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Solving 3-vector equations

Hi Mathgroup,

How to solve vector equations? For example, I want to solve

x + beta1 . y == gamma1                    (1)

y + (beta2 . y) y + beta3 y^2 == gamma2    (2)

where x,gamma1,gamma2 are scalars and y,beta1,beta2,beta3 are
3-vectors. The unknown are x and y. The actual problem is more
difficult, but this gives an idea. beta2 and beta3 depend algebraiclly
on x (the functional form is known and is relatively simple).

When computing by hand, one typically starts by taking dot products
of equation (2) with vectors beta1 and y and substitutes back.
When computing by Mathematica, however, I thus far have found no other
way but to write the equations in component form and give them to Solve.
A simpler example which I already solved by hand is still running
on Mathematica and it has consumed 50 minutes.

My question is: has anyone written a package to solve vector equations
directly, without throwing them back in component form?

Pekka.Janhunen at                 \  /o- o -o-oo-o-o-o-o-o-
Any coincidences with my opinions and  \/ Having tables to hash
those of FMI/GEO are purely accidental /\ being able to crash

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