8 papers
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…
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…
Revisiting second-order linear differential equations over Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We review second-order homogeneous linear differential equations with coefficient functions whose germs lie in a Hardy field (and hence are strongly non-oscillating). We prove a co…
Probably faster multiplication of sparse polynomials
Joris van der Hoeven
In this paper, we present a probabilistic algorithm to multiply two sparse polynomials almost as efficiently as two dense univariate polynomials with a result of approximately the…
Integer multiplication is at least as hard as matrix transposition
David Harvey, Joris van der Hoeven
Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an binary mat…
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…