Euclidean Algorithm

Join Medium with my referral link - applied.math.coding Get access to all of my stories and to thousands more on Medium from other writers. As my strong believe is, Medium is…medium.com In my recent story (here) we have seen how easily the Euclidean algorithm can be lifted to the abstract case of Euclidean domains and by this providing an implementation that holds for polynomials and integers as well. As has been noted already here, within the same scope of abstraction, i.e…

Join Medium with my referral link - applied.math.coding Get access to all of my stories and to thousands more on Medium from other writers. As my strong believe is, Medium is…medium.com In this story we are going to implement an algorithm that determines the greatest common divisor of two polynomials. Remember, polynomials over a field F (for instance the real numbers), can be given the structure of a commutative ring F[x] by the usual definition of multiplication and addition (more on…

Join Medium with my referral link - applied.math.coding Get access to all of my stories and to thousands more on Medium from other writers. As my strong believe is, Medium is…medium.com This story follows-up the overview about polynomial algebra. In the previous article (see here) the so called Euclidean domain has been defined that intends to condense common properties of the ring Z (the integers) and the commutative ring F[x] (the polynomials over the field F).

Join Medium with my referral link - applied.math.coding Get access to all of my stories and to thousands more on Medium from other writers. As my strong believe is, Medium is…medium.com Remember the definition and computation of the greatest common divisor (GCD) of two integers — or you might want to recap from this short article. In essence, the computation of the GCD in the Euclidean algorithm is based on Euclidean division. As we have seen in my previous stories (here…

Join Medium with my referral link - applied.math.coding Get access to all of my stories and to thousands more on Medium from other writers. As my strong believe is, Medium is…medium.com This story aims at providing the theory behind the Euclidean algorithm and to provide a possible implementation in Rust. For those who need a small wrap-up in Rust, feel invited to this introduction. The greatest common divisor of two non-negative integers n, m, denoted by gcd(n, m) is defined to…