As a library author. I can tell you implementing HTM from scratch is not an easy task - see my thread Hierarchical Temporal Memory Agent in standard Reinforcement Learning Environment to see what I’ve gone though to build a working HTM implementation. Especially section 3 and 4. There’s two route you can go. a) Go the OO style and build classes of synapses and neurons. Then combine them to build HTM. Or b) Build a computational framework of HTM (this is what I did) mostly composed by sparse matrix and tensors. Then implement HTM over these concepts.
Option a) does not require a computational framework of HTM to build. While b) does. Also I’ld like to clarify that a mathematical framework is not a computational framework. A mathematical framework refers to a system which one can use to infer properties of the subject. While a computational framework refers to a system one use to guide the implementation of a certain algorithm.
TL;DR Implementing HTM from scratch is hard. Years of programming experience among other skills are needed to produce one. You should try to use ones built by others like HTM.core or Etaler. Both framework have their documentation and tutorial online. For HTM.core and for Etaler