The Gauss-Jordan-Floyd-Warshall-McNaughton-Yamada Algorithm

I read this and had a bunch of trouble understanding. I'm mostly a Python/C++/Java programmer and quite familiar with graph algorithms. When I started reading this post, I quickly got confused by the code dives quickly into set theory and ring theory, etc.

Does using those features really help? My guess is that, by implementing it this way, the various applications (RE finite automata conversion, etc) are more straightforward, presuming you understand ring theory, and that the implementation uses the theory directly, while implementations in other languages that don't expose this kind of functionality would have to refer to derivations in the literature.

Is it also "faster"? I used to work in HPC and implementing ultra-fast versions of graph algorithms was a major research topic, so I'm curious if the implemention has faster runtimes.