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| * make code usable from Python (involves Cython); see [[http://code.google.com/p/purplesage/issues/detail?id=13|this psage issue]]. | * smalljac |
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| * use code: | * make smalljac code usable from Python (involves Cython); see [[http://code.google.com/p/purplesage/issues/detail?id=13|this psage issue]]. * use code: |
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| - replicate and extend data in Kate's talk | - replicate and extend data in Kate's talk |
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| - maybe try genus 2 analogue? | - maybe try genus 2 analogue? |
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| * possibly implement cubic and sextic residue symbol. make it really really fast, even if it is implemented, since Kate wants lots of data. | * cubic and sextic residue symbol |
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| * explicit calculation of Grossencharacters. | * there's a [[http://trac.sagemath.org/sage_trac/attachment/ticket/8485/trac_8485.patch|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). |
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| * Make a table. Starting with "van Wamelen"'s table. See also Kohel. | * Make a table. Starting with [[https://www.math.lsu.edu/~wamelen/CMcurves.txt|"van Wamelen"'s table]]. See also [[http://echidna.maths.usyd.edu.au/kohel/dbs/index.html|Kohel's tables]]. * Incorporate Robert Bradshaw's code into Purple Sage. http://code.google.com/p/purplesage/issues/detail?id=14 |
PROJECT GROUPS
Contents
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
- List why Magma/PARI aren't good enough (bugs, issues, speed, etc.)
- Write really really fast code to implement some of this.