RE: [Axiom-math] Solving symbolic vector equations: How do I do thisin Axiom?

[Billinghurst, David \(RTATECH\)]

> From:  Zach
>
> (The original problem was to find tuples of reals (n1, n2, m1, m2) 
> such that n1*a1 + n2*a2 = m1*b1 + m2*b2 (where a1, a2, b1, and b2 are
2D vectors).)

Firstly, the solution is not unique.  If (n1, n2, m1, m2) is a solution
then 
so is (k*n1, k*n2, k*m1, k*m2).

Now write this as a matrix equation, where a1 = (a1x, a1y) and so on

[ a1x  a2x  -b1x  -b2x ] [ n1 ]    [ 0 ]
[ a1y  a2y  -b1y  -b2y ] [ n2 ]  = [ 0 ]
                         [ m1 ]
                         [ m2 ] 

and solve as an underdetermined linear system. The nature of the
solution will depend
on the rank of the coefficient matrix.


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