[Axiom-math] Solving symbolic vector equations: How do I do this in Axiom?

[Zach]

Please excuse me, I am really quite new to Axiom and much of abstract algebra terminology.  I hope this is the right place for these questions.  If not, could someone point me in the right direction.  I am currently reading the Axiom tome, er.. book, but it is good to have a human to bounce ideas off of.

Here is a really simple example, we have real number `a' and vectors `v1' and `v2'.  Given:

a*v1=v2

solve(a*v1=v2)
==> [a = v2/v1]

I would like to solve for a.  If I put this in, Axiom assumes v1 and v2 to be things that have a defined division (a field I guess).  But really we have no division by a vector (a ring, perhaps?), so what I would like is for axiom to solve this by

a * v1 . v1 = v2 . v1
a = (v2 . v1) / (v1 . v1)

I assume that I do this by giving Axiom some type information, like specifying v1 and v2 as Vector (or Matrix) Fraction Integer or something.  What is the best way of tackling these types of problems?

Thanks,
Zach