3 papers
math.NT2026
Belyi map verification using certified path tracking
Alexandre Guillemot, John Voight
We provide an end-to-end workflow to rigorously compute the monodromy of Belyi maps from exact equations over number fields using certified homotopy continuation. We then apply thi…
math.NT2022
Ideal classes of orders in quaternion algebras
Stefano Marseglia, Harry Smit
We provide an algorithm that, given any order in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right -ideals, includ…
math.NT2008
Algorithmic enumeration of ideal classes for quaternion orders
Markus Kirschmer, John Voight
We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the ru…