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Big Sage projects

Add general extensions of p-adic fields in Sage #23218 (David Roe)
Add Julian's Mac Lane package which provides a general framework for discrete valuations to Sage #21869 (Julian)
Add Julian's Completion package, for general p-adic extension backed by number fields, to Sage #22956 (Julian)
Polynomial factorization, using Julian's Mac Lane package and/or Brian Sinclair's ticket #12561 (Brian - meeting in UHS 115)
- make sure simpler factoring methods are in good shape, like Hensel lifting and Panayi's root finding.
Precision models for p-adic matrices, polynomials (Xavier)
Power series via p-adic templates (Adriana)
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 (Tristan)
- 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 (Edgar)
Roadmap for regular models in Sage using Mac Lane package, Suchandan Pal's code and Stefan Wewers' work. (Julian)
Etale algebras (maybe see also ticket #21413) (Ricky)
For an old list of possible projects, see padics

Norms, traces, frobenius, matrix mod pn for relative p-adic extensions (David)
Add more black-box testing to p-adics, performance benchmarketing (Aly)
nth roots, square roots that create extensions (extend=True as for integers) #12567 (Marc)
Artin-Hasse exponentials #12560 (Xavier)
p-adic gamma functions (Adriana)
Better coercion/conversion to and from residue fields (Aly, Marc)
Optimized implementation of Frobenius automorphism #12657
p-adic polylogarithms #20260 (Jen)
bug in matrix of Frobenius when p = 3 #11960 (Jen)
Switching to exact defining polynomials for p-adic extensions #23331 (David)
Change p-adic constructors to not care about the base ring of a defining polynomial #18606 (David)
Investigate slowness in unramified extensions #23172 (Xavier)
Review Xavier's fast exponential code #23235 (Xavier)
Ray class groups and Hecke characters #15829 (Rob)
Add Monge-reduction for Eisenstein polynomials (first over \mathbb{Q}_p, then over unramified extensions) (Sebastian)
Generic zeta function method for schemes #20308 (Edgar)
Elliptic curve point counting over F_q using PARI #16931 (J-P Flori)
Expose PARI code for Frobenius matrix on hyperelliptic curves #20309 (Marc)
Raise coverage of schemes/hyperelliptic_curves/monsky_washnitzer.py to 100% #15645 (Edgar)