Previous Ateliers:

2015 (Bordeaux), 2016 (Grenoble), 2017 (Lyon)

Welcome to Atelier PARI/GP 2017b (Clermont)

Tutorials

New features

Genuine Bianchi modular forms for Pari/GP :

Alexander D. Rahm wants to find out if there is interest in a script for the Pari/GP scripts library, computing dimensions of genuine Bianchi modular forms. Details will be given in his talk on Thursday morning, summarized here :

http://math.uni.lu/~rahm/genuine_Bianchi_modular_forms_in_PARI-GP.txt

Tasks

• Doctesting-2017b (Karim Belabas)
• Everything and anything (Karim, Bill, Henri) <<<<<<< edited
• Rational points on elliptic and hyperelliptic curves over Q_p (Devika, Nicolas)

• Doctesting done. Improved my own code on p-adic modular forms with the new functions. Now running some tests for a conjecture of mine relative to minimal slopes of p-adic modular forms for p=5. (Dino D.)

  Lots of progress!
• Rational points on elliptic and hyperelliptic curves over Q_p (Devika, Nicolas M., Pascal) Nicolas gas implemented 2-descent for hyperelliptic curves in the simplest case. The plan is to use it to do Chabauty style work and determine all rational points.
• Clean and maybe improve my own code on p-adic modular forms with the new functions (Dino D.) >>>>>>> c98cf94ff8622e2c40cc517da3151a7c44dadad1
• ECPP (Jared, Jean-Pierre) <<<<<<< edited tuning and experiments running decomposition of the Galois towers is still missing
• PARI-GNUMP (Andreas E., Fredrik) autotools support is ready a preliminary interface with arb has been written; the exact semantics needs to be decided =======

1. currently experimenting in plafrim
2. looking to implement Galois decomposition to be able to get roots for class polynomials which are b-smooth where b is small (b <= 32)

• PARI-GNUMP (Andreas E.) >>>>>>> 7a5d5272c9b6e4807ff544b4d688de399adcfc76
• Generalise ellisomat to curves over number fields (Nicolas B.) Bill has extended ellisomat inclusion of Nicolas’s script is on-going CM curves still pose problems
• Tannakian symbols and multiplicative functions (Torstein, Andreas H.) some functions have been translated from Sage to GP and are running faster now
• Improve GP scripts for inclusion into PARI/GP: points on elliptic curves over Q using 2-descent (Denis) the code (ell2descent) has been imported into a git repository on the pari server an open problem is to determine linear combinations of points with finally small coefficients: use real embeddings or modular arithmetic
• documentation of modular symbols and forms (Bernadette)
• statistics of Frobenius actions of curves over finite fields (Florent)
• revive the git branch of the Wednesday talk (Pascal) there are bugs, in the process of being collected (and maybe resolved)
• encrypted matrix multiplication with Paillier cryptosystem (Matthieu)
• fundamental units of totally complex quartic fields (祝辉林) progress is being made for special number fields
• iterators over fundamental discriminants (Jared)
• functions for modular curves (Antonin)
• dimensions of Bianchi modular forms (Alexander)
• Finding the rational expression for the generating function of a given linearly recursive sequence. Application: Recognizing reciprocity laws (Olav, Magnus)
• Computing Meissel-Mertens constants for abelian number fields (Alex M., Preben)
• 2-descent on hyperelliptic curves over Q (Nicolas M.)

Planning for PARI/GP 2.10