# Welcome to [Atelier PARI/GP 2015](http://pari.math.u-bordeaux.fr/Events/PARI2015/)

## [New features / Tasks]()

##Beginning in GP
* Jean-Robert, Coline

##Paridroid
* Get it into the Fdroid and Google Play app stores (Andreas and Laurent)

* And FirefoxOS Marketplace too! (Luca) Note: Won't work natively, need to compile using [emscripten](https://github.com/kripken/emscripten). Then, we can have Pari in the browser :)

##Windows port
* Check status on Cygwin64 (JPF)
* Issue on cygwin64 linked to mmap (disabling mmap fix them) (Bill A.)
* Compare perfs using Cygwin32/64 and MinGW32/64 (JPF)

##Julia
* Develop a wrapper of Pari ideal arithmetic and maximal orders in the Julia programming language (Bill Hart - Kaiserslautern)

## Cleaner Sage integration

[Sage](http://sagemath.org) would benefit from a better integration of pari, see [sage]().

Vincent Delecroix, Jeroen Demeyer, Peter Bruin, Hamish, Luca.

##Zariski closure of matrix groups
* Given a finite set of integer matrix, compute (or at least approximate from below) the Zariski closure of the group generated by them (Vincent)

##Two descent for elliptic curves over Q (version in C?)
* Denis and Jeroen and Tadic
* Mark has a GP script from 2007, that is quite efficient, about 500 lines of code

##Point searching on cubic models and quadric intersections (3-covers of 4-covers of EC/Q)
* Denis + Mark

##Hecke characters
* Mark

##Elliptic curves over number fields
* Global minimal equations (François Brunault+ Tadic)

##L-functions (which?)
* Pascal + Henri + Amalia + Charlotte

##Modular polynomials
* Hamish + Luca

##(Even) faster point counting on (hyper)elliptic curves over finite fields
* JPF

##Central simple algebras
* Aurel + Denis
* see [Central simple algebras]()

##Local root number of families of elliptic curves
* Christophe

##Markov Models with Pari
* Implementation of Forward Backward Algorithm
* Implementation of Expectation Maximization Algorithm (Kevin, Guenaelle)

##Representations of fractional ideals of a number field
* Two-element representation (Thomas Camus)

##Testing and improving parallelism with PARI/GP
* testing, evaluation and improvement (Philippe EV, Kevin, Thomas, Marie, Guenaelle)

##Isometries and automorphisms of quad. form.
* testing and evaluation of qfisom and qfauto with several families of lattices (Philippe EV, Thomas, Guenaelle, Kevin)

##Applications of GP2C
* Compilation of the GP script library Bianchi.gp with GP2C (project of Alexander Rahm - NUI Galway)
(gp2c bug fixed [Bill A.])

##Fix Pari's AGM of real or complex power series
* Example: agm(1.0, 1.0*I + x + O(x^200)) [Fredrik]

##Pisot numbers and matrices
1. Write an algorithm to generate Pisot numbers of fixed degree (this is a discrete set)
2. Given a Pisot number of degree d, try to find a dxd matrix which admits the given Pisot number as eigenvalue



The gp script [localization.gp](/localization.gp) localizes roots of polynomials with respect to the unit disk (i.e. counts roots outside the unit disk, on the unit circle, and inside) [Christelle,Vincent].

##Improve linear algebra (especially over finite fields)
* Use standard "building blocks" like LU factorisation instead of custom functions like gauss_pivot
* Use Kronecker representation to multiply matrices over non-prime finite fields
* Strassen multiplication (preliminary version exists, but should probably be done after the above things)

(Peter Bruin)

##Discuss prefix uses in gp
* [GP prefix]() (Pascal)

##About modular symbols for Gamma_0(N)
* test the ms functions
* check the p-adic bsd conjecture for elliptic curves
* look at the genus 2 jacobian of curves coming from the modular symbols

(Bernadette Perrin-Riou)



##Planned features for 2.8/2.9
* [minutes]()