In a bunch of papers, Kamal Khuri Makdisi outlines how standard techniques to compute with coherent sheafs via global sections of their twists can be used to obtain (at least asymptotically) efficient algorthims to compute in the Picard group of an algebraic curve (he outlines Pic^0, but the ideas readily generalize to all of Pic).

A little experimentation shows that these techniques can be fairly efficient in practice as well (and certainly usable!). We'll have to see if the method can be truly competitive with the Hess-type "function field as finite extension of k(x)" approach.

In any case, Kamal's approach is much easier to implement and, thanks to its uniformity, much easier to trust, so at least as a stepping stone, it's useful to have an implementation available.

CC: @pjbruin

Component: algebraic geometry

Keywords: sd86.5

Branch/Commit: u/roed/implement_computations_in_picard_groups_via_global_sections_of_line_bundles @ 1ea07dd

Issue created by migration from https://trac.sagemath.org/ticket/15113