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I want to turn a sum like this

sum =a-b+c+d

Into a List like this:

sumToList[sum]={a,-b,c,d}

How can I achieve this?

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    $\begingroup$ I am a professor of "vectorial analysis" in Mexico. I try to teach the subjects with the use of "Mathematica". I solved a problem seeing this page and also this: mathematica.stackexchange.com/questions/100758/… ... in which I was not allowed to comment. This was what I did to find the "scalar potential function". i.stack.imgur.com/ugIlP.png $\endgroup$ Feb 6, 2017 at 17:43
  • $\begingroup$ @David I converted your answer to a comment, as it seems more appropriate as such. I know that new users do not have the "privilege" to comment everywhere (a "spam" control measure I believe) but if you continue to participate you will find that you soon do. $\endgroup$
    – Mr.Wizard
    Feb 6, 2017 at 19:12

3 Answers 3

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List @@ sum

{a, -b, c, d}

From the docs on Apply (@@):

f@@expr replaces the head of expr by f.

So List@@sum replaces Head[sum] (that is, Plus) with List.

You can also get the same result by changing 0th Part of sum (which is its Head) to List:

sum[[0]] = List; sum

{a, -b, c, d}

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    $\begingroup$ There is a slight hiccup that you can encounter using this. If you're not explicitly doing a sum, you will list over whatever the head of the function is. e.g. List @@ 2*3 will result in {2,3} $\endgroup$
    – Alex DB
    Feb 10, 2017 at 17:10
  • $\begingroup$ @AlexDB, you are right; List@@expr does change the head of expr, whatever it is, to List. $\endgroup$
    – kglr
    Feb 10, 2017 at 17:16
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    $\begingroup$ So what's the most general way to make a list, so that we include both distinct cases where there is one and multiple terms? $\endgroup$
    – hal
    Aug 7, 2020 at 18:30
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Try :

a - b + c + d /. Plus -> List

You can have a look at a - b + c + d //FullForm to see why this works.

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    $\begingroup$ Good one. And maybe sum[[0]] = List; sum $\endgroup$
    – user1066
    Oct 22, 2012 at 19:32
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    $\begingroup$ @TomD that is the one I like to use :) $\endgroup$ Oct 22, 2012 at 22:24
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Still another route:

Last[CoefficientArrays[#]] Variables[#] &[a - b + c + d]
   {a, -b, c, d}
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