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Re: Odd ordering of results?

• To: mathgroup at smc.vnet.net
• Subject: [mg99558] Re: [mg99527] Odd ordering of results?
• From: "David Park" <djmpark at comcast.net>
• Date: Fri, 8 May 2009 00:13:21 -0400 (EDT)
• References: <3523611.1241694912508.JavaMail.root@n11>

I think the order of the returned rules is an artifact of the particular
solution method. But you could always sort the resulting rule set.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: AES [mailto:siegman at stanford.edu] 

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)