2
$\begingroup$

Let $K$ be an algebraic number field of class number 1. Let $\frak{O}$ be the ring of algebraic integers in $K$. Let $A$ be a nonzero $m\times n$ matrix over $\frak{O}$. Since $\frak{O}$ is a PID, $A$ has Smith normal form $S$. I'm looking for an algorithm to compute $S$. It seems to me that we need to solve Bézout's identity. If it's too difficult, we may assume K is a quadratic number field of class number 1.

1 Answers 1