       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)

```

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