SFU Crest CECM Logo Nils Bruin
Department of Mathematics
Simon Fraser University
Burnaby, BC
Tel : (778) 782 3794
Fax : (778) 782 4947
Email : nbruin@sfu.ca
Racoon picture

This is my personal page. Currently I am an Assistant Professor at the Department of Mathematics of Simon Fraser University.
For various redirections, see my links page.

Previous track

September 1990 - July 1995  Undergraduate Mathematics at Leiden university, resulting in Master Thesis Generalization of the ABC-conjecture, under supervision of Prof. Dr. R. Tijdeman.
July 1995 - July 1999 AIO (Graduate student) at Leiden University, working on the generalised Fermat equation, under supervision of Prof. Dr. R. Tijdeman and Dr. F. Beukers.
6 October 1999 Defense of PhD thesis Chabauty Methods and covering techniques applied to generalised Fermat equations.
September 1999 - August 2000 NWO-researcher at Utrecht University, under supervision of Dr. F. Beukers
July 2000 - September 2000 Clay Mathematical Institute Liftoff Mathematician at Utrecht, Netherlands and MSRI Berkeley, CA.
September 2000 - December 2000 MSRI Postdoctoral fellow
Januari 2001 - August 2002 PIMS Postdoctoral fellow at Simon Fraser University and University of British Columbia, Canada
September 2002 - September 2003 Senior Research Associate with the MAGMA group within the School of Mathematics at the University of Sydney
October 2003 - Assistant Professor at the Department of Mathematics of Simon Fraser University



For the thesis, the stellingen (dutch) are also available.

Online Lecture

MSRI makes its workshop lectures available via RealVideo. During the workshop on arithmetic geometry, December 11 - 15, I gave a lecture on explicit covering techniques. If you are far from MSRI, then you may prefer to contact a mirror site.

Slides and talks

Dagstuhl meeting Algorithms and Number Theory, Friday May 18, Visualising Sha[2] in Abelian surfaces, pdf slides, postscript abstract.

Workshop Computational Arithmetic Geometry, 18-20 June 2003, Sydney, Prym varieties of curves of genus 3, pdf slides



Algorithms for arithmetic on elliptic curves over general number fields, based on KASH. The main feature is an implementation of 2-descent and 2-isogeny-descent routines (taking care of even class numbers).

Current version: Algae 0.beta. You can download it as ell.shar. You may be interested in reading the README and the (at this time very crude and perhaps intimidating) documentation.

UPDATE March 27, 2001. Bug fix. The full 2-descent code did not compute properly at the infinite primes where ec.gamma is negative. Most people would probably not use this feature anyway, but it is fixed now.

WARNING. Selmer group computations also involve places at infinity. Precision settings may affect their outcome. The curve $y^2=x^3-1042011$ is an example of this phenomenon. With OrderPrec(50), you get a rank bound of 3, where with OrderPrec(300) the bound is 4, which is the rank of the curve. This is due to incorrect answers returned by EltCon. The command HEAP(O, "USE_ELT_PROD_REP", 50) has been recommended by the KASH team and seems to remedy the problem. It tells KASH to use another, safer, method for computing EltCon in O. If the package constructs an order automatically, then it sets this flag for that order.

NEW. A development version for computing 2 (isogeny) Selmer groups of elliptic curves over number fields in MAGMA is now available as m-Algae.

You might also be interested in TECC. It is another elliptic curve package, also based on KASH. It offers functionality mostly complimentary to ell.g. Unfortunately, the packages do not have compatible data structures for representing elliptic curves (yet?). I have not tested using both packages within the same session.

Denis Simon also has a program for computing 2-Selmer groups of elliptic curves over number fields, based on PARI/GP.

Software related to x^3+y^3=z^p

Software related to my thesis

A precursor to the 2-descent program mentioned above. These come without any documentation or warranty, so you're pretty much on your own if you want to use them. Should you do so and find them useful, I'd be glad to hear.


Conferences and Workshops

  • February 4 - 9, 2007: BIRS workshop on Explicit Methods for Rational Points on Curves
  • July 9 - 14, 2006: CNTA IX in Vancouver
  • July 5 - 9, 2004: PIMS Workshop Computational Arithmetic Geometry

  • Various other (mathematical) subjects

    Maple bug

    Be aware that Maple's simplify command does not always test for invertibility of x when simplifying 0/x. Waterloo software is aware of this and they have acknowledged that it is a bug and have promised to repair it in future versions. There is an example script of this behaviour. Short example: