4
$\begingroup$

I get intrigued about Gather behavior on this post. I thought that Gather was invariant under list order?

Here is the result I spect:

l1={{1, 1}, {0, 0}, {2, 2}, {5, 5}, {4, 4}, {6, 6}}
Gather[l1,ManhattanDistance[#1, #2] <= 2 &]

{{{1,1},{0,0},{2,2}},{{5,5},{4,4},{6,6}}}

When the list order is changed, I get this:

l2={{0, 0}, {1, 1}, {2, 2}, {4, 4}, {5, 5}, {6, 6}}
Gather[l2,ManhattanDistance[#1,#2]<= 2&]

{{{0,0},{1,1}},{{2,2}},{{4,4},{5,5}},{{6,6}}}

Someone know why?

Improve this question
$\endgroup$
8
  • $\begingroup$ Documentation is obscure about this. $\endgroup$
    – Murta
    Sep 21, 2013 at 0:09
  • $\begingroup$ Counter question: how can it determine the correct order? E.g. {4,5}>{5,4} or {4,5}<{5,4}? $\endgroup$
    – ybeltukov
    Sep 21, 2013 at 0:09
  • $\begingroup$ Well.. I got the point. I don't know if I should delete this question. $\endgroup$
    – Murta
    Sep 21, 2013 at 0:15
  • $\begingroup$ I don;t know where's @ssch 's comment but I think he's right. Relation has to be transitive. If it's not the result may vary with order. For example, for the case of l2 the result {{{0,0}}, {{1,1}, {2,2}}, {{4,4}}, {{5,5}, {6,6}}} is as good as the one you obtained. $\endgroup$
    – Kuba ♦
    Sep 21, 2013 at 0:15
  • 4
    $\begingroup$ @Murta No, it starts again as soon as it meets False. Try Reap@Gather[l2, (Sow[{#, #2}]; ManhattanDistance[#1, #2] <= 2) &] $\endgroup$
    – Kuba ♦
    Sep 21, 2013 at 0:21

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.