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Symbolic vectors possible?


Colleagues,

Is it possible to create functions in Mathematica
for manipulating expressions with symbolic vectors?
Just like we do on paper, without representing them with lists.
Something like the following for Dot and similar for Cross:

In[] := vectors = { v, u, w }; (* these symbols should be treated as
vectors *)

In[] := VectorExpand[(a v + b u) . w]
Out[] = a v.w + b u.w

In[] := VectorFactor[a v.w + b u.w]
Out[] = (a v + b u) . w

In[] := VectorSimplify[v.v + 2 v.u + u.u]
Out[] = (v + u) . (v + u)

To get the above results, simple replacement rules would suffice,
but the real challenge is to make it work for any expression.
Do you have any ideas?

--
Vladimir


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