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)

Welcome to Atelier PARI/GP 2025 (Saclay)

Doctesting

Topics

• Bill Allombert : helping around
• Albin Ahlbäck : build/configure system
• Eric Ahlqvist : class field theory, Galois cohomology - norms and product forms - speed improvements
• Ayoub Aluartassi : n-th power Hilbert symbol - nfhilbert - roots of unity in p-adic fields
• Salma Arrahmani : completions of number fields - formal series - discussions about p-adic extensions
• Martin Azon : modular forms - discussions with Nicolas and Nicolas - algebraic curves
• Safia Batla : S-integers, S-units, S-class groups, S-cohomology - discussions with Denis - discussions about ambiguous classes
• Dominique Bernardi : TBD
• Yves Benoist : L-functions and modular forms - theta functions with Jean - Stark units
• Nicolas Billerey : congruences between modular forms
• Raymond van Bommel : local arithmetic of curves and Jacobians - testing Nicolas’s package, doctesting
• François Brunault : quasi-periods of modular forms - experiments on Manin’s constant - formulated a conjecture
• Ricardo Buring : doctesting, bugs
• Pierre Charollois : Stark units, kernels of matrices in Q(x1,…,xn) - discussions, bnrL1
• Henri Cohen : quasi-periods of modular forms - discussions, progress - ok dim 1, in progress for larger dim - discussions with Vasily and Marc
• Julien Coolen : interface with CAML, fine typing
• Marc Coulomb : quasi-periods - continued fractions (Henri’s package)
• Andreas Enge : Gentry-Szydlo over large number fields - discussions with Alice, reading previous code - first working nontrivial example! - interesting examples?
• Chimène Fischler : primality tests - doctesting - improving Cholesky
• Nihar Gargava : Hecke characters - tried package, read paper
• Vasily Golyshev : quasi-periods - Hodge cycles - discussions with Henri and Marc
• Rob de Jeu : point counting - discussions with Nicolas - cup products in H^1_dR
• Jean Kieffer : theta functions - gp script for fast evaluation - progress on the script - finished
• Péter Kutas : doctesting, quaternion algebras, quadratic forms - doctesting, isomorphisms between rational quaternion algebras - common splitting field - finished implem
• Emmanuel Lecouturier : values of L-functions
• Samuel Lelièvre : installation
• Afonso Li : lattices and S-units - CVP - S-units, ideal-SVP algorithms - pseudocode for ideal-SVP, discussions about S-class groups
• Céline Maistret : models of curves, arithmetic invariants, local arithmetic of curves and Jacobians
• Nicolas Mascot : algebraic curves package, point counting, models of curves - discussions, basis of de Rham cohom - implem basis and cup product, discussions with Martin & Raymond - finished
• Marc Mezzarobba : doctesting, D-finite functions - discussions with Pascal, periods of curves
• Thibaut Misme : doctesting
• Pascal Molin : modular forms, Galois theory - p-adic extensions - discussions with Marc, computing L-functions - checked Emmanuel’s conjecture
• Pierre Morain : class field theory, Stark units, L-functions - edge cases of class field theory
• Mateo Crabit Nicolau : modular forms, quaternion algebras - units in quaternion algebras, Green functions on Shimura curves - embedding of quadratic fields into rational quaternion algebras
• Aurel Page : helping around, p-adic fields, algebras, p-adic polylogs … - discussions - old branch on p-adic fields
• Alice Pellet-Mary : ideal lattices, norm relations, Gentry-Szydlo - discussions with Andreas on Gentry-Szydlo - bugfix in Aurel’s code!
• Bernadette Perrin-Riou : Manin’s constant with François
• Eric Pichon-Pharabod : doctesting, periods, L-functions - discussions with Vasily and Henri
• Léo Poyeton : p-adics - discussions on p-adic fields - testing
• Marine Rougnant : doctesting
• Denis Simon : quadratic equations, Newton polygons, gp contributions - discussions with Safia; work with Péter - wrote scripts for quaternion algebras, more discussions
• Himanshu Shukla : Selmer groups, local arithmetic of curves and Jacobians - discussions about p-adics
• Márton Tot Bagi : root finding in finite fields, elliptic curves - fixed a bug on sqrt, now n-th roots - finished implementation, merging and testing

Demos: - Jean: Riemann theta function - Marton: n-th roots in finite fields - Nicolas: de Rham cohomology of curves and cup product - Eric A.: cup products and Massey products in étale cohomology of number fields - Péter: isomorphism between quaternion algebras

Future projects

• p-adic fields 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.

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

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

• qfauto using roots (Olivier)
• Cvr package (Nicolas)
• inner twists of mf (François)
• norm relations (Aurel, Fabrice)
• higher-dimensional isogenies (Pierrick)
• mod p mf (Baptiste)
• quaternion algebras functionalities from SQISign (Benjamin)
• splitting of algebras (Mickaël, Aurel)
• p-adic fields (Leo, Rob, 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
• p-adic polylogs
• Coleman integration
• Wishlist items in the bug tracking system
• 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
• CVP
• make qfminim rigorous
• p-adic fields
• better polgalois
• 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
• congruences between modular forms (Baptiste)

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)