3 papers
math.AC2026
On exceptional cliques in matrix rings
Milan Boutros, Ignacio Cascudo, Ronald Cramer +2
We study the notion of exceptional clique, a subset of a ring such that the difference of any two distinct elements of the subset is invertible. Motivated by applications in crypto…
math.NT2026
On canonical roots of fractional ideals
Daniel M. H. van Gent
We give an algorithm to compute in polynomial time the roots of a fractional ideal of an order . We take care not to assume is Dedekind, since the maximal order of a number…
math.NT2025
Polynomial-time algorithms in algebraic number theory
Daniël M. H. van Gent
This document contains notes based on lectures given by Hendrik Lenstra at the PCMI summer school 2022. There are many problems in algebraic number theory which one would like to s…