6 papers
Power Sum Varieties over Finite Fields
Nardo Giménez, Juan Francisco Gottig, Miguel Palacios +2
We study a family of affine algebraic varieties over a finite field defined by systems of power sum polynomials. Our main goal is to investigate their geometric and…
A Kronecker algorithm for locally closed sets over a perfect field
Nardo Giménez, Joos Heintz, Guillermo Matera +3
We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety defined over a perf…
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…
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…