# Tagged Questions

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Special problem: Let $G(z)$ be a probability generating function(pgf, the $z$ can be seen as real number or complex number), that is $$G(z) = \sum\limits_{i = 0}^\infty {{p_i}{z^i}} ,(\left| z ... 1answer 359 views ### Probability that random cubic polynomials meet in a square Let p_1(x) and p_2(x) be cubic polynomials with random coefficients in [-1,1]. I wanted to compute the probability that p_1 and p_2 share at least one point within the square [-1,1]^2. Of ... 1answer 231 views ### Random algebraic numbers are linearly disjoint almost surely? I already posted this question at MSE here, but since it received no answer or comment so far I cross-post it here. It is well-known that if one considers a “random” monic polynomial of fixed degree, ... 3answers 646 views ### Probability of coprime polynomials Given positive integer N, we choose m_1, m_2, n_1, n_2 independently and with equal probabilities from \{0,1,\ldots,N\}, and let f_1 = x^{m_1} + (1+x)^{n_1} and f_2 = x^{m_2} + (1+x)^{n_2} ... 4answers 757 views ### Distribution of roots of complex polynomials I generated random quadratic and cubic polynomials with coefficients in \mathbb{C} uniformly distributed in the unit disk |z| \le 1. The distribution of the roots of 10000 of these polynomials are ... 0answers 91 views ### Two Different Representations of Multivariate Bernstein Polynomials In the literature the multivariate Bernstein polynomial of a function f:[0,1]^m\rightarrow\mathbb{R} is often defined as the following:$$B_{f,n}(x_1,\dots,x_m)=\sum_{\mathbf{k}\in ...
Let $f(x), g(x), h(x)$ be randomly chosen irreducible polynomials over the finite field $GF(2^n)$. What would the probability be for $\sum_{(i,j,k:i,j,k\in\mathbb{N},i+j+k=C)} f^i(x)g^j(x)h^k(x)=0$, ...