Solving 3-vector equations

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1076] Solving 3-vector equations*From*: Pekka.Janhunen at fmi.fi (Pekka Janhunen)*Date*: Fri, 12 May 1995 18:01:04 -0400*Organization*: Finnish Meteorological Institute/Geophysics Dept.

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 unfinished 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 fmi.fi \ /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