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.
• 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.

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