5 papers
Algebraic Closure of Matrix Sets Recognized by 1-VASS
Rida Ait El Manssour, Mahsa Naraghi, Mahsa Shirmohammadi +1
It is known how to compute the Zariski closure of a finitely generated monoid of matrices and, more generally, of a set of matrices specified by a regular language. This result was…
Differential Tree Automata
Rida Ait El Manssour, Vincent Cheval, Mahsa Shirmohammadi +1
A rationally dynamically algebraic (RDA) power series is one that arises as (a component of) the solution of a system of differential equations of the form $\boldsymbol{y}' = F(\bo…
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…
D-Algebraic Functions
Rida Ait El Manssour, Anna-Laura Sattelberger, Bertrand Teguia Tabuguia
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure propertie…
Multiplicity structure of the arc space of a fat point
Rida Ait El Manssour, Gleb Pogudin
The equation defines a fat point on a line. The algebra of regular functions on the arc space of this scheme is the quotient of by all differe…