Bill,
> > so what I would like is for axiom to solve this by > > > > a * v1 . v1 = v2 . v1 > > a = (v2 . v1) / (v1 . v1) > > > > ??? This is not a solution to the original equation! Hmm, the problem is that this equation is in danger of having no solution. I guess there is an implicit assumption that this has a solution for some nonzero v2, meaning the vectors must be parallel. My boss gave me a problem something like this and I am walking on shaky legs at the moment as I haven't tried to solve problems like these before. I guess the correct thing to do is notice that v1 and v2 must be parallel, and then deal with the magnitudes, a=|v2|/|v1|. Once you accept this my solution works too, as with unit vector u in the direction of v1 and v2, v1 = |v1| u and v2 = |v2| u, v1 . v2 = |v1| |v2| u . u = |v1| |v2| and v1 . v1 = |v1|^2. Right? Please feel free to point out any misconceptions I am fostering. Anyway, I guess I chose too simple of an example. But never mind that. (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).) > Well no, not really. Currently Axiom has no domain for symbolic > computations with vectors. I was afraid of that. Over at Maxima they had no facility either. > > What is the best way of tackling these types of problems? > > > > It would be possible (and quite interesting) to create a new domain in > Axiom for symbolic vector calculations. > Hmm, okay. So, it would be a good idea to understand how this is done in polynomial symbolic manipulation before approaching such a task? Thanks, Zach
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