1 citations · 3 across the 4 of their papers we have counts for
7 papers
The theory of maximal Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field of transseries, and give various applications of this…
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…
Fast interpolation of sparse multivariate polynomials
Joris van der Hoeven, Grégoire Lecerf
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbi…
Factoring sparse polynomials fast
Alexander Demin, Joris van der Hoeven
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms…
Surreal numbers as hyperseries
Vincent Bagayoko, Joris van der Hoeven
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be r…