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| * from Alice's talk: * Implement the algorithm (use Sage's pseudoprime function to check) * What other primality tests does Pari have? Wrap these. * Make things faster: implement as a python (maybe cython??) file * How does GIMPS work? * Ask Drew Sutherland what he's done? * Implement Larry Washington's formulas for dealing with elliptic curves over integral domains * [[attachment:KateWishList.sws]] * Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime) * See what exactly is going on in E.global_minimal_model(), is it returning the unique restricted model? If so, update documentation * Implement Singular Weierstrass Equations and functionality similar to Elliptic Curves * make E.reduction(bad_prime) able to return this singular cubic object (maybe with a flag?) * change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc * Compute lots of examples to find guesses for bounds on "C" * p-adic Tate's algorithm * Put Kate's EDS class into sage (document properly)? |
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| *#7926: Bring coverage of Monsky-Washnitzer up to 50% *#8241: p-adic fields should have Witt Frobenius *#8685: evaluation of Monsky-Washnitzer objects (is really about power series over p-adics) *#9887: Slow coercion from integer ring to integer mod ring *#11319: Cannot create homomorphism from prime residue field to finite field *#11777: Coercion/printing problem with p-adics |
* [[http://trac.sagemath.org/sage_trac/ticket/7926|#7926: Bring coverage of Monsky-Washnitzer up to 50%]] * [[http://trac.sagemath.org/sage_trac/ticket/8241|#8241: p-adic fields should have Witt Frobenius]] * [[http://trac.sagemath.org/sage_trac/ticket/8685|#8685: evaluation of Monsky-Washnitzer objects (really about power series over p-adics)]] * [[http://trac.sagemath.org/sage_trac/ticket/9887|#9887: Slow coercion from integer ring to integer mod ring]] * [[http://trac.sagemath.org/sage_trac/ticket/11319|#11319: Cannot create homomorphism from prime residue field to finite field]] * [[http://trac.sagemath.org/sage_trac/ticket/11777|#11777: Coercion/printing problem with p-adics]] |
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| * computing with chi_18 | * wrapping of gauss composition (in pari: QuadClassUnit) * [[http://trac.sagemath.org/sage_trac/ticket/11697|#11697: Global minimal models over number fields with class number >= 1]] * this is in Connell and probably wouldn't take to long to get at least a python toy version * Sage already has this for class number 1 fields * [[http://trac.sagemath.org/sage_trac/query?status=needs_info&status=needs_review&status=needs_work&status=new&order=priority&col=id&col=summary&col=status&col=type&col=priority&col=milestone&col=component&keywords=~beginner&report=38| Open beginner tickets]] * Reviewing number theory and elliptic curve tickets * L-function Project Project Leader - William Group Members - Cassie, Amy, Lola From William: For L-series lovers: Getting the doctest coverage to 100% on this might be a good project: http://code.google.com/p/purplesage/source/browse/psage/lseries/eulerprod.py That may discover "issues" (bugs), which I would likely have to fix, but would also be fun because one gets to come up with lots of creative examples of L-series all over the place. Also, the top of that file has a todo list for new features to implement -- most would be bad projects, but one which would be good would be to make it so the Lseries object can use Lcalc (Rubinstein's program) to compute L-series instead of Dokchitser. This would be a good project, because it would mainly involve thinking about the annoying mathematics involved in going between normalizing L-series with the center of the critical strip at 1/2 versus not doing that. Also, it is all pure Python, so easier to get going. Anyway, I'd say 1 could be a good project for people who know the basics of L-series, but want to get a much more concrete feel for them. In fact, instead of just trying to get coverage to 100%, writing a *tutorial* for computing with L-series using that package would be really nice. E.g., one could walk through how to find missing information, create new L-series classes, etc. |
To do list
* from Alice's talk:
- Implement the algorithm (use Sage's pseudoprime function to check)
- What other primality tests does Pari have? Wrap these.
- Make things faster: implement as a python (maybe cython??) file
- How does GIMPS work?
- Ask Drew Sutherland what he's done?
- Implement Larry Washington's formulas for dealing with elliptic curves over integral domains
- Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime)
- See what exactly is going on in E.global_minimal_model(), is it returning the unique restricted model? If so, update documentation
- Implement Singular Weierstrass Equations and functionality similar to Elliptic Curves
- make E.reduction(bad_prime) able to return this singular cubic object (maybe with a flag?)
- change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc
- Compute lots of examples to find guesses for bounds on "C"
- p-adic Tate's algorithm
* Put Kate's EDS class into sage (document properly)?
* p-adics
#8685: evaluation of Monsky-Washnitzer objects (really about power series over p-adics)
#11319: Cannot create homomorphism from prime residue field to finite field
* wrapping of gauss composition (in pari: QuadClassUnit)
* #11697: Global minimal models over number fields with class number >= 1
- this is in Connell and probably wouldn't take to long to get at least a python toy version
- Sage already has this for class number 1 fields
* Reviewing number theory and elliptic curve tickets
* L-function Project
Project Leader - William Group Members - Cassie, Amy, Lola
From William: For L-series lovers: Getting the doctest coverage to 100% on this might be a good project:
That may discover "issues" (bugs), which I would likely have to fix, but would also be fun because one gets to come up with lots of creative examples of L-series all over the place. Also, the top of that file has a todo list for new features to implement -- most would be bad projects, but one which would be good would be to make it so the Lseries object can use Lcalc (Rubinstein's program) to compute L-series instead of Dokchitser. This would be a good project, because it would mainly involve thinking about the annoying mathematics involved in going between normalizing L-series with the center of the critical strip at 1/2 versus not doing that. Also, it is all pure Python, so easier to get going.
Anyway, I'd say 1 could be a good project for people who know the basics of L-series, but want to get a much more concrete feel for them. In fact, instead of just trying to get coverage to 100%, writing a *tutorial* for computing with L-series using that package would be really nice. E.g., one could walk through how to find missing information, create new L-series classes, etc.