Say if I have two lists of vectors of the same length, for example:

u = {{1,0,0},{0,1,0},{0,0,1}}
v = {{1,0,1},{1,1,0},{1,1,1}}

I want to add (modulo 2) u1 + v and then u2 + v and then u3 + v, so I want to obtain:

u1 + v = {{0,0,1},{1,0,0},{1,1,0}}
u2 + v = {{1,1,1},{1,0,0},{1,1,0}}
u3 + v = {{1,0,0},{1,1,1},{1,1,0}}

The only way I can do this so far is:


However, this involves manual/clunky computation. Is it possible to iterate through the positions of u as well as iterating through the position of v, so that I would be able to calculate this in one go without writing out all the equations?

This is a frequent problem I encounter where I want to define two pure functions to be mapped over different lists in the same line of code. Is it possible?

  • 7
    $\begingroup$ Does Outer[Mod[Plus[##], 2] &, u, v, 1] do what you want? $\endgroup$ Sep 20, 2023 at 14:46
  • 3
    $\begingroup$ For your current attempt: You can map over the elements of v themselves, without having to take the roundtrip over indices: Mod[u[[1]]+#,2]&/@v $\endgroup$
    – Lukas Lang
    Sep 20, 2023 at 14:55
  • $\begingroup$ @LukasLang That is certainly a better way of doing it! I wonder then if there is a way to iterate through the index of u simultaneously? $\endgroup$
    – am567
    Sep 20, 2023 at 15:08
  • $\begingroup$ @J.M.'slackofA.I. This is exactly what I was looking to do, thank you! I am still interested as to whether it can be done in the format I'd tried, although my suspicion is that I was just going about it the wrong way. $\endgroup$
    – am567
    Sep 20, 2023 at 15:10
  • 2
    $\begingroup$ Also: Table[Mod[Plus[u[[i]], v[[j]]], 2], {i, #1}, {j, #2}] & @@ Rest@Dimensions@{u, v} $\endgroup$ Sep 20, 2023 at 19:18


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