ReplaceAll and ReplaceRepeated Strange Behavior

*To*: mathgroup at smc.vnet.net*Subject*: [mg111460] ReplaceAll and ReplaceRepeated Strange Behavior*From*: blamm64 <blamm64 at charter.net>*Date*: Mon, 2 Aug 2010 07:04:48 -0400 (EDT)

Given the expression: eff = (L*(-L*mu+dm*Pi*Cos[b]))/(dm*Pi*(dm*Pi*mu+L*Cos[b])) After this I enter eff /. {dm*Pi -> L/Tan[a]} and get a result that does not, for a reason I cannot fathom and believe to be a bug, replace one instance of dm*Pi. The result of the evaluation yields L*(-L*mu+L*Cos[b]*Cot[a])/(dm*Pi*(L*Cos[b]+L*mu*Cot[a])) Precisely the same result occurs with eff //.{dm*Pi->L/Tan[a]} Why is the one remaining dm*Pi not replaced with L/Tan[a]? In fact, when define manually define eff1 as eff1 = (L*(-L*mu + L*Cos[b]*Cot[b]))/(dm*Pi*(L*Cos[b]+L*mu*Cot[a])) which is as you can see the result of the first ReplaceAll execution, and then enter eff1 /. {dm*Pi->L/Tan[a]} Mathematica returns eff1 unaltered! Now, I say this is a bug, so of course I'm probably missing something and it isn't a bug. I have to jump through syntactic hoops to get the 'right' answer: FullSimplify[eff /.{dm*Pi->L/Tan[a]}]/.{dm*Pi->L/Tan[a]}//FullSimplify and FullSimplify[eff /. {dm*Pi->L/Tan[a]} does no good either. It is not at all obvious to me what I might be missing with such an apparently simple replacement. By the way, how do you guys copy input or output from Mathematica notebook into this usergroup window? I had to do all this by hand, copy it from here into a notebook, and execute the notebook cells just to make sure I was getting it correct. I ran across this originally when I was constructing a simple notebook for doing some Acme power screw calculations. -Brian Lamm (Windows XP x64 Version 2003 SP2, Mathematica 7.0.1)