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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)
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