# Atelier 2018

# Previous Ateliers:

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

# Welcome to Atelier PARI/GP 2018 (Besançon)

## Tutorials

## New features

## Tasks

doctesting

(Marine, Coline, Paul, Gautier) Finished misc section, and linear algebra section, finite fields section.ECPP (Paul)

- Use L-function functionality from PARI in Sage; requires a review of current Sage functionality (Jeroen)

Tried to replace Lcalc but eventually realized it was not a good idea. Work on PariTwine and python bindings and pari errors. - Hyperelliptic curves over finite fields and the rationals (Nicolas)

Working on 2-descent. Maybe getting something by the end of the week. More work on 2-descent. - Point counting on elliptic curves and improvements on elliptic curves over finite fields (Jean-Pierre, Cyril, Vincent)

Made a patch, already included. - p-adic number field embeddings and regulator (Razvan, Xavier C.)

First version of the p-adic regulator. Working for Galois fields, extending to general case. - Coefficients of Hecke eigenforms of half-integral weight and Eisenstein series; doctesting of mf* (Ilker)

Worked with Henri, made some good progress using the Rankin-Cohen bracket (mfbracket), can do many examples easily, mostly done. Confirmed results from several papers, about Dedekind zeta functions. - Little delta function by Zagier (Zeynep)
- Dedekind eta function (Banu)
- Modular forms and symbols (François, Bernadette)
- Improve PariTwine (Andreas, Fredrik) and maybe use it in SageMath? (Jeroen)

Autotools support works, detecting the available libraries to wrap

GP script for inclusion of appropriate functions created

Texinfo documentation created

Some discussions with Jeroen about library organisation so that Sage can depend on PariTwist for conversions only

Functions from MPFR, MPC and CMH are wrapped and documented

Web page updated: paritwine.multiprecision.org

TODO:

finish documentation (ARB and FLINT)

wrap all useful functions from ARB (and FLINT?)

add more tests (?)

make a release 0.1 - Modular forms help centre (Henri)

Wrote a bracket function specific to theta to be faster (still slower than magma for silly reasons) Worked on p-rational fields. - Sato-Tate conjecture (Zakariae)

Worked on p-adic regulators and bounds for the p-adic regulator (Xavier,Zakariae,Razvan).(program to be documented and tested by Bill) - Theta functions (Enea)
- ECPP (Luca)

Chasing segfaults :-) - p-adic L-functions (Xavier R.)
- Algebra package (Aurel)
- Infinite order Hecke characters (Aurel, Pascal) Theory and design choice Ok. First GP implem in progress. C implem in progress.
- Theta series of quadratic forms (Elif)

Succeeded to compute in pari/gp with theta functions of binary quadratic forms. Extended to more variables. - SIDH (Cyril)

Working on presentation and implementation of SIDH. Good work on implementation of SIDH. - level 1 MS (Karim)
- (Jared) parallel ECPP
(Bill) implement nfredmodpowers using idealispower, fixed MacOS binaries, updated LTS binaries for OSX.

## Planning for 2.11

- [x] Use ECPP in isprime.
- mfcoef(f)(s) and siblings
- [x] finalize svg export. Output of export plot functions as a string?
- helpsearch: find function names / doc content matching some kind of regexp (perl)
- permconjugate?
- [x] remove sumaltrat
- nfsplitting: allow reducible polynomial, even with multiple roots, but want a single field as output (containing all the roots)
- rnfsplitting
- [?] Jeroen: in libpari, allow setting values of gp variables

## Feedback on the atelier

- Paul: during tutorials, the speaker should go slow enough so people can reproduce the commands. KB: links to all past tutorials are being collected on a single webpage.
- Thanks a lot to the Besançon organizers !!!!

## Next ateliers

- candidates for ateliers: Beirut, Bordeaux by default
- several formats are possible
- Bill: there is a mini-atelier in Rome in April (2018b)