PROJECT GROUPS
Contents

PROJECT GROUPS
 Computing the Cartier operator acting on 1forms
 Making Drew Sutherland's smalljac code usable in Sage and extending Kate's data
 Computing Lseries of Jacobians of Certain Hyperelliptic Curves
 Computing in the class group of nonmaximal orders of quadratic imaginary fields
 Sara's (mostly Combinatorics) wishlist
 Some combinatorics projects from Anne's talk
 Symbolic projects
Computing the Cartier operator acting on 1forms
PEOPLE: Rachel P., Aly, Gagan, Anja, Sarah, Marina, Kate
See this page.
 sage worksheet that is slow and just implements algorithm (correctly!)
this appears to be done here: Computing N for Hyperelliptic curve.sws
 need data to check that this is correct.
 for what range of primes is this code reasonable?
 make it really, really fast (cython).
get included in sage itself Trac ticket #10457
make a big table or something? Rachel: "I would love to find a curve with prank 0 and anumber 1. I did genus 4 and p=3." Some examples
Making Drew Sutherland's smalljac code usable in Sage and extending Kate's data
PEOPLE: Kate, William S., Lola, Aly, Erin, Bianca
See the Project Page. Subprojects are:
 make smalljac code usable from Python (involves Cython)
 cubic and sextic residue symbol
 explicit calculation of Grossencharacters (aka Hecke characters).
Computing Lseries of Jacobians of Certain Hyperelliptic Curves
PEOPLE: Jennifer B., Jennifer P., Jennifer J., Bianca
 Decide if curve is attached to a modular form, and if so find it, then use that to compute Lseries (use Sturm bound  see paper of Ribet with appendix by Agashe/Stein)
 Need the analogue of Tate's algorithm to get from the NamikawaUeno classification to the Euler factor at the bad primes
 Plug Lseries into Dokchitser and get numbers.
Make a table. Starting with "van Wamelen"'s table. See also Kohel's tables.
Incorporate Robert Bradshaw's code into Purple Sage. http://code.google.com/p/purplesage/issues/detail?id=14
Computing in the class group of nonmaximal orders of quadratic imaginary fields
PEOPLE: William S., Bianca,
 Make a list of what you want to be able to do:
 Such computations come up for Stein in http://wstein.org/papers/kolyconj2/
 List why Magma/PARI aren't good enough (bugs, issues, speed, etc.)
 Write really really fast code to implement some of this.
Sara's (mostly Combinatorics) wishlist
PEOPLE: Needs people!
 Better index of software
 sbcl in Sage
 Quasisymmetric function bases (Jason Bandlow has preliminary implementations on sagecombinat)
 hyperplane arrangements
 wikipedia and Sage pages linked to each other
Some combinatorics projects from Anne's talk
 LaTeX support for tableaux, compatible with jsmath/mathjax for visualization in the notebook, see trac#4355
 Implementation of cyclage graph. PEOPLE: Anne S.
 Implementation of the Schuetzenberger involution Omega_2 on tableaux and words:
 tableaux > word > something > tableaux: result is a sage worksheet, then function included in sage?! done! see trac ticket http://trac.sagemath.org/sage_trac/ticket/10446#comment:1 PEOPLE: Erin, Ilke
 Faster implementation of crystal graph isomorphisms (would have implications for the energy function and Rmatrix). PEOPLE: Anne S., William S.
  view crystal graph and check if it is isomorphic to another graph (would build on Robert Miller's "NICE" package, which will check if any two graphs are isomorphic, which is fully available in Sage). Hopefully this makes this project easy?
 make the kSchur function and their duals live in the right subspace/quotient of the ring of symmetric functions
  in Sage, but live in the wrong space. Should live in a subspace. Have sample code in worksheet that "does the job" (see this link in Sage Days 20.5 in Toronto in May). Want to put this code into Sage. PEOPLE: Erin.
Symbolic projects
PEOPLE: Flavia, Karen