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>