Sage Days 16: Barcelona, Spain -- Computational Number Theory

Sage Days 16 will take place June 22-27, 2009, the week after MEGA 2009. The event will be organised by the CRM ( and the OSRM of the UPC (, and will take place at the FME, in the campus of the UPC, in Barcelona.

Mailing lists


Monday, June 22

CRM Thematic Day on Mathematics and Computation


William Stein

Sage: open source mathematical software

This will be an overview talk about Sage, which explains the history and motivation for the project, demos some key features of Sage, and discusses where we are going next. It will be accessible to people in all research areas and assumes no prior experience with Sage.


Coffee Break


Henri Cohen

Experimental methods in number theory and analysis

In this talk, I would like to give a number of examples of numerical experiments coming from number theory and analysis, mention the tools used to perform them, and show how they sometimes can lead to interesting and deep conjectures.


Àngel Jorba

Developing tailored software for specific problems

We will discuss the advantages and inconveniences of developing software (in a general purpose language like C) for concrete problems. I will also mention the results of a pool done by the Spanish project "i-Math" on the use of computational resources of the mathematical research groups in Spain.


Coffee Break


Round Table



Coding Sprint Organization

Tuesday, June 23



Jordi Guàrdia

New ideas for computing integral bases

The determination of the ring of integers of a number field is one of the main tasks of computational algebraic number theory. The use of higher Newton polygons provides a new insight in the problem, leading to a fast method to compute integral bases, discriminants and prime ideal factorization in number fields.


Coffee Break


William Stein

How to use Sage to compute with Elliptic Curves

I will explain how to use Sage to define elliptic curves over various fields, do arithmetic on them, and compute standard invariants. Then I'll talk about elliptic curves over finite fields, and how to count points and compute the group structure. Next, I'll talk about elliptic curves over number fields and Sage's implementation of Tate's algorithm. Finally, I'll discuss computing the invariants in the BSD conjecture for elliptic curves over QQ.




Clement Pernet & Majid Khonji

Computing exactly with unsafe ressources: fault tolerant exact linear algebra and cloud computing

In several ways, challenges in computational mathematics (including computational number theory, graph theory, cryptanalysis, ...) involve large linear algebra computations over Z or Q. Distributed, peer-to-peer or Cloud computing represent nowadays the best perspectives to access to a large and cheap computing power, but based on unrealible ressources. Fault tolerant techniques are therefore developped in order to increase the confidence in the computations, or even to certify it. In the case of exact computations, the algebraic properties of the problems are well suited for the developpment of algorithm based fault tolerant protocols. In particular, the Chinese Remaindering Algorithm, offering an embarassingly easy parallelization, can be adapted to work as an error correcting code and tolerate errors. We will present an demonstrate these algorithms and protocols in the case of a distributed computation of the determinant of a matrix over Z.


Martin Albrecht

How to get started developing Sage

In this talk, we will try to highlight a few interesting and relevant bits and pieces for getting into Sage development. We will give an overview of how Sage is structured and step through the Sage development process. The talk is meant to be fairly interactive with people asking questions etc.

Free evening

Sant Joan festivity



  1. Michael Abshoff, Technische Universität Dortmund
  2. Martin Albrecht, University of London
  3. Maite Aranes, University of Warwick
  4. Tomasz Buchert, Adam Mickiewicz University
  5. Michal Bulant, Masaryk University
  6. Gabriel Cardona, Universitat de les Illes Balears
  7. Wouter Castryck, Leuven
  8. Henri Cohen, Bordeaux
  9. Francesc Creixell, UPC
  10. Christian Eder, TU Kaiserslautern
  11. Burcin Erocal, RISC, JKU - Linz
  12. Julio Fernández, UPC
  13. Imma Gálvez, UAB
  14. Enrique González-Jimenez, Universidad Autónoma de Madrid
  15. Josep González, UPC
  16. Jordi Guàrdia, UPC
  17. Xavier Guitart, UPC
  18. Amir Hashemi, Isfahan University of Technology (Iran)
  19. Nikolas Karalis, National Technical University of Athens
  20. Hamish Ivey-Law, Sydney-Marseille
  21. David Kohel, Institut de Mathématiques de Luminy
  22. Joan Carles Lario, UPC
  23. Offray Vladimir Luna Cárdenas, Javeriana (Colombia)
  24. David Loeffler, University of Cambridge
  25. Robert Miller, University of Washington
  26. Antonio Molina, Addlink Software Científico
  27. Enric Nart, UAB
  28. Sebastian Pancratz, University of Oxford
  29. Clement Pernet
  30. Joaquim Puig, UPC
  31. Jordi Quer, UPC
  32. Anna Río, UPC
  33. Víctor Rotger, UPC
  34. Bjarke Roune, University of Aarhus
  35. Utpal Sarkar, HP (+UPC)
  36. Diana Savin, Ovidius University (Romania)
  37. Rainer Schulze-Pillot, Universitaet des Saarlandes
  38. Mehmet Sengun, University of Duisburg-Essen
  39. Jaap Spies, Holland
  40. William Stein, University of Washington
  41. Emmanuel Thome, INRIA Lorraine
  42. Andrew Tonks, London Metropolitan University
  43. Gonzalo Tornaría, Universidad de la República (Uruguay)
  44. Eulàlia Tramuns, UPC
  45. Montrserrat Vela, UPC
  46. Preston Wake, McMaster

  47. Christian Wuthrich, University of Nottingham
  48. Brian Wyman, Univ of Michigan