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Another way is with Tuples. A = {1, 2, 3}; B = {a, b, c}; MinkowskiSum[lis__] := Total /@ Tuples[{lis}] MinkowskiSum[A, B] {a+1, b+1, c+1, a+2, b+2, c+2, a+3, b+3, c+3} A1 = {1, 2}; A2 = {a, b}; A3 = {x, y}; MinkowskiSum[A1, A2, A3] {a+x+1, a+y+1, b+x+1, b+y+1, a+x+2, a+y+2, b+x+2, b+y+2}


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For example x = {{1, 0}, {0, 1}, {0, -1}}; y = {{0, 0}, {1, 1}, {1, -1}}; Union @@ Outer[Plus, x, y, 1] {{0, -1}, {0, 1}, {1, -2}, {1, 0}, {1, 2}, {2, -1}, {2, 1}} You can use CirclePlus (⊕) (entered as \[CirclePlus] or Escc+Esc) to define your Minkowski sum: CirclePlus[x__] := Flatten[Union @@ Outer[Plus, x, 1], Length@{x} - 2] x⊕y {{0, -1}, ...



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