About random matrices: Random integer matrices. With no arguments, the majority of the entries are -1 and 1, never zero, and rarely "large." ::
sage: random_matrix(ZZ, 5, 5) [ -8 2 0 0 1] [ -1 2 1 -95 -1] [ -2 -12 0 0 1] [ -1 1 -1 -2 -1] [ 4 -4 -6 5 0]"Never zero", but even the given example has zeros. A bug, or maybe I don't quite understand this.
-- Jori Mäntysalo