Atelier 2019

Previous Ateliers:

2015 (Bordeaux), 2016 (Grenoble), 2017 (Lyon) 2017b (Clermont-Ferrand) 2017c (Oujda) 2018 (Besançon) 2018b (Roma)

Welcome to Atelier PARI/GP 2019 (Bordeaux)

Proposed topics (partial reports in brackets)

doctesting: Paul + Marine + Julien + Thomas (lots of doctesting done)

modular curves and Galois representations in libpari: Nicolas + Xavier C. + Razvan (nice discussions)

Hecke characters: Aurel+Pascal (automatic increase of precision)

supersingular isogenies: Cyril

integrating and summing oscillating functions: Henri Cohen + KB (new functions, new methods)

Bianchi modular forms: Hao Zhang

sorting and labeling ideals in number fields: John Cremona (JEC) + Aurel Page (review of sorting/labeling, implemented standard two-generator method in gp)

interfacing modular forms with Sage: JEC + Jeroen

interfaces pari / python / sage / jupyter: Jeroen (fixed some bugs, worked with Vincent Klein)

1/2-integral weight modular forms: Ilker+Elif

p-rational fields: Youssef (worked with Razvan and Bill)

modular forms and abelian varieties, explicit construction: Mohammed Amin (worked on calculations related to abelian varieties)

abelian surfaces, p-adic methods, canonical lifts: Maiga + Damien

arithmétique des corps de nombres, corps de classes de Hilbert: Mohammed Taous + Abdelkader Zekhnini (used class group, class field and galois gp functions)

Jeroen’s slave: Luca

porting elliptic curves to sage: Luca, JEC, Jeroen

isogenies between abelian surfaces, porting Damien’s code: Jean Kieffer

identity-based encryption, webassembly: Adam + Attila (lots of progress, faster and better)

générateurs aléatoires, LLL: Mohammed Traoré (found problems in doc, work on random generators)

LLL on Hermitian forms: Etienne (practiced with pari, implemented LLL)

L-function computations: Francesco (work on enumeration of number fields: found new interesting condition to eliminate polynomials, efficiency not clear yet (coredisc(P) <= disc(F) <= disc(P)))

Steinitz classes in number fields / Dedekind domains: Angelo (explored pari functions for steinitz classes)

Hecke operators and automorphic forms, lattices: Thomas (general methods not successful, came back to specialised methods; doctesting; explored the abilities of the Switch processor)

discover pari, l-functions, elliptic curves: Julien (discovered pari + doctesting)

class groups of abelian fields: Takashi Fukuda (new version incoming)

cyclotomic fields: Jean-Robert (proofread Fukuda’s documentation)

p-adic L-functions of number fields: Xavier R.

p-adic L-functions (of modular forms?): Bernadette (read about Pollack’s database of p-adic lambda invariants)

espaces de modules, fonctions theta, des trucs comme ça: Enea + Marius?

generators of cubic extensions, relative Thue equations: Ibrahim

PariDroid: Andreas + Laurent (ported parisize to PariDroid)

elliptic curves over finite fields, point counting: Titouan (compared codes for scalar multiplication on elliptic curves)

parallel GP, p-Selmer group of elliptic curves: Denis (learned gp parallelism, improving programs on elliptic curves)

Mahler measure of polynomials: François + Pascal (worked on the problem of propagating the factorisation of a polynomial under perturbations)

elliptic curves over Q(t): Christophe (progress on computing some p-adic valuations)

continued fractions of Laurent series over finite fields: Salah Beldi + Ayedi Khalil (worked on continued fractions using pari/gp)

fusion cypari+cypari2: Vincent K

galois groups of polynomials / Q via Gap+pari, multizetas and polylogs: Vincent D + Bill

Planning for next release (2.12.0 and 2.13.0)

Feature requests

Future projects from previous Ateliers (no work done since)

  • LU decomposition of matrices (Peter Bruin)
  • algebraic lattices: qfauto and 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)
  • Falting heights over Q and nf (Pascal Molin)
  • rnfsplitting
  • in libpari, allow setting values of gp variables (?)
  • Hecke characters of infinite order (Pascal Molin, Aurel Page)
  • ffmaprel, ffintersect, ffcompositum, ffsubfield, ffsplitting (Bill)
  • better rnfkummer, bnrclassfield wrapper (Bill, Aurel)
  • parallelism: walltime (Bill)
  • help search with regular expressions (KB?)
  • mfgaloisrep for weight 1 (Bill, Aurel)
  • integrate Denis’s scripts (Bill, Denis)

Finalize

  • helpsearch: find function names / doc content matching some kind of regular expression (trivial flag to gphelp: what to do with the output ?)
  • permconjugate, cycle decomposition, functions for permutation groups (exist: what to export?)
  • compact units (merge branch kb-compact-units: “only” need to rewrite makematal)
  • write final report for OpenDreamKit deliverables (Ateliers [DONE] + parallelism)
  • Fukuda’s package

Next workshops

  • 2020: ? (Bordeaux by default)
  • 2021: Besançon ?