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Please help in executing the following problem in Mathematica:

I have the following set:$A=\{1, 2,3,4,5,6,7,8,9,10\}$ (my actual data has more than 10 points). I need to do the following three steps:

(A) Form all possible pairs of two digits in the above set, like $(1,2), (4,6)$ etc. Remember $(1,2)$ and $(2,1)$ are to be treated as different pairs. Since my actual data is big, I want Mathematica to find all these possible pairs.

(B) Then I have to put these pairs in the following expression: $\eta(x_1,x_2)= x_1+5x_2+10$ and compute the value of $\eta(x_1,x_2)$, for the pair $(x_1,x_2)$.

(C) Similarly, I have to this for all pairs and arrange the values of $\eta(x_1,x_2)$ is decreasing order.

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  • $\begingroup$ Look at Tuples eg Tuples[Range@10, 2] and eta@@@Tuples[Range@10, 2] $\endgroup$ – OkkesDulgerci Jul 10 '18 at 17:20
  • $\begingroup$ What is the size of data? $\endgroup$ – OkkesDulgerci Jul 10 '18 at 17:21
  • $\begingroup$ My actual data contains around 100 points. $\endgroup$ – H. Kenan Jul 10 '18 at 17:28
  • $\begingroup$ If you don't want (1,1) then use Permutations[Range@10, {2}] $\endgroup$ – OkkesDulgerci Jul 10 '18 at 17:28
  • $\begingroup$ Thank you, friends. I would appreciate if you put a slightly detailed answer. $\endgroup$ – H. Kenan Jul 10 '18 at 17:30
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f[x1_, x2_] := x1 + 5 x2 + 10
SeedRandom@2;
data = RandomReal[10, 100];
pair = Permutations[data, {2}];
values=Sort[f @@@ pair];
ListPlot[values]
| improve this answer | |
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  • $\begingroup$ Never knew mathematica had permutation function. Neat answer! $\endgroup$ – Giovanni Baez Jul 10 '18 at 18:42
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    $\begingroup$ Thanks. It says "Introduced in 1988 (1.0) | Updated in 2007 (6.0)" $\endgroup$ – OkkesDulgerci Jul 10 '18 at 22:42

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