Decidability of the Orbit Problem Over $\mathbb{Q}(X)$

Joshua Holden, Alexa Renner

The orbit problem is the problem of whether, given $x,y\in {\mathbb{Q}}^n$ and an $n\times n$ matrix $A$, there exists an $i\in \mathbb{N}$ such that $A^{i}x=y$. In 1980, Kannan and…