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Odd ordering of results?

• To: mathgroup at smc.vnet.net
• Subject: [mg99527] Odd ordering of results?
• From: AES <siegman at stanford.edu>
• Date: Thu, 7 May 2009 06:35:51 -0400 (EDT)
• Organization: Stanford University

I'm evaluating an optical interferometer problem in which an input wave 
e1 produces internal, reflected and transmitted waves e2 thru e7 that 
are connected by the linear equations

   waveEqns = {e1 == 1, e2 == rho12 e1 + t42 e4, e3 == rho43 e4 + t13 e1,
       e4 == gL e6, e5 == gL e3, e6 == rho56 e5, e7 == t57 e5};

where the rho_nm and t_nm are reflection and transmission coefficients 
and the input wave amplitude is arbitrarily set to e1==1; and then 
solving these using 

  waveSolns = Solve[waveEqns, {e2, e3, e4, e5, e6, e7}]

and getting a set of rules en-><stuff> for e2 thru e7 which are ordered 
in the sequence

   Out[] = {{e2  e7  e3  e6  e5  e4 }}

with the "stuff" stripped out for brevity.

What puzzles me -- not a problem, just curious -- is the _order_ in 
which these rules appear.

Even more puzzling:  If I take out the leading "e1==1," statement in 
waveEqns I get the same results, except each "stuff" becomes 
"e1*same_stuff" -- and the set of rules produced by waveSolns is now in 
the different order

   Out[] = {{e2  e7  e3  e4  e5  e6 }}

Odd . . .  (seems like the natural thing would be to order the list on 
the left side of the en-><stuff> terms, getting e2 to e7 in either case)

• Follow-Ups:
  • Re: Odd ordering of results?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Odd ordering of results?
    • From: peter <plindsay.0@gmail.com>