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  * Design a framework for lattice precision   * Design a framework for lattice precision [[https://trac.sagemath.org/ticket/23505|#23505]]
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 * Change root_field to return a p-adic field [[https://trac.sagemath.org/ticket/14893|#14893]], --([[https://trac.sagemath.org/ticket/20244|#20244]])-- (Aly)  * Change root_field to return a p-adic field [[https://trac.sagemath.org/ticket/14893|#14893]], --([[https://trac.sagemath.org/ticket/20073|#20073]])--,--([[https://trac.sagemath.org/ticket/20244|#20244]])-- (Aly)
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  * --([[https://trac.sagemath.org/ticket/23479|#23479]] (Sara))--   * [[https://trac.sagemath.org/ticket/23479|#23479]] (Sara)
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  * [[https://trac.sagemath.org/ticket/23473|#23473]] (David A.)   * [[https://trac.sagemath.org/ticket/23473|#23473]] (This tickets now need a review ! -- David A.)
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  * [[https://trac.sagemath.org/ticket/12657|#12657]]
  * [[https://trac.sagemath.org/ticket/20308|#20308]]

Contents

  1. Big Sage projects
  2. Smallish Sage projects
  3. Beginner Sage projects
  4. LMFDB projects

A list of tickets we're working on can be found here. If you work on a ticket, please add sd87 to the list of keywords so that it appears!

Most of the code for working with p-adics can be found here and here if you want to browse.

Big Sage projects

  • Add general extensions of p-adic fields in Sage #23218 (David Roe)

  • Add Julian's Mac Lane package which provides a general framework for discrete valuations to Sage #21869 (Julian)

  • Add Julian's Completion package, for general p-adic extension backed by number fields, to Sage #22956 (Julian)

  • Polynomial factorization, using Julian's Mac Lane package and/or Brian Sinclair's ticket #12561 (Ticket needs review) (Brian - meeting in UHS 115)

    • make sure simpler factoring methods are in good shape, like Hensel lifting and Panayi's root finding.
  • Lattice precision for p-adics (in particular p-adic matrices, polynomials) (Xavier)

    • Smith normal form #23450 (ready for review), determinant #23478 (ready for review)

    • Hermite normal form #23486 (ready for review)

    • Lattices in p-adic vector spaces: this is handled by the generic code for modules over PID (after the implementation of HNF above and this simple ticket #23503)

    • Design a framework for lattice precision #23505

  • Power series via p-adic templates (Adriana)

  • Linkage files for p=2 and/or using longs for the case that p^{\text{prec}} < 2^{62}

  • Implementation of Gröbner bases and tropical Gröbner bases algorithm (F4, F5, FGLM), doctest and submission (Tristan)

    • We might finish reviewing the inclusion of openf4 at #18749 and patch it to avoid going through strings all the time

    • And also look at the performance of Singular, polybori, giac, ...
  • Zeta function tickets

  • Roadmap for regular models in Sage using Mac Lane package, Suchandan Pal's code and Stefan Wewers' work. (Julian)

  • Etale algebras (maybe see also ticket #21413) (Ricky)

  • For an old list of possible projects, see padics

Smallish Sage projects

  • Norms, traces, frobenius, matrix mod pn for relative p-adic extensions (David)
  • Add more black-box testing to p-adics, performance benchmarketing (Aly)

  • nth roots, square roots that create extensions (extend=True as for integers) #12567 (Marc, Kevin)

  • Artin-Hasse exponentials #12560 (Xavier)

  • Gauss sums via the Gross-Koblitz formula, which uses code on p-adic gamma functions #23456 (Adriana and Ander) (Found and fixed a small mistake, still needs review)

  • Better coercion/conversion to and from residue fields (Aly, Marc)

  • Optimized implementation of Frobenius automorphism #12657 (Ander)

  • p-adic polylogarithms #20260 (Alex)

  • bug in matrix of Frobenius when p = 3 #11960 (Jen)

  • Switching to exact defining polynomials for p-adic extensions #23331 (David)

  • Change p-adic constructors to not care about the base ring of a defining polynomial #18606 (David)

  • Investigate slowness in unramified extensions #23172 (Xavier)

  • Review Xavier's fast exponential code #23235 (Xavier)

  • Ray class groups and Hecke characters #15829 (Rob)

  • Add Monge-reduction for Eisenstein polynomials (first over \mathbb{Q}_p, then over unramified extensions) (Sebastian)

  • Generic zeta function method for schemes #20308 (Edgar)

  • Elliptic curve point counting over F_q using PARI #16931 #16949 (J-P Flori, Kevin)

  • Expose PARI code for Frobenius matrix on hyperelliptic curves #20309 (Marc)

  • Raise coverage of schemes/hyperelliptic_curves/monsky_washnitzer.py to 100% #15645 (Edgar)

  • Requested by Anna Haensch: A weak approximation function

Beginner Sage projects

LMFDB projects

days87/projects (last edited 2017-08-04 09:44:00 by saraedum)