Student Projects
The final project is due on December 7, 2007.
Robert Bradshaw: Class numbers for real cyclotomic fields
Code and data can be found here http://sage.math.washington.edu/home/robertwb/cyclo/ (extended table here).
Michael Decker: Determining monogenicity of fields
This project is a pdf paper.
Alyson Dienes: Polynomial factorization over ZZ
This project consists of two Sage worksheets that give a complete implementation of the LLL algorithm, and also draw animations that show the steps of the algorithm. There are two Sage worksheets. In each case, you will have to evaluate a bunch of code at the *bottom* of the worksheets in order to use the examples at the top.
HTML Pages (warning -- matrices look funny, but animations look fine)
SAGE Worksheet versions
Daniel Finkel: Witt Vectors
This project is a pdf paper.
Jacob Lewis: Modular curves, galois thoery, Sturm's theorem
This project is a pdf paper.
James Merryfield: Linear algebra over number fields
Robert Miller: The Long Shadow of Evariste Galois
This project consists of a PDF paper along with a Wiki page of examples.
Dustin Moody: Sums of squares
This project is a Sage program that computes many things about sums of squares.
Eina Ooka: Ramification groups
This project is a pdf paper about ramification groups.
Lee Patrolia: Zeta functions of number fields
This project is a pdf paper about the analytic class number formula.
Daniel Shumow: Toy implementation of GNFS
Handed in as GNFS Sage Notebook (this is an update of the original handed in as this: The first handed in project was a wrong version of the code that used sage functions to compute a square root mod N. This is a minor point, I had all the data laying around to do this, but just calling a square root oracle leads to a much simpler algorithm for factoring. I updated the toy implementation to compute the square root in a much more honest fashion.) -- here is the raw notebook code.
Stephanie Vance: Quaternionic lattices
This project is a PDF paper.
Wenhan Wang: Nonessential discriminant divisors; gens for O_K
This project is a PDF paper.
Luke Wolcott -- maximal and nonmaximal orders: compare and contrast
This project is a PDF paper.