**Note:** Documents can differ from the ones handed in class
(format change, typos). LaTeX style files [kb.sty | kbexo.sty] are needed to compile the
TeX files (UTF-8 encoded).

The lectures take place on Thursdays 10am-12am
and 2pm-4pm (Lamartine, salle de l'École).

First lecture on Thursday Sep. 10th.

We will be using the PARI/GP
system. Here are the reference card and the GP User's guide.

Some course notes: [PDF] The exam in [2013-2014].

Lecture 1 | Algorithms, Complexity, Examples |

Lecture 2 | The Fast Fourier Transform and basic complexity results |

Lecture 3 | Z-modules/HNF |

Lecture 4 | Z-modules/SNF & lattices |

Lecture 5 | The LLL Algorithm |

Lecture 6 | Polynomials over finite fields (1) |

Lecture 7 | Polynomials over finite fields (2) |

- The seminal LLL paper by Arjen Lenstra, Hendrik Lenstra Jr. and László Lovász (Math. Annalen, 1982).
- Phong Nguyen and Damien Stehlé's floating point LLL.
- Arne Storjohann's PhD thesis and his preprint on space efficient HNF.
- A nice rendition by Dan Bernstein of the AKS primality test.
- A survey of mine (in french) about computational algebraic number theory, and a more difficult paper (in english) on the same subjects.
- François Morain's paper on his implementation of FastECPP.

Karim Belabas | |

2016-07-18 16:45:32 |