Question

A third method for computing the ged (in addition to the two methods presented in Section 3.1) is obtained from the property $c|a \wedge c| b, a>b$ implies $c \mid a-b$. 1. What is the termination condition? 2. Find rules that implement this method, similar to the rules for the division method from Section 3.1.2. 3. Write a function with a While [] loop that uses this idea. 4. Find the loop invariant and prove correctness and termination using the methods outlined in Section 3.3.2. Test your programs for a set of inputs that includes all special cases.

   A third method for computing the ged (in addition to the two methods presented in Section 3.1) is obtained from the property $c|a \wedge c| b, a>b$ implies $c \mid a-b$.
1. What is the termination condition?
2. Find rules that implement this method, similar to the rules for the division method from Section 3.1.2.
3. Write a function with a While [] loop that uses this idea.
4. Find the loop invariant and prove correctness and termination using the methods outlined in Section 3.3.2.
Test your programs for a set of inputs that includes all special cases.

Computer science with Mathematica: theory and practice for science, mathematics, and engineering

Roman Maeder 1st Edition

Chapter 3, Problem 2

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Step 1

At this point, the greatest common divisor (gcd) of $a$ and $b$ is $a$, because any number is divisible by 0, and the only divisor common to $a$ and 0 is $a$ itself. Step 2: Define the Rules Implementing the Method The rules for this gcd computation method can be Show more…

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A third method for computing the ged (in addition to the two methods presented in Section 3.1) is obtained from the property $c|a \wedge c| b, a>b$ implies $c \mid a-b$. 1. What is the termination condition? 2. Find rules that implement this method, similar to the rules for the division method from Section 3.1.2. 3. Write a function with a While [] loop that uses this idea. 4. Find the loop invariant and prove correctness and termination using the methods outlined in Section 3.3.2. Test your programs for a set of inputs that includes all special cases.

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