# Lecture 2: Polynomial Algebra

### Date: Jan. 12

### Background Material and Further Resources

### Reading

- Chap. 2 of the text.
- Handout: "Computer Algebra of Polynomials and Rational Functions"

### Topics

- Go over assignment 1
- Computing time of the Euclidean Algorithm
- Extended Euclidean algorithm and modular inverses
- Polynomial Rings
- Euclidean Domains
- Integers
- Gaussian Integers
- Polynomials over a field

- Field of fractions
- Integral and multivariate polynomial gcds
- Primitive polynomials and Gauss' lemma
- Computing over the rationals
- Pseudo remainder and the primitive PRS

### Maple Worksheet

### Assignment

The assignment description contains a summary of the material
introduced in this lecture.
Created: Jan. 12, 2000 by
jjohnson@mcs.drexel.edu