@Stefan: I have been looking at the implementation of vectors in the 
mechanics module and, just as you said, it would be better to extend the 
methods already used in the mechanics module. I am still in the process of 
looking at the code. I'll report back soon.
@Raoul: I have not yet taken a course in abstract algebra though I am 
currently enrolled in a course of linear algebra. I can read it up of 
course. Do you foresee any problems with not knowing abstract algebra just 
yet?

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