  The Calkin-Wilf tree is an infinite binary tree whose vertices are the
positive rational numbers. Each number occurs in the tree exactly once and in
the form $a/b$, where are $a$ and $b$ are relatively prime positive integers.
For every $2\times 2$ matrix with nonnegative integral coordinates and nonzero
determinant, it is possible to construct an analogous tree with this root. If
the root is the identity matrix, then the tree consists all matrices with
determinant 1, and this tree possesses the basic properties of the Calkin-Wilf
tree of positive rational numbers. The set of all matrices with nonzero
determinant decomposes into a forest of rooted infinite binary trees.
