Should RotationMatrix work with symbolic vectors?

*To*: mathgroup at smc.vnet.net*Subject*: [mg85952] Should RotationMatrix work with symbolic vectors?*From*: Steve Gray <stevebg at roadrunner.com>*Date*: Thu, 28 Feb 2008 02:56:49 -0500 (EST)

It works fine when the "source" and "destination" vectors are numeric (it gives a matrix, say rm2, such that rm2.a2 is parallel to b2): a2 = {1, 2, 3}; b2 = {3, 5, 7}; rm2 = N[RotationMatrix[{a2, b2}]] {{0.997846, 0.028474, 0.059102}, {-0.0301974, 0.999138, 0.028474}, {-0.0582406,-0.0301974,0.997846}} and Normalize[rm2.a2] (* rm2.Normalize[a2] also works *) {0.329293, 0.548821, 0.76835} which is a unit vector parallel to b2. So far, great. But unless a2 and b2 have numeric values, RotationMatrix does nothing. avec = {a2x, a2y}; bvec = {b2x, b2y}; RotationMatrix[{avec, bvec}] (* gives *) RotationMatrix[{{a2x, a2y}, {b2x, b2y}}] Can't it handle symbolics like most functions? While I'm asking about vectors, consider this example: av = {avx, avy, avz}; bv = {bvx, bvy, bvz}; Normalize[av\[Cross]bv] (* which gives *) {(-avz bvy + avy bvz)/Sqrt[Abs[-avy bvx + avx bvy]^2 + Abs[avz bvx -avx bvz]^2 + Abs[-avz bvy + avy bvz]^2], (avz bvx - avx bvz)/Sqrt[Abs[-avy bvx + avx bvy]^2 + Abs[avz bvx - avx bvz]^2 + Abs[-avz bvy + avy bvz]^2], (-avy bvx + avx bvy)/Sqrt[ Abs[-avy bvx + avx bvy]^2 + Abs[avz bvx - avx bvz]^2 + Abs[-avz bvy + avy bvz]^2]} All three vector components have the same denominator. What's a good way to automatically show that for clarity and speed? I'd appreciate any information. Steve Gray