How do symbolic math software work? As the answer to a question of mine I was referred to a website (see here please)
How can WolframAlpha do it like humans?

The internal implementation of symbolic systems are closely related to how compilers work and you can find a lot of the internal implementation details in this Wikipedia article: https://en.wikipedia.org/wiki/Computer_algebra but to really understand it or implement a simplified version of something of that caliber you will probably need to get experience with some functional programming language like Haskell and then gain a lot of knowledge of how compilers in general(and specifically for functional languages) work.
