>
> > (%i1) tellrat(u^2+v^2+w^2=1);
> Yes, this is close enough. I suppose I am expecting
> too much if I then ask uniteigenvectors() to figure
> out that [u v w]' has unit length, just from that
> tellrat() rule:
I don't have time to look at the details, but did you try
ratsimp(expr),algebraic:true (with the tellrat in force) on the result?