Due Date: Wednesday, February 15, 2023.

Note. The results of the entire exercise should be in one file with the extension .el to be uploaded to Canvas.

Write a function in Lisp called gcd computing the greatest common divisor (GCD) of two numbers. You can assume that both parameters of this function are positive numbers. Use Euclid's algorithm for this and a while loop.

Euclid's algorithm. Let n and m be the two numbers. Let dividend = n, divisor = m, and remainder be 3 local variables. Then the algorithm will perform the operations:

remainder = dividend % divisor;
dividend = divisor;
divisor = remainder;

until the remainder is equal to 0 (use the predicate =). Then the value of the dividend at that point is the result of the function.

Examples of calls:
(gcd 12 18) ; return 6
(gcd 33 64) ; returns 1
(gcd 100 15) ; returns 5

See the function copy2 in copy_list.el for similar example.

Write in Lisp a function that replaces all the occurrences of a value in a list with something else. For example, if the first line in the function is

(defun replace (L z y)

Inside this function, define a lambda expression taking one parameter, let's call it x. In this lambda expression, compare the parameter to the parameter x with z, and if they are equal, return y. Otherwise, return x. Store this lambda expression in a variable.

Next, use mapcar and the variable containing the lambda expression to apply the anonymous function just described to all the elements of the list L. The result should be the same list where x is replaced with y. For example, evaluating

(replace '(3 1 5 6 3 2 3) 3 9)

(9 1 5 6 9 2 9)

When you compare the two parameters x and z, use the predicate equal instead of =. This will allow the replacement to work for things that are not numbers too.

Write a function in Lisp called print-list taking one parameter which we can assume to be a list. The function should print all the elements of the list using the function princ and a space between them. Use the function mapc for this purpose.

Show a few examples of testing this function. Show one example using the function apply and one using the function funcall.

a. Write a function called make-multiples receiving two parameters n and m and creating a list of the first m multiples of the number n starting from n. For example,

(make-multiples 3 4)

should return the list

'(3 6 9 12).

b. Write a function called is-multiple that takes one parameter that is a list of numbers and returns true (t) if all the elements of the list are multiples of the first one and nil otherwise. This said, a list generated by the function make-multiples could be passed to this new function and the result should be true. On the other hand, show an example of a list that could not have been generated by the first function for which the result is still true.

Note. You are allowed to define helper functions if you think it's necessary.

Upload the Lisp file to Canvas, Assignments, Homework 5.