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Results tagged with polynomials
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user 69320
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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polynomials with similar maxima-minima
Assume $p$ and $q$ are n-variate degree d, homogeneous polynomials. …
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Reference for multivariate orthogonal polynomials
I want to learn about multivariate orthogonal polynomials. Is there a good textbook/survey that you could suggest? … I need to see common examples like Jack's polynomials etc .. and also general theorems.
Thanks in advance. …
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local bernstein type inequality for multivariate polynomials
Let's say $p(x_1,...,x_n)$ is an n-variate degree d homogenous polynomial. Assume $U \subset S^{n-1}$ and $ vol(U) > 0 $ is there any Bernstein type inequality saying
$$ \max_{x \in U , y \in S^{n- …
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How can I distinguish a genuine solution of polynomial equations from a numerical near miss?
There is a technique called Smale's $\alpha$ theory that is used to certify solutions to polynomial equations. This technique is implemented by Haunstein and Sottile, it is sometimes considered to be …
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Biggest Cartesian Product Included in a Real Plane Curve
Suppose an irreducible smooth $p \in \mathbb{R}[x_1,x_2]$ is given, and we would like to find finite sets $S_1 , S_2 \subset \mathbb{R}$ such that $p(S_1 \times S_2)=0$ and $|S_1 \times S_2|$ is as b …
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Average nastiness of a Newton polytope
This quantity $A_P$ helps to control computationwise how nasty can a polynomial system created out of $n-1$ polynomials with support $P$ be. …
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