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SortBy won't order irrationals

• To: mathgroup at smc.vnet.net
• Subject: [mg124028] SortBy won't order irrationals
• From: Chris Young <cy56 at comcast.net>
• Date: Fri, 6 Jan 2012 04:16:42 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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}}

• Follow-Ups:
  • Re: SortBy won't order irrationals
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: SortBy won't order irrationals
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>