= Workshop on Algorithms in Number Theory and Arithmetic Geometry =

This wiki is intended for projects related to SageMath during the workshop ''Algorithms in Number Theory and Arithmetic Geometry'' (Leiden, 31 July-4 August 2017).

Workshop webpage:
https://www.universiteitleiden.nl/en/events/2017/07/workshop-on-algorithms-in-number-theory-and-arithmetic-geometry

!CoCalc project for discussion/coding sessions (not necessarily SageMath-related): https://cocalc.com/projects/24e6bfa2-6cc4-425e-95e4-7a2c92ce446f/
(please send an e-mail to P.J.Bruin@math.leidenuniv.nl to be added to this project)

== Projects ==

 * '''Put your project here!'''

 * Finish tickets related to $p$-adic fields from Sage Days 87 (https://wiki.sagemath.org/days87/projects)

 * Access new PARI functionality from SageMath

 * Review open tickets (https://trac.sagemath.org/):

   * Shioda invariants for hyperelliptic curves with genus 3: https://trac.sagemath.org/ticket/22173

 * [[PariDevInSage|How to use PARI/GP development version inside Sage]]

 * Update the SageMath version of Denis Simon's GP scripts (http://www.math.unicaen.fr/~simon/) to the latest version

 * SageMath 8.0 has now `sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface` for numerical computation of period matrices. See August 1 presentation [[attachment:RiemannMatrixPresentation.ipynb]]. Perhaps this is more easily viewed via the (slightly broken) [[https://nbviewer.jupyter.org/url/www.cecm.sfu.ca/%7Enbruin/Leiden_presentation.ipynb]]. Integrate this code better into the rest of sage, e.g.:
   * put a method on plane algebraic curves to get the corresponding Riemann surface?
   * Improve the Gauss-Legendre integrator to compute the integration nodes in a more efficient way?
   * There is already code to compute a $\mathbb{Z}$-basis for the endomorphism ring numerically. Perhaps support computations of isogenies as well?
   * Make the Rosati involution available?