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Say we have a list:

{{1/2, -(Sqrt[3]/2)}, {1, 0}, {1/2, Sqrt[3]/2}, {-(1/2), Sqrt[3]/2}, {-1, 0}, {-(1/2), -(Sqrt[3]/2)}}

now we want to sort that list by looking at the second component of each sub list (call it y coordinate for ease), i.e. sort it s.t. y is in the descending order. So we'd get

{{1/2, Sqrt[3]/2},{-1/2, Sqrt[3]/2},{1,0},{-1,0},{1/2,-(Sqrt[3]/2)},{-1/2,-(Sqrt[3]/2)}}

And yeah, I should mention that if there are more than one sub lists with equal y, we would additionally (sub)sort them by descending x (first component in each of the sub lists).

I tried to use SortBy, in different forms, but I don't seem to be able to figure it out by myself. I'd appreciate any help.

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    $\begingroup$ "I tried to use SortBy" What did you try, specifically? $\endgroup$
    – Szabolcs
    Commented Feb 13, 2019 at 13:57
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    $\begingroup$ Likely a duplicate of mathematica.stackexchange.com/q/2729/12 $\endgroup$
    – Szabolcs
    Commented Feb 13, 2019 at 13:59
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    $\begingroup$ Try SortBy[list, N[-Last[#]]&] instead. $\endgroup$
    – Sjoerd Smit
    Commented Feb 13, 2019 at 14:25
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    $\begingroup$ You did not say what you tried originally. N[Last] is not a function, so it's not appropriate here. Use N@*Last or N[Last[#]]&. $\endgroup$
    – Szabolcs
    Commented Feb 13, 2019 at 14:26
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    $\begingroup$ @amator, if you've figured it out from the comments, you can answer your own question. Helps the silent majority of lurkers develop their knowledge too. $\endgroup$
    – MikeY
    Commented Feb 13, 2019 at 14:51

3 Answers 3

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As suggested in the comments, the following works as desired:

Reverse[SortBy[list, N[Last[#]]&]].

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    $\begingroup$ If you use SortBy, you might as well put a minus sign in front of the sorting function so you don't have to reverse the list after sorting it. $\endgroup$
    – Sjoerd Smit
    Commented Feb 13, 2019 at 16:13
  • $\begingroup$ Nice, wasn't aware of that, thank you @SjoerdSmit ! $\endgroup$
    – amator2357
    Commented Feb 13, 2019 at 16:14
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list = 
  {{1/2, -(Sqrt[3]/2)}, {1, 0}, {1/2, Sqrt[3]/2}, 
  {-(1/2), Sqrt[3]/2}, {-1, 0}, {-(1/2), -(Sqrt[3]/2)}};

Using ReverseSortBy (new in 12.0)

ReverseSortBy[N @* Last] @ list

{{1/2, Sqrt[3]/2}, {-1/2, Sqrt[3]/2}, {1, 0}, {-1, 0}, {1/2, -1/2 Sqrt[3]}, {-1/2, -1/2 Sqrt[3]}}

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l = 
  {{1/2, -(Sqrt[3]/2)}, {1, 0}, {1/2, Sqrt[3]/2}, 
  {-(1/2), Sqrt[3]/2}, {-1, 0}, {-(1/2), -(Sqrt[3]/2)}};

The ordering using OrderingBy:

o = Flatten[RotateRight[Sort /@ Partition[Reverse@OrderingBy[#, Abs], 2]]] &@l;

Apply the ordering:

l[[o]]

{{-(1/2), Sqrt[3]/2}, {-(1/2), -(Sqrt[3]/2)}, {1, 0}, {-1, 0}, {1/2, -(Sqrt[3]/2)}, {1/2, Sqrt[3]/2}}

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