# 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

- 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.
- 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?
- 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?