# 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 3-4. This week we will study the p-adic numbers Qp and formal power series Q[[x]].
Week 5-6.
• 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 p-adic Hensel lifting by x-adic 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 p-adic numbers into a Hensel lift algorithm for the x-adic case. This project is part of test 1.
• Study these worksheets at home: introduction to resultant, definition of resultant, properties of the resultant.
Week 7-12.
Last Week Factoring integers.