I'm very interested in improving upon a patented software method (A) which, in it's turn, is an improvement over a relatively old existing method (B).
Originally, my understanding was that the old method (B) would fall as prior art, and thus, the patent application (A) be rejected. However, there was adequate disclosure and the original paper is referenced to in the patent grant.
According to 35 USC 101-103, 112, improvements to processes, machines, manufactures, or compositions of matter, are patentable but only if they are new and useful, and non-obvious (among other requirements like adequate disclosure etc.) reference
As most legal concepts, these all seem very abstract to me, and I couldn't find any trusted source that could give me an adequate answer of what constitutes new and useful or non-obvious improvements. Or at least examples of it.
My question is, what should be taken into account for something to be considered new and useful, and non-obvious?
Also, in order to not infringe the patent, should the new method not violate all claims, or is it an infringement to violate anyone claim? I ask this because there's a series of chained claims in the referred document.