Does anyone know how I can treat abstract (un-coordinatized) vectors in Mathematica? For example if I have
v = (r0 + p r1 + p^2 r2 + ...), a sum of abstract vectors (ri) with coefficients as powers of the scalar p and I input
Dot[v,v], then I get an expression with the terms FOIL'd out, and the juxtaposition of the ri terms can be interpreted as dot products between the (ri) vectors. However, of I then square or cube this scalar expression, there is no way to decipher which (ri) terms were dotted with which. Is there a way to indicate that a quantity is a vector and have Mathematica associate dot products between terms? I would like to get an expression consisting of products of dot (inner) products.
Thank you for any suggestions.