Re: SortBy won't order irrationals

*To*: mathgroup at smc.vnet.net*Subject*: [mg124052] Re: SortBy won't order irrationals*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 7 Jan 2012 05:20:30 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201060916.EAA26862@smc.vnet.net>

Numeric symbols like Sqrt[2],Pi,E etc. etc are not sorted by their value but in the same way as all other symbols. Compare: Sort[{Pi, 4, Sqrt[2], 2, 3*E}] {2, 4, Sqrt[2], 3*E, Pi} with Sort[{Pi, 4, Sqrt[2], 2, 3*E}, Less] {Sqrt[2], 2, Pi, 4, 3*E} Note also that you can use Sort with a custom ordering function. Andrzej Kozlowski On 6 Jan 2012, at 10:16, Chris Young wrote: > Have to use N[ ] on them first. Combined with Sort's refusal to accept > multiple keys, this is extremely exasperating. > > In[1218]:= ptsIrr = > { > {0, 2}, {1, Sqrt[2]}, {2, 2}, > {4, 1}, {Sqrt[5], 1}, {6, 1}, {Sqrt[3], 1}, > {7, 0}, {-1, 0} > } > > Out[1218]= {{0, 2}, {1, Sqrt[2]}, {2, 2}, {4, 1}, {Sqrt[5], 1}, {6, > 1}, {Sqrt[3], 1}, {7, 0}, {-1, 0}} > > In[1219]:= sortIrrY = SortBy[ptsIrr, #[[2]] &] > > Out[1219]= {{-1, 0}, {7, 0}, {4, 1}, {6, 1}, {Sqrt[3], 1}, {Sqrt[5], > 1}, {0, 2}, {2, 2}, {1, Sqrt[2]}} > > In[1220]:= sortIrrYN = SortBy[ptsIrr // N, #[[2]] &] > > Out[1220]= {{-1., 0.}, {7., 0.}, {1.73205, 1.}, {2.23607, 1.}, {4., > 1.}, {6., 1.}, {1., 1.41421}, {0., 2.}, {2., 2.}} > > In[1221]:= sortIrrYN2 = SortBy[ptsIrr, N[#[[2]]] &] > > Out[1221]= {{-1, 0}, {7, 0}, {4, 1}, {6, 1}, {Sqrt[3], 1}, {Sqrt[5], > 1}, {1, Sqrt[2]}, {0, 2}, {2, 2}} > >

**References**:**SortBy won't order irrationals***From:*Chris Young <cy56@comcast.net>