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<<TableOfContents>>
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 * Zeta function tickets [[https://trac.sagemath.org/ticket/20264|#20264]], [[https://trac.sagemath.org/ticket/20265|#20265]]  * Zeta function tickets [[https://trac.sagemath.org/ticket/20264|#20264]], [[https://trac.sagemath.org/ticket/20265|#20265]], [[https://trac.sagemath.org/ticket/19865|#19865]]
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 * Generic zeta function method for schemes [[https://trac.sagemath.org/ticket/20308|#20308]]
 * Elliptic curve point counting over F_q using PARI [[https://trac.sagemath.org/ticket/16931|#16931]]
 * Expose PARI code for Frobenius matrix on hyperelliptic curves [[https://trac.sagemath.org/ticket/20309|#20309]]
 * Raise coverage of schemes/hyperelliptic_curves/monsky_washnitzer.py to 100% [[https://trac.sagemath.org/ticket/15645|#15645]]
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 * Work on the isogeny classes of abelian varieties over finite fields. See http://beta.lmfdb.org/Variety/Abelian/Fq/
 * Fix poldredabs related issues https://github.com/LMFDB/lmfdb/issues/2135 (talk with JJ)
 * 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)
 * Work on the isogeny classes of abelian varieties over finite fields. See http://beta.lmfdb.org/Variety/Abelian/Fq/
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 * Finish up: https://github.com/LMFDB/lmfdb-collab/wiki//Warwick-workshop-June-2017  * Finish up: https://github.com/LMFDB/lmfdb-collab/wiki//Warwick-workshop-June-2017, precisely: https://github.com/LMFDB/lmfdb/issues/414, https://github.com/LMFDB/lmfdb/issues/418, and https://github.com/LMFDB/lmfdb/issues/396
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 * 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)
 * Prototype a Sage/LMFDB interface. See https://github.com/LMFDB/lmfdb/issues/1360 and https://github.com/LMFDB/lmfdb/issues/2169
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 * 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/

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, #19865

  • 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)

  • Generic zeta function method for schemes #20308

  • Elliptic curve point counting over F_q using PARI #16931

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

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

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

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