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 pprec < 262
- 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, ...
For an old list of possible projects, see padics
== Smallish Sage projects ==
- Norms, traces, frobenius, matrix mod pn for relative p-adic extensions
- Switching to exact defining polynomials for 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)
- Artin-Hasse exponentials, p-adic gamma functions
- Better coercion/conversion to and from residue fields
Optimized implementation of Frobenius automorphism #12657
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