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I have a list $(d_1, d_2, .. d_k)$ and I want to create all sums that I get for adding only two elements for my list $(d_1+d_2, d_1+d_3,...d_{k-1}+d_k)$. The RotateLeft function gives me only some of my sums and I need all of them.

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6 Answers 6

l = {a, b, c, d};
Plus @@@ Subsets[l, {2}]
(*
  {a + b, a + c, a + d, b + c, b + d, c + d}
*)

edit

Some timings

Mathematica graphics

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Come downvote @Verde

l = {a, b, c, d}

l~Subsets~{2}~Total~{2}
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(deleted comment) –  belisarius Sep 4 '12 at 12:41
1  
This one is six times faster than the Plus @@@ solution, twice as fast as the Outer solution, and three times faster than the Table solution. –  whuber Sep 4 '12 at 12:50
    
And ten times slower than Total /@ Subsets[l, {2}] –  belisarius Sep 4 '12 at 13:39
2  
@whuber l = RandomReal[1, 10^3]; {(Timing@(l~Subsets~{2}~Total~{2}))[[1]], (Timing[ Plus @@@ Subsets[l, {2}]])[[1]]} -> {2.89, 0.547} ... –  belisarius Sep 4 '12 at 13:43
    
@Verde You're right: that's astounding, given how similar the Total /@ and ~Total~2 constructs are!. –  whuber Sep 4 '12 at 14:34

Just to show that there's more than one way to do things in Mathematica:

test = {a, b, c, d, e};
Total /@ (Join @@ MapIndexed[Drop[#1, First[#2]] &,
          Outer[List, test, test]])
   {a + b, a + c, a + d, a + e, b + c, b + d, b + e, c + d, c + e, d + e}

Of course, Oleksandr's and Verde's suggestions are the more compact way of going about it.

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Something like :

data = {a, b, c, d}; 

Flatten[Table[data[[i]] + data[[j]], {i, 1, Length[data] - 1}, {j, i + 1, Length[data]}],1]

(* {a + b, a + c, a + d, b + c, b + d, c + d} *)

Alternatively (plus suggestion from @Oleksandr R.) :

Total /@ Subsets[data, {2}]

And just because RotateLeft was mentioned :

Union[Flatten[Total /@ Subsets[NestList[RotateLeft[#] &, data, Length[data] - 1], {2}], 1]]
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The third one seems a memory hog :) –  belisarius Sep 4 '12 at 14:52
l = {a, b, c, d};

Let's make use of pattern matching ( even though there are faster methods especially for list manipulations) :

ReplaceList[ l, {___, x_, ___, y_, ___} -> x + y]
{a + b, a + c, a + d, b + c, b + d, c + d}   

Typically, efficiency of pattern matching solutions is worse than that of functional approach, nevertheless we point out a remarkable feature of the result of ReplaceList: it is identical with other (functional) methods, e.g. (taking a longer list) we have:

ls = {a, b, c, d, e, f, g, h, i, j, k, l, , m, n, o, p, q, r, s};

ReplaceList[ls, {___, x_, ___, y_, ___} -> x + y] == 
Plus @@@ Subsets[ls, {2}] == ls~Subsets~{2}~Total~{2} 
True
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Since somebody mentioned timings...

Module[{x = Outer[Plus, l, l]},
 Flatten[x[[#, # + 1 ;;]] & /@ Range[Length@x - 1]]]
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