I would like to ask in a next future how a CAS (I mean a symbolic calculator in mathematics, but I don't understand/know basics in symbolic calculus) does to calculate some operations in mathematics.
Example 1. I do not want to ask about how finds, for example Wolfram Alpha, a root of a non-linear equation. Since the users that provide me answers should said that is only an implementation of, for example, Newton method. Or for example how calculated the LU factorization, a limit or a definite integral. I accept also that there are methods to solve certain problems as plot graphics.
But from my ignorance there is a kind of questions that I don't want to discard because are curious. My problem is that I don't know noting about how symbolic calculators work.
Example 2. I would like to know for example for an identity yet solved in Mathematics Stack Exchange, how a CAS (for example the cited) can obtain such solution. Since it seems magic, and is curious how knows that a series converges or what it is sum, how calculates double integrals or define the convergence or functions.
Question. How one can ask (in my situation since I ignore how works such calculator) about how did such calculations (I say for a fixed example) a symbolic calculator? Are rights any of cited questions in Example 2? Since I don't know nothing about how are working with my questions, for example Wolfram Alpha, and I don't know nothing about its engineering, if my example is tagged with (wolfram-alpha) are there more interesting cases, different of those that I cited in Example 2? Thanks in advance.