# Previous Ateliers: [2015 (Bordeaux)](Atelier%202015), [2016 (Grenoble)](Atelier%202016), [2017 (Lyon)](Atelier%202017) [2017b (Clermont-Ferrand)](Atelier%202017b) [2017c (Oujda)](Atelier%202017c) [2018 (Besançon)](Atelier%202018) [2018b (Roma)](Atelier%202018b) [2019 (Bordeaux)](Atelier%202019) [2019b (Roma)](Atelier%202019b) [2020 (Grenoble)](Atelier%202020) [2021b (Oujda)](Atelier%202021b) [2022 (Besançon)](Atelier%202022) [2023 (CIRM)](Atelier%202023) [2024 (Lyon)](Atelier%202024) [2024b (Roma)](Atelier%202024b) # [Welcome to Atelier PARI/GP 2025 (Saclay)](https://pari.math.u-bordeaux.fr/Events/PARI2025/) [Doctesting](doc2025) ## Topics - Bill Allombert : helping around - Albin Ahlbäck : build/configure system - Eric Ahlqvist : class field theory, Galois cohomology - norms and product forms - Ayoub Aluartassi : n-th power Hilbert symbol - nfhilbert - roots of unity in p-adic fields - Salma Arrahmani : completions of number fields - formal series - 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 - 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 - Ricardo Buring : doctesting, bugs - Pierre Charollois : Stark units, kernels of matrices in Q(x1,...,xn) - Henri Cohen : quasi-periods of modular forms - discussions, progress - ok dim 1, in progress for larger dim - 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! - Chimène Fischler : primality tests - doctesting - improving Cholesky - Nihar Gargava : Hecke characters - tried package, read paper - Vasily Golyshev : quasi-periods - Hodge cycles - 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 - Péter Kutas : doctesting, quaternion algebras, quadratic forms - doctesting, isomorphisms between rational quaternion algebras - common splitting field - Emmanuel Lecouturier : values of L-functions - Samuel Lelièvre : installation - Afonso Li : lattices and S-units - CVP - S-units, ideal-SVP algorithms - 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 - 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 - 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 - Aurel Page : helping around, p-adic fields, algebras, p-adic polylogs ... - discussions - 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 - 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 ## 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) ## 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](http://pari.math.u-bordeaux.fr/cgi-bin/pkgreport.cgi?pkg=pari#_0_4_4) - 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 - [x] 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](/localization.gp) [pol_tests.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)