20 citations · 52 across the 24 of their papers we have counts for
27 papers
Smooth symmetric systems over a finite field and applications
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
We study the set of common -rational solutions of "smooth" systems of multivariate symmetric polynomials with coefficients in a finite field . We show t…
The distribution of defective multivariate polynomial systems over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
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: ide…
On the computation of rational solutions of underdetermined systems over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
We design and analyze an algorithm for computing solutions with coefficients in a finite field of underdetermined systems defined over . The algorithm…
Interpolation by decomposable univariate polynomials
Joachim von zur Gathen, Guillermo Matera
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…
Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
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 polyno…
Shifted varieties and discrete neighborhoods around varieties
Joachim von zur Gathen, Guillermo Matera
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 i…