6 papers
A parametric version of the Hilbert Nullstellensatz
Rida Ait El Manssour, Nikhil Balaji, Klara Nosan +2
Hilbert's Nullstellensatz is a fundamental result in algebraic geometry that gives a necessary and sufficient condition for a finite collection of multivariate polynomials to have…
Multiplicity Problems on Algebraic Series and Context-Free Grammars
Nikhil Balaji, Lorenzo Clemente, Klara Nosan +2
In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polyno…
The Membership Problem for Hypergeometric Sequences with Quadratic Parameters
George Kenison, Klara Nosan, Mahsa Shirmohammadi +1
Hypergeometric sequences are rational-valued sequences that satisfy first-order linear recurrence relations with polynomial coefficients; that is, a hypergeometric sequence $\langl…
Identity Testing for Radical Expressions
Nikhil Balaji, Klara Nosan, Mahsa Shirmohammadi +1
We study the Radical Identity Testing problem (RIT): Given an algebraic circuit representing a polynomial and nonnegative integers $a_1, \ldots,…
The Membership Problem for Hypergeometric Sequences with Rational Parameters
Klara Nosan, Amaury Pouly, Mahsa Shirmohammadi +1
We investigate the Membership Problem for hypergeometric sequences: given a hypergeometric sequence of rational numbers and a target $t \in \math…
On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices
Klara Nosan, Amaury Pouly, Sylvain Schmitz +2
We investigate the complexity of computing the Zariski closure of a finitely generated group of matrices. The Zariski closure was previously shown to be computable by Derksen, Jean…