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?