Sage Days 16 Project Idea Page

Create a Cython class for points on elliptic curves and optimize basic arithmetic

PEOPLE: William Stein

Create elliptic curve classes for elliptic curve models in the Explicit-Formulas Database

PEOPLE: David Kohel

See the EFD: http://www.hyperelliptic.org/EFD/

Rewrite abelian groups

PEOPLE: William Stein

Optimize/better document/generally improve graph theory library in Sage

PEOPLE: Robert Miller

Cliquer SPKG for Sage

PEOPLE: Robert Miller, Nathann Cohen (remotely)

Take a look at the possibility of making GAP a dynamically loadable library

PEOPLE: Robert Miller, Martin Albrecht (hopefully)

Python implementation of Ford-Fulkerson algorithm

PEOPLE: Robert Miller

I plan on at least copying the Python implementation on wikipedia, since now we have nothing at all for max flow problems. Hopefully then someone who really cares about it will try to use it, realize it is slow, start improving it, etc. etc. etc.

Frobenius number and genus of numerical semigroups using toric Grobner bases

PEOPLE: Bjarke Hammersholt Roune

I plan to code Frobenius number (largest gap) and genus (number of gaps) functions for numerical semigrups using two related algorithms based on toric ideals. These algorithms can handle random numerical semigroups generated by numbers with thousands of digits, as long as there are not too many minimal generators (10 or more gets hard). I'm happy to explain either algorithm if you want to help or are just curious.

The first step is to find the best way to compute toric Grobner bases in Sage (4ti2?), then to improve the integration of the library Frobby, which we will use for irreducible decomposition of the initial ideal, and possibly also for the Hilbert series if Frobby turns out to be faster than Sage is now for that.

Help welcome!