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 * Roadmap for regular models in Sage using Mac Lane package, [[http://www-personal.umich.edu/~psuchand/projects.html|Suchandan Pal's code]] and Stefan Wewer's work.  * Roadmap for regular models in Sage using Mac Lane package, [[http://www-personal.umich.edu/~psuchand/projects.html|Suchandan Pal's code]] and Stefan Wewers' work.
 * Etale algebras
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 * nth roots, square roots that create extensions (extend=True as for integers)  * nth roots, square roots that create extensions (extend=True as for integers) [[https://trac.sagemath.org/ticket/12567|#12567]]
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 * Switching to exact defining polynomials for p-adic extensions  * Switching to exact defining polynomials for p-adic extensions [[https://trac.sagemath.org/ticket/23331|#23331]]
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 * Investigate slowness in unramified extensions [[https://trac.sagemath.org/ticket/23172|#23172]]
 * Review Xavier's fast exponential code [[https://trac.sagemath.org/ticket/23235|#23235]]
 * Ray class groups and Hecke characters [[https://trac.sagemath.org/ticket/15829|#15829]]
 * Add Monge-reduction for Eisenstein polynomials (first over $\mathbb{Q}_p$, then over unramified extensions)
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 * Display Hecke eigenvalues in terms of an integral basis. See: https://github.com/LMFDB/lmfdb/issues/975  * 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

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

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