My question was more like, will all those four mathematical objects (alongside other stuff like scalars) be represented as a single data type in a given library

My question was more like, will all those four mathematical objects (alongside other stuff like scalars) be represented as a single data type in a given library that implements geometric algebra, or will they be given distinct data types? Someone else answered that they might be given a single data type, but it's possible to give more precise types, which seem cool! (do you have any library to mention, alongside the ones already mentioned?)