomes intractable. $\endgroup$