Math 583: Homework Assignment 3; Due 2006-04-19

1. Compute the matrix of $T_2$ on the Victor Miller basis for $M_{32}$.
   Then compute its characteristic polynomial and verify it factors as
   a product of two irreducible polynomials.


2. Work through the SAGE tutorial, which is available here:

  http://modular.math.washington.edu/sage/documentation.html

Anser the following questions:

(a) Describe your experience getting access to SAGE.  Note that if you
have any trouble installing SAGE, let me know, and I can give you an
account on modular.math.washington.edu.  Also, you can paste in
snipets of SAGE code to:

       http://modular.math.washington.edu/calc/  

Finally, I'm working on having SAGE installed on zeno.

(b) How long did it take you to read through the tutorial?

(c) List any typos you find, any badly worded paragraphs, or anything
that was confusing.

(d) Do you think certain topics in the tutorial should be reordered,
removed, or added?

(e) In which format did you view the tutorial?  (HTML, PDF, etc.?)	

(f) What (if anything) in the tutorial did not work for you?