Transform a Sum into a List

Question

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?

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: http://mathematica.stackexchange.com/questions/100758/finding-scalar-potential-function/100763 ... in which I was not allowed to comment. This was what I did to find the "scalar potential function". https://i.stack.imgur.com/ugIlP.png — David Gardea, Feb 06 '17 at 17:43
@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. — Mr.Wizard, Feb 06 '17 at 19:12

kglr · Accepted Answer · 2017-02-06T19:15:22.867

27

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}

edited Feb 06 '17 at 19:15

answered Oct 22 '12 at 10:30

kglr

2

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} – Alex DB Feb 10 '17 at 17:10
@AlexDB, you are right; List@@expr does change the head of expr, whatever it is, to List. – kglr Feb 10 '17 at 17:16
2

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? – hal Aug 07 '20 at 18:30

score 12 · Answer 2 · answered Oct 22 '12 at 10:27

12

Try :

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

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

answered Oct 22 '12 at 10:27

3

Good one. And maybe sum[[0]] = List; sum – user1066 Oct 22 '12 at 19:32
1

@TomD that is the one I like to use :) – Mike Honeychurch Oct 22 '12 at 22:24

score 7 · Answer 3 · answered Oct 22 '12 at 11:25

7

Still another route:

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

answered Oct 22 '12 at 11:25

3 Answers3