Current
Unless stated otherwise, the seminar takes place on Tuesdays,
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2018-07-05
10:00
Salle 385
Jean-François Biasse (University of South Florida)
Fast multiquadratic S-unit computation and application to the calculation of class groups
Let $L=Q(√d_1, … ,√d_n)$ be a real multiquadratic field and S be a set
of prime ideals of L that does not contain any divisors of 2. In this
paper, we present a heuristic algorithm for the computation of the
S-class group and the S-unit group that runs in time
$Poly(log(∆),Size(S)) e^{Õ(√ln d)}$ where $d=max_{i≤n} d_i$ and ∆ is the
discriminant of L. We use this method to compute the ideal class group
of the maximal order $O_L$ of L in time $Poly(log(∆)) e^{Õ(√log d)}$. When
$log(d)≤log(log(∆))^c$ for some constant $c < 2$, these methods run in
polynomial time. We implemented our algorithm using Sage 7.5.1.
