Editing Atelier 2025

# 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 - 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

## Next ateliers

- 2026 Bordeaux
- 2027 Clermont-Ferrand

## Future projects (to be finalised)

- algebraic curves (Nicolas)
- 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) 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)
- p-part étale cohomology, cup and Massey products (Eric)

## 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)
- 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)

Description of changes: