# Lecture 3: Polynomial Representations and Data Structures

### Date: Jan. 19

### Background Material and Further Resources

### Reading

- Chap. 3 of the text.
- Handout: "Computer Algebra of Polynomials and Rational Functions"

### Topics

- Go over assignment 2
- Maple programs for computing the probability that two integers
are relatively prime and the average number of division steps
in the Euclidean algorithm.
- Polynomial normal and canonical forms.
- factored vs. expanded
- distributed vs. recursive
- expanded normal and canonical forms
- factored normal and canonical forms

- Rational number and rational function canonical forms
- Maple data structures and internal representations
- dismantle
- disassemble
- addressof

### Maple Worksheet

- gigcd.mws(Gaussian Integer GCD
algorithm)
- avg.mws(Probability calculation
of relative primality and average number of divisions in the
Euclidean algorithm)
- polyrep.mws(Polynomial
expressions, normal and canonical forms)
- internal.mws(Maple data structures
and internal representations)

### Assignment

Created: Jan. 20, 2000 by
jjohnson@mcs.drexel.edu