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add Ray class groups and Hecke characters (trac 15829)
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* Ray class groups and Hecke characters [[https://trac.sagemath.org/ticket/15829|#15829]] |
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, ...
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
Beginner Sage projects
- 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