# 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.