Re: Sorting coefficients

*To*: mathgroup at smc.vnet.net*Subject*: [mg124041] Re: Sorting coefficients*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sat, 7 Jan 2012 05:16:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201060914.EAA26796@smc.vnet.net>

pts = Prepend[ Table[{Re, Im}[E^(k (2 \[Pi])/6 I)] // Through, {k, 0, 5}], {0, 0}]; n = 1; Graphics[Text[n++, #] & /@ pts] To sort by layer and then within layer order2 = SortBy[pts, {N[Last[#]], N[First[#]]} &]; Note that the coordinates need to be converted to Reals for the canonical order to be the same as numerical order. n = 1; Graphics[Text[n++, #] & /@ order2] Sorting from lower left to upper right order3 = SortBy[pts, {Norm[N[#] - order2[[1]]], Last[N[#]]} &]; n = 1; Graphics[Text[n++, #] & /@ order3] Bob Hanlon On Fri, Jan 6, 2012 at 4:14 AM, Chris Young <cy56 at comcast.net> wrote: > I'm trying to get my points sorted first by rows first. But I'm having > trouble figuring out how to do the kind of double sorting I need with > Sort. SortBy seems very hard to figure out and I'm not sure if it's > what I need here. > > I've just got a hexagonal layout of point coordinates, with another one > on the origin, and I'm trying to sort everything from lower left to > upper right. I.e., the usual ordering of going through the bottom row > from left to right, then through the middle row from left to right, etc. > > Any help appreciated. > > Chris Young > cy56 at comcast.net > > > In[1043]:= Prepend[ > Table[{Re, Im}[ E^(k (2 \[Pi])/6 I)] // Through, {k, 0, 5}], {0, 0}] > > Out[1043]= {{0, 0}, {1, 0}, {1/2, Sqrt[3]/2}, {-(1/2), Sqrt[3]/ > 2}, {-1, 0}, {-(1/2), -(Sqrt[3]/2)}, {1/2, -(Sqrt[3]/2)}} > > In[1046]:= Sort[%1043, #1[[2]] < #2[[2]] &] > > Out[1046]= {{1/2, -(Sqrt[3]/2)}, {-(1/2), -(Sqrt[3]/2)}, {-1, 0}, {1, > 0}, {0, 0}, {-(1/2), Sqrt[3]/2}, {1/2, Sqrt[3]/2}} > > In[1073]:= Sort[%1046, #1[[2]] < #2[[2]] &] > > Out[1073]= {{-(1/2), -(Sqrt[3]/2)}, {1/2, -(Sqrt[3]/2)}, {0, 0}, {1, > 0}, {-1, 0}, {1/2, Sqrt[3]/2}, {-(1/2), Sqrt[3]/2}} >

**References**:**Sorting coefficients***From:*Chris Young <cy56@comcast.net>