RE: Re: Changing the Natural Sort Order

*To*: mathgroup at smc.vnet.net*Subject*: [mg49238] RE: [mg49192] Re: Changing the Natural Sort Order*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 9 Jul 2004 02:26:08 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Thanks to everybody for the many suggestions on this. Basically I'm trying to establish a canonical order for a wedge product of 1-forms. The 1-forms may be expressed in several different manners. The product may contain general symbolic indices and base indices. The base indices might be {1,2,3) or {0,1,2,3} or {t,x,y,z}. I want the list of base indices to specify their order. The ones listed are no problem because they are in natural order. But a user might specify {x,y,z,t} or (in Greek characters) {rho, theta, phi}, which are not in natural order. But there are many problems. Using replacement rules can cause difficulties because the same symbols or values might be in non-indexed positions and they should not be replaced. So I have to think about this and will probably have to retreat from trying to implement such a general capability. Most likely I will have to limit or specify the possible Mathematica forms of the 1-forms. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Paul Abbott [mailto:paul at physics.uwa.edu.au] To: mathgroup at smc.vnet.net In article <ccb5hr$ekg$1 at smc.vnet.net>, "David Park" <djmp at earthlink.net> wrote: > Is it possible to change the natural sort order of symbols that is used in > Sort? > > I would like something like the following statement (that does not work). > > Assuming[d < b < c, Sort[{a, b, c, d, f}]] > > giving the desired output > > {a,d,b,c,f} > > I won't be sorting simple lists of symbols, but lists of similar, but > unspecified, expressions that contain the symbols. For example... > > {h[x,g[a]], h[x,g[b]], h[x,g[c]], h[x,g[d]], h[x,g[f]]} > > which should give > > {h[x,g[a]], h[x,g[d]], h[x,g[b]], h[x,g[c]], h[x,g[f]]} > > Is there any way to do this? I cannot see a simple way (via OrderedQ) to change the sort order of symbols. However, here is one way to achieve what you want: [1] Use Ordering to define a set of replacement rules for your symbols: OrderRule[l_] := Thread[l[[Ordering[l]]] -> l] For your example, OrderRule[{d, b, c}] {b -> d, c -> b, d -> c} [2] If you would like to use ordering like d < b < c, you could overload OrderRule as follows: OrderRule[Unevaluated[Less[l__]]] := OrderRule[{l}] OrderRule[Unevaluated[Greater[l__]]] := OrderRule[Reverse[{l}]] [3] Then use Sort followed by OrderRule: Sort[{a, b, c, d, f}] /. OrderRule[d < b < c] {a, d, b, c, f} Sort[{h[x,g[f]], h[x, g[d]], h[x, g[c]], h[x, g[b]], h[x, g[a]]}] /. OrderRule[d < b < c] {h[x, g[a]], h[x, g[d]], h[x, g[b]], h[x, g[c]], h[x, g[f]]} Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul