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)