# Lecture 3: Polynomial Representations and Data Structures

• Review Maple

### Reading

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

### Topics

1. Go over assignment 2
2. Maple programs for computing the probability that two integers are relatively prime and the average number of division steps in the Euclidean algorithm.
3. Polynomial normal and canonical forms.
• factored vs. expanded
• distributed vs. recursive
• expanded normal and canonical forms
• factored normal and canonical forms
4. Rational number and rational function canonical forms
5. 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