Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Matera, Guillermo"'
We study the set of common $\mathbb{F}_q$-rational solutions of "smooth" systems of multivariate symmetric polynomials with coefficients in a finite field $\mathbb{F}_q$. We show that, under certain conditions, the set of common solutions of such pol
Externí odkaz:
http://arxiv.org/abs/2312.09477
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely irreducible varieti
Externí odkaz:
http://arxiv.org/abs/2208.08572
We design and analyze an algorithm for computing solutions with coefficients in a finite field $\mathbb{F}_q$ of underdetermined systems defined over $\mathbb{F}_q$. The algorithm is based on reductions to zero-dimensional searches. The searches are
Externí odkaz:
http://arxiv.org/abs/2206.12516
Publikováno v:
In Journal of Complexity December 2024 85
Publikováno v:
In Journal of Algebra 15 February 2025 664 Part A:362-413
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two polynomials of deg
Externí odkaz:
http://arxiv.org/abs/2103.15926
We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field F_q of q elements when the highest-degree polynomial g is fixed. Considering all the elements f of fixed degree, we es
Externí odkaz:
http://arxiv.org/abs/2001.03222
In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for Newton's r
Externí odkaz:
http://arxiv.org/abs/1812.07020
We estimate the number $|\mathcal{A}_{\boldsymbol\lambda}|$ of elements on a nonlinear family $\mathcal{A}$ of monic polynomials of $\mathbb{F}_q[T]$ of degree $r$ having factorization pattern $\boldsymbol\lambda:=1^{\lambda_1}2^{\lambda_2}\cdots r^{
Externí odkaz:
http://arxiv.org/abs/1807.08052
Publikováno v:
In Journal of Symbolic Computation March-April 2022 109:31-49