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| * this appears to be done here: [[attachment:Computing N for Hyperelliptic curve.sws]] * need data to check that this is correct. * for what range of primes is this code reasonable? |
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| * make it really, really fast. | * make it really, really fast (cython). |
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| PEOPLE: Jennifer B., Jennifer P., Jennifer J. | PEOPLE: Jennifer B., Jennifer P., Jennifer J., Bianca |
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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) * Need the analogue of Tate's algorithm to get from the Namikawa-Ueno classification to the Euler factor at the bad primes |
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| * Make a list of what you want to be able to do | * Make a list of what you want to be able to do: - Such computations come up for Stein in http://wstein.org/papers/kolyconj2/ |
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| == Sara's (mostly Combinatorics) wishlist == | |
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| PEOPLE: Needs people! * Better index of software * sbcl in Sage * Quasisymmetric function bases * hyperplane arrangements * wikipedia and Sage pages linked to each other |
PROJECT GROUPS
Contents
-
PROJECT GROUPS
- Computing the Cartier operator acting on 1-forms
- Making Drew Sutherland's smalljac code usable in Sage and extending Kate's data
- Computing L-series of Jacobians of Certain Hyperelliptic Curves
- Computing in the class group of non-maximal orders of quadratic imaginary fields
- Sara's (mostly Combinatorics) wishlist
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
- 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:
- 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
- hyperplane arrangements
- wikipedia and Sage pages linked to each other