Diff for "days87/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

  • Design new parents (ZpLCR, ZpLCA) for p-adics handled with lattice precision
• 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

  • #20264 (Edgar, Vishal Aru, Nicholas Triantafillou)

  • #20265 (Edgar, JP)

  • #19865

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

• Optimized implementation of Frobenius automorphism #12657 (Ander) (ready for review)

• 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

• Change root_field to return a p-adic field #14893, #20244 (Aly)

• Update and improve the p-adic tutorial (Rob)
• Add more thematic tutorials in number theory (Rob)
• Here are some tickets that should be easy to review (feel free to add more!):

  • #12657 (GaYee)

  • #16949 (GaYee)

  • #23190 (Adele)

  • #23185 (Sara)

  • #23482 (Claire)

  • #23483 (Adele)

  • #23484 (David A.)

  • #23376

  • #23479 (Sara)

  • #23473

LMFDB projects

• Fix polredabs related issues #2135 (JJ)

• Display Hecke eigenvalues in terms of an integral basis. See: #975 (note see also https://github.com/LMFDB/lmfdb/issues/2135 and talk to JJ for how it is related) (Edgar, Sam Schiavone)

• Finish up: https://github.com/LMFDB/lmfdb-collab/wiki//Warwick-workshop-June-2017, precisely:

  • Compute Elliptic Curves over number fields L-functions #396 (Edgar)

  • Compute Hilbert Modular Form L-functions #418 (Edgar)

  • Compute the Asai L-functions #414

• Sanitize API interface: https://github.com/LMFDB/lmfdb/issues/2053 (Edgar)

• Prototype a Sage/LMFDB interface. See https://github.com/LMFDB/lmfdb/issues/1360 and https://github.com/LMFDB/lmfdb/issues/2169 (Edgar, Simon Brandhorst and David Lowry-Duda)

• Hecke algebras: see https://github.com/sanni85/HeckeAlgebras and https://github.com/sanni85/lmfdb/tree/hecke_alg (Samuele) pull request #2189

• Dirichlet characters modulo l: see https://github.com/sanni85/Dirichlet_modL (Samuele)

• Galois representations modulo l: see https://github.com/sanni85/Mod-l-galois-representations and http://beta.lmfdb.org/Representation/Galois/ModL/ (Samuele)

• Display local algebras (JJ)
• Better handling of character tables (JJ)
• Some done work:

  • Issue #1959 pull request #2190

  • Issue #2187 pull request #2188

  • Moving import scripts: pull request #2186

  • Issue #2172 pull request #2176

• Idle:

  • Work on the isogeny classes of abelian varieties over finite fields. See http://beta.lmfdb.org/Variety/Abelian/Fq/ (Christelle)

  • Work on Hypergeometric Motives over ℚ. See http://beta.lmfdb.org/Motive/Hypergeometric/Q/ (Dave Roberts)

  • Use Monge-reduced polynomials (and ones related to them) for defining polynomials (JJ)