Previous Ateliers:

2015 (Bordeaux), 2016 (Grenoble), 2017 (Lyon) 2017b (Clermont-Ferrand) 2017c (Oujda) 2018 (Besançon) 2018b (Roma) 2019 (Bordeaux) 2019b (Roma) 2020 (Grenoble) 2021b (Oujda) 2022 (Besançon) 2023 (CIRM) 2024 (Lyon) 2024b (Roma) 2025 (Orsay) LIBPARI2025 (Bordeaux)

Welcome to Atelier PARI/GP 2026 (Bordeaux)

doctesting

Topics

• Eric : local units mod p and unramified extensions, done! (demo)
• Haetham : snf forms etc.
• Bill : helping around, fixed 2 bugs (demo of polynomial linear recurrence script)
• Salma : doctesting, elliptic curves over number fields, crypto, CRT
• Rayane : presentations by coverings, slides
• Safia : doctesting, using git
• Daniel : snf stuff, homology computations (demo)
• Karim :
• Nicolas B.: congruences between modular forms, CM modular forms
• Zakariae : Eisenstein series attached to quadratic fields, mf package (demo)
• Alina : factorisation of Hecke L-functions in terms of Dirichlet L-functions
• Henri : helping around, modular forms from quadratic fields (demo), improving mfshimura
• Mateo : computing coefficients of generating series
• Alejandro : Voronoi complex
• Vincent :
• Philippe : cohomology of arithmetic groups
• Tim : trying things, reading doc, finite topological spaces (demo)
• Andreas : scheme bindings for the pari library [compiles then crashes], reading doc
• Fabrice : class group computations with norm relations
• Sam : 3 and 5 descent, coverings
• Jean :
• Vasily :
• Pengju : charpoly of Frobenius of varieties, p-adic regulators
• David : helping, doctesting, tutorials, p-adic extensions
• Tao : reading tutorials, SNF
• Gabriel : Voronoi’s algorithm for Hermitian forms
• Rob : doctesting (bnfinit), p-adic polylogs
• Fredrik : benchmarking primality tests - profiling
• Kiran : joining others, hypergeometric motives, abelianbnf, sparse matrices
• Bernard :
• Antoine : polynomial factorisation over Fp
• Pierre L. :
• Afonso : discrete gaussian in lattices, testing (demo)
• Nicolas M.: algebraic curves, looking for volunteers to help
• Thibaut : doctesting, theta characteristics of jacobians
• Pascal : artin representations, mfsaturate (demo)
• Pierre M. : class field theory, p-adic fields, bnfinit
• Aurel : helping around
• Baptiste : modular forms, congruences, class field theory, projective Artin representations (demo)
• Alice : S-units with norm relations, bnfinit and residue of the Dedekind zeta function
• Bernadette: doctesting, reading
• Léo :
• Fotios : doctesting, action on additive structure of ideals
• Damien : experiments on formulas for elliptic curves
• Marine : doctesting
• Denis : Mahler measure of polynomials: 1 variable, 2 variables; helping around (demo?)
• Julien : elliptic curves over finite fields and quaternion algebras; localising quaternion algebras (demo)
• Giacomo : elliptic curves over number fields
• Alexander : automorphism groups of fields, alnuth, second cohomology for polycyclic groups in GAP, compute the action
• Wenwen : Verify the correctness of reduction between RLWE and MP-LWE

Next ateliers

• 2027 Clermont-Ferrand
• 2028 ??

Planning for 2.19

• statistics (statinit, characteristic function = Fourier transform)
• Riemann theta (Jean Kieffer)
• Heegner points on twists
• Harvey-Sutherland
• polmahler
• mfeisensteinnf, mfsaturate

Planning for 2.21

• curves (Nicolas)
• p-adic fields (Aurel, Bill, Leo)
• Fuchsian groups (James, Rayane, Aurel)
• dim 2 Artin reps (Bill, Aurel) nflist(“A4cond” / “S4cond”)
• abelianbnf / bnrclassgroup (Aurel)
• mfcongruence (Baptiste, Nicolas B.)

Long term projects

• rewrite Galois groups (polgalois)
• Massey products and cup products (Eric, since 2025)
• Gentry-Szydlo algorithm (Bill, Alice, Andreas)
• sparse matrices (Aurel)
• Satoh algorithm, Damien and Abdoulaye’s version

Wishlist

• faster factorization of bivariate polynomials over finite field.
• idealstarmap (same as bnrmap but for idealstar)
• map (ZK/pr^k)* -> Cl_F(N) for pr^k||N (name? bnrlocalunits?)
• Wishlist items in the bug tracking system

Checklist of TODOs from 2025 Atelier

• algebraic curves (Nicolas, since 2024)
• n-th roots in finite fields (Marton)
• isomorphism and splitting of quaternion algebras (Péter, Denis) Suggestions: isomorphism of quadratic spaces, addition in the Brauer group

Future projects (long term)

• p-adic fields (Aurel, Leo, since 2020) wishlist: Compute extensions (effective Krasner’s lemma), compositum of extensions, finding a uniformizer and determine wether the extension is Galois. Decompose extension as totally ramified over unramified extension of Qp. Function like padicfield but starting from any p-adic field. Factoring polynomials over any p-adic field. Classical transcendental functions (over any p-adic field): log, exp, polylogs. Solutions of differential equations. Creating unramified extension of Qp of degree d from F_{p^d} (Witt vectors W(F_p^d)). Local class field theory: structure of units and construction of abelian extensions.
• p-adic polylogs (Bill, Aurel, Rob)

Feature requests

• functions for manipulating finitely generated Abelian groups
• polmahler: Mahler measure of polynomials in 1 and 2 variables, over C (Denis)
• random generation for various distributions
• computing spherical polynomials

Checklist of Future projects from 2024 Atelier (significant work needed)

• qfauto using roots (Olivier)
• inner twists of mf (François)
• norm relations (Aurel, Fabrice)
• higher-dimensional isogenies (Pierrick)
• mod p mf / congruences between modular forms (Baptiste, since 2020)
• quaternion algebras functionalities from SQISign (Benjamin)
• splitting of algebras (Mickaël, Aurel)
• include James Rickards code for fundamental domains (Aurel)

Feature requests

• foreach(L,[a,b],…)
• export coprime factorisation, cf ?? “Coprime factorization”@ factorcoprime coprimepart
• interface gcharidentify with prec argument (like lindep)
• gchar: algebraic characters with algebraic evaluation: one char, one field per modulus, one field (+cyclotomic) per bnf, p-adic evaluation.
• gchar: change of field (two directions)
• gchareval: how to obtain the chosen uniformiser? / evaluating the local character at a p-adic place (nfeltval + ideallog) gcharlocaleval?
• courbe ell CM -> gchar
• nfiscm (if the cm involution exists then you know it in all the embeddings so you can reconstruct it)
• give a starting non-maximal order to nfinit
• matrix groups over finite fields
• Coleman integration
• Fourier transform of finite abelian groups

Checklist of TODOs from 2020 Atelier

Future projects (significant work needed)

• algebraic lattices: LLL, qfauto, qfisom (Thomas Camus, Cyril Hugounenq, Titouan Coladon, Etienne Marcatel, Thomas Mégarbané, Aurel Page)
• merge the existing t_REAL branches (?); remove incompatibility with polgalois (Karim Belabas)
• primepi (Dana Jacobsen)
• rnfsplitting
• help search with regular expressions (KB)
• BKZ
• HKZ
• make qfminim rigorous
• parallelize MPQS
• parallelize multiplication table in nf
• rnfinit without maximal order (KB: definitely not available under GP. Cf nf_rnfeq & nf_rnfeqsimple).

Future projects (to be finalized)

• helpsearch: find function names / doc content matching some kind of regular expression (trivial flag to gphelp: what to do with the output ?)
• mfgaloisrep for weight 1 (Bill, Aurel)
• permconjugate, functions for permutation groups (exists: what to export?)
• abelian groups (Jared)
• root localisation (Christelle) localization.gp pol_tests.gp

Long-term feature requests

• nfinit for large degree number fields (say ~500). Problem: which functionalities should work?

Checklist of TODOs from 2019 Atelier

• ffintersect, ffcompositum, ffsubfield, ffsplitting (Bill)