How to take a list and build sets of 2 elements without duplicates?

I am new to Mathematica so the answer to this question is probably easy.

I have a list of 2D-points in the form {{x1, y1}, {x2, y2}, ...} Then I have a function that will take two points and test some condition based on their distance. I want to test all points against each other, without duplicates.

How can you do that?

• Look up DistanceMatrix[]. "Without duplicates" means you'll only need the strict upper triangle of that matrix. Jun 25, 2016 at 17:28
• What about yourCondition/@yourDistanceFunction@@@Permutations[list]? Jun 25, 2016 at 17:31
• Following @J.M. 's solution, UpperTriangularize[] would be appropriate to use with DistanceMatrix[]. Jun 25, 2016 at 17:34
• EuclideanDistance @@@ Subsets[yourList, {2}]
– yode
Jun 25, 2016 at 17:34
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Based on comment from yode

Let us suppose a list:

list = {{1, 1}, {2, 1}, {7, 8}, {8, 9}}


$\left( \begin{array}{cc} 1 & 1 \\ 2 & 1 \\ 7 & 8 \\ 8 & 9 \\ \end{array} \right)$

With this function you can calculate the distances of each point without repetitions:

EuclideanDistance @@@ Subsets[list, {2}]


$\left\{1,\sqrt{85},\sqrt{113},\sqrt{74},10,\sqrt{2}\right\}$

Here below only a presentation of the steps

EuclideanDistance[list[[2]], list[[1]]]


$1$

EuclideanDistance[list[[3]], list[[1]]]


$\sqrt{85}$

EuclideanDistance[list[[4]], list[[1]]]


$\sqrt{113}$

EuclideanDistance[list[[2]], list[[3]]]


$\sqrt{74}$

EuclideanDistance[list[[2]], list[[4]]]


$10$

EuclideanDistance[list[[3]], list[[4]]]


$\sqrt{2}$