Groups, Rings, and Fields

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1. Quick introductions by everybody:
   1. Who are you?
   2. Project idea?
2. Announcement: The new Crypto Seminar!

The seminar meets at 1:30pm on Thursdays in 415L Guggenheim (the Applied Math Building):

April 17, 2008: Reinier Broker -- Modular polynomials for genus 2

Modular polynomials are an important tool in many algorithms involving elliptic curves. In this talk we generalize this concept to the genus 2 case. We give the theoretical framework describing the genus 2 modular polynomials and discuss how to explicitly compute them.

1. Groups, Rings and Field -- introduction to Sage in Algebra: worksheet.pdf worksheet.sws

   1. Definition of groups, examples, use in Sage.
   2. Definition of rings, examples, use in Sage.
   3. Definition of fields, examples, use in Sage.
   4. General remarks about how only Sage and Magma make groups, rings, and fields themselves very much first class objects, and that this leads to very natural efficiency gains and organization of code. Also it very nicely models mathematics as it is viewed by mathematicians.