Quaternary quadratic lattices over number fields

We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q)

Algorithmic enumeration of ideal classes for quaternion orders

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 run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.Comment: 39 pages, includes 2 tables; corrections made to Table 8.

The explicit membership problem for discrete free subgroups of PSL(2,R)

Non UBCUnreviewedAuthor affiliation: RWTH Aachen UniversityPostdoctora