# 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 [email protected] 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

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 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?