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)
• 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)
• 2-descent on hyperelliptic curves over Q (Nicolas M., Pascal) Nicolas has 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.)
• ECPP (Jared, Jean-Pierre)<<<<<<< edited
  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., Fredrik) autotools support is ready a preliminary interface with arb has been written; the exact semantics needs to be decided
• 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) I consider the family E_t: y^2=f(x)(x-t) over Fq. Here f is a monic integral separable polynomial of degree 2g. I am interested in statistics for the numerator L_{f,t} of the zeta function of E_t over Fq. It is a polynomial of degree 2g and maximal Galois group over Q isomorphic to W_{2g} (the ‘signed’ permutations of pairs of roots in S_{2g}). Results: overwhelming evidence that the typical Galois group is W_{2g}. Very few exceptions. Next task: what are the other Galois groups that can be realized in this way. What is the occurence of these ‘pathologic’ groups? What are the groups that do NOT occur as the Galois group of some L_{f,t}?
• 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) more details to be expected during the Thursday talk
• Finding the rational expression for the generating function of a given linearly recursive sequence. Application: Recognizing reciprocity laws (Olav, Magnus) code is being implemented in GP, no special problems to report
• Computing Meissel-Mertens constants for abelian number fields (Alex M., Preben) the code for quadratic number fields has been ported from Sage to GP and is faster now work for higher degree number fields is on-going
• Congruences of modular forms (François)

Planning for PARI/GP 2.10