A geometric approach to the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but which exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an automorphism of a certain rational surface and can therefore be considered to be the action of an extended Weyl group of indefinite type. A method to construct the mappings associated with some indefinite root systems is presented. A method to calculate their algebraic entropy by using the theory of intersection numbers is presented. It is also shown that the degree of the $n$-th iterate of every discrete Painlev\'{e} equation in Sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.