Diff for "days87/projects"

Big Sage projects

• Add general extensions of p-adic fields in Sage #23218

• Add Julian's Mac Lane package to Sage #21869

• Add Julian's Completion package to Sage #22956

• Polynomial factorization, using Julian's Mac Lane package and/or Brian Sinclair's ticket #12561

  • make sure simpler factoring methods are in good shape, like Hensel lifting and Panayi's root finding.
• Precision models for p-adic matrices, polynomials
• Power series via p-adic templates

• 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

  • 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, #20265

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

• Etale algebras

• For an old list of possible projects, see padics

Smallish Sage projects

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

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

• Artin-Hasse exponentials #12560

• p-adic gamma functions
• Better coercion/conversion to and from residue fields

• Optimized implementation of Frobenius automorphism #12657

• p-adic polylogarithms #20260

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

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

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

• Investigate slowness in unramified extensions #23172

• Review Xavier's fast exponential code #23235

• Ray class groups and Hecke characters #15829

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

Beginner Sage projects

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

• Update and improve the p-adic tutorial
• Add more thematic tutorials in number theory

LMFDB projects

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

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

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

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

• Prototype a Sage/LMFDB interface. See https://github.com/LMFDB/lmfdb/issues/1360

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

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

• Hecke algebras: see https://github.com/sanni85/HeckeAlgebras and https://github.com/sanni85/lmfdb/tree/hecke_alg

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

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