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  * Decide if curve is attached to a modular form, and if so find it, then use that to compute L-series.   * 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)

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!)
  • 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

  • smalljac
    • make smalljac code usable from Python (involves Cython); see this psage issue.

    • use code:
      • - replicate and extend data in Kate's talk - maybe try genus 2 analogue?
  • cubic and sextic residue symbol
    • there's a ticket that has only partial implementation (cubic residue of rational prime and element of Q(sqrt(-3))) -- not at all a general implementation

    • there are artin symbols etc. -- big machinery
    • we think a fast independent implementation of the cubic (and sextic) residue symbol is worthwhile
    • what does SAGE do to compute quadratic residue symbols?
  • 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:
  • 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
  • hyperplane arrangements
  • wikipedia and Sage pages linked to each other

days26/projects (last edited 2010-12-10 19:57:07 by AlysonDeines)