Bezout’s identity is a way to present the greatest common divisor of two integers m, n as linear combination of these two. That is, it ensures the existence of two integers a, b such that gcd(m, n) = am - bn A particular useful case is when m, n are…

A field is an important concept often appearing in applied and theoretical subjects of mathematics as for instance in cryptography. In this story we will construct one specific field which you encounter especially when dealing with finite group structures, i.e. Z_p. A field can be described as a set together…

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…

The Euclidean division is a well-known method to divide two integers by each other and having the result split into a unique integer part and a unique remainder. In this short story we are going to look at how to implement this algorithm in Rust. But first let us consider…

This story is a direct follow-up of the previous account about computing a determinant numerically. As we have pointed out, or as you might have observed when running the code, the given method very quickly ceases to return in a feasible amount of time for larger matrices. This story is…

In these stories (here and here), we have looked at some basic properties of determinants. Our goal in this story is to compute a determinant numerically. To do this there exists several ways and most of these are not efficient at all. The first implementation we are going to look…

Permutations are an often appearing construct in many applied and theoretic subjects. This story intends to put together some of the most fundamental facts about permutations. Finally, we will look at some implementations of its core features.