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| * Add general extensions of p-adic fields in Sage | * Add general extensions of p-adic fields in Sage [[https://trac.sagemath.org/ticket/23218|#23218]] * Add Julian's Mac Lane package to Sage [[https://trac.sagemath.org/ticket/21869|#21869]] * Add Julian's Completion package to Sage [[https://trac.sagemath.org/ticket/22956|#22956]] * Polynomial factorization, using Julian's Mac Lane package and/or Brian Sinclair's ticket [[https://trac.sagemath.org/ticket/12561|#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 $p^{\text{prec}} < 2^{62}$ |
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| == 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 [[https://trac.sagemath.org/ticket/12657|#12657]] * p-adic polylogarithms [[https://trac.sagemath.org/ticket/20260|#20260]] * bug in matrix of Frobenius when p = 3 [[https://trac.sagemath.org/ticket/11960|#11960]] |
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, ...
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
p-adic polylogarithms #20260
bug in matrix of Frobenius when p = 3 #11960
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