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

• 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. 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?