PROJECT GROUPS

Computing the Cartier operator acting on 1-forms

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
• make a big table or something? Rachel: "I would love to find a curve with p-rank 0 and a-number 1. I did genus 4 and p=3."

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 L-series 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 L-series (use Sturm bound -- see paper of Ribet with appendix by Agashe/Stein)
• Need the analogue of Tate's algorithm to get from the Namikawa-Ueno classification to the Euler factor at the bad primes
• Plug L-series 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 non-maximal 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 sage-combinat)
• 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
• Implementation of the Schuetzenberger involution Omega_2 on tableaux and words
• Faster implementation of crystal graph isomorphisms (would have implications for the energy function and R-matrix)
• make the k-Schur function and their duals live in the right subspace/quotient of the ring of symmetric functions