18 citations · 69 across the 34 of their papers we have counts for
10 papers · 1 filter
The reciprocal complement of a polynomial ring in several variables over a field
Neil Epstein, Lorenzo Guerrieri, K. Alan Loper
The *reciprocal complement* of an integral domain is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of ar…
Constructing -free Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every Hardy field extends to an -free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations.…
Normalizing Asymptotic Differential Equations
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection wit…
Maximal immediate extensions of valued differential fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an ex…
An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings
Matthias Aschenbrenner, Christopher J. Hillar
A \textit{symmetric ideal} is an ideal that is invariant under the natural action of the infinite symmetric group. We give an explicit algorithm to…
Degree Bounds for Gröbner Bases in Algebras of Solvable Type
Matthias Aschenbrenner, Anton Leykin
We establish doubly-exponential degree bounds for Gröbner bases in certain algebras of solvable type over a field (as introduced by Kandri-Rody and Weispfenning). The class of alge…