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Results tagged with polynomials
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user 507148
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Maximizing the ratio of multilinear polynomials
Consider two multilinear Polynomials $A(x_1,x_2,x_3,\dotsc,x_n)$ and $B(x_1,x_2,x_3,\dotsc,x_n)$ of $n > 2$ variables $x_i \in \mathbb{R}$ and their ratio
\begin{equation*}
F(x_1,x_2,x_3,\dotsc,x_n) = … ,\dotsc, x_n)
\end{equation}
Question: Can $G$ be written as
\begin{equation*}
G(x_3,\dotsc,x_n) = \frac{\widetilde{A}(x_3,\dotsc,x_n)}{\widetilde{B}(x_3,\dotsc,x_n)}
\end{equation*}
with multilinear polynomials …
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