This is really more of a general question about the process of solving a certain type of problem than it is an actual problem. Concerning invariance of the interval, ds, in relativity, say you have an interval ds^2, ℝ(1,3), and a certain equation for a metric space. I know that there are isometries that must exist such that the interval is rendered invariant, and that these are basically the Poincare group of transformations. But how do you find the isometries for a specific space (defined by whatever ds2 is equal to, some combination of dx2, dy2, and dz2), say ds2 = -dx2-dy2-dz2? How exactly do you express these isometries, and the transformations that would constitute invariance of the interval?