simplifying RotationMatrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg96321] simplifying RotationMatrix*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Wed, 11 Feb 2009 05:23:42 -0500 (EST)*References*: <23667197.1234176058052.JavaMail.root@m02>*Reply-to*: drmajorbob at longhorns.com

If I calculate the rotation matrix from one vector to another in spherical coordinates, the result is HUGELY complicated: Needs["VectorAnalysis`"] SetCoordinates[Spherical]; mean = {1, t0, p0}; pt = {1, t, p}; xy = CoordinatesToCartesian /@ {mean, pt}; rot = RotationMatrix@xy; LeafCount@rot 32798 I don't know what to tell Simplify about this, but it seem there are MANY unnecessary Conjugate mentions: Cases[rot, Conjugate[z_], Infinity] // Length 1575 and MANY unnecessary cases like this, too: Cases[rot, Power[Abs[z_], 2], Infinity] // Length 1980 Each of these could be simply z^2, I think. Trying to eliminate these with rules doesn't seem to help much, if any. The first thing I thought of was PowerExpand, but Map[PowerExpand, rot, {2}] // LeafCount 32798 What am I missing? How can it be that complicated in the first place? Bobby