# Assignment 3

### CS 680-503 Computer Algebra I Instructor: Jeremy Johnson  Due Wed. Jan. 26 in class

For this assignment you should refer to the Maple worksheets from the previous lecture.

### Problems to Hand in

1. Determine Maple's internal representation for the expression
y^2*(x^2+1) + y*(x^2+1) + 2
Use the function dismantle. Make sure to look at the addresses of the various components. Can you determine how much space is used? See the worksheet from lecture 3 that illustrates this function. Also look at the help page.
2. Write a Maple program to compute the probability that two Gaussian Integers are relatively prime. You should generate all pairs of Gaussian Integers z and w, with Norm(z), Norm(w) <= N and z and w in the upper right quadrant. Compute this probability for several different values of N. How does this compare to the integer case we did in class?
3. Write a Maple program to compute the average number of division steps required by the Euclidean algorithm for Gaussian Integers. You should generate all pairs of Gaussian Integers z and w, with Norm(z), Norm(w) <= N and z and w in the upper right quadrant. Compute this probability for several different values of N. How does this compare to the integer case we did in class?