Computer Algebra, Spring 2002.
Note: I have moved to another office: 211 LOV
Week 1.
Week 2.
 Study the algorithms in this worksheet
and do the assignment about sqrfree.
The worksheet explains how the following algorithms work:

The Extended Euclidean Algorithm (only implemented for the case
of positive integers, but it works in the same way for
polynomials).
 How to do divisions modulo an integer p. Note: one can use a similar
algorithm to do divisions modulo a polynomial.
 How to compute quotients and remainders.
 Euclidean Algorithm for polynomials.
 Chinese Remainder Theorem (only implemented for two integer moduli m1,m2.
Of course a very similar algorithm would work when m1,m2 are polynomials).
 We'll start on this assignment in class, finish
it at home.
Week 34. This week we will study the padic numbers
Q_{p} and formal
power series
Q[[x]].
Week 56.
 Factoring polynomials in Q[x].
 Project: Implement factorization in Q[x,y] in the same
way as factorization in Q[x] is done in the worksheet.
You may use Maple's "sqrfree" for squarefree factorization,
and may only use Maple's "factor" for factoring univariate
polynomials. Replace "icontent" by "content", replace
padic Hensel lifting by xadic Hensel liften, replace
the bound on the length of the coefficients by a bound
on the degree of the coefficients, etc.
Turn the Hensel lift algorithm from the worksheet on
padic numbers into a Hensel lift algorithm for the xadic
case. This project is part of test 1.
 Study these worksheets at home:
introduction to resultant,
definition of resultant,
properties of the
resultant.
Week 712.
Last Week
Factoring integers.