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Author: William A. Stein

Friday January 8, 2016, 1:00 p.m.-5:50 p.m. AMS Special Session on Number Theory and Cryptography, II Room 606, Washington State Convention Center - See more at: http://jointmathematicsmeetings.org/meetings/national/jmm2016/2181_program_ss72.html#sthash.0qhNOcdn.dpuf

I will talk about how the SageMath (http://sagemath.org) software is incredibly useful for number theory and cryptography research.


15 minutes to talk about what SMC provides for writing a paper in practice.

8 min. A research project

  • background: mazur-stein-watkins-bektemerov bulletins 2006: give a freshman a student project and see what happens

  • crazy plots: the rank just keeps getting bigger in the data

  • random matrix heuristics and other conjecture: rank is 1/2 in the limit

  • manjul bharghava: the rank definitely doesn't just keep getting bigger!

  • challenge: systematically compute the ranks of all elliptic curves BLAH of height BLAH far enough that we can finally see the rank going down!

  • here's when it happens

  • bonus: some other statistics

4 min. Features of SMC for writing this paper

  • collaborative editing of latex documents

  • collaborative persistent terminals (e.g., ssh to cluster somewhere)

  • edit Python code; run from sage worksheets

  • use sqlite easily

  • run project on a 32-core big-memory VM at Google

  • chat: post little comments on the side of any file being edited

4 min. Features of Sage for writing this paper

    • mwrank
  • Simon Spicer's Elliptic curve enumeration

  • Simon Spicer's L-function bounding code

  • Magma interface