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?

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kglr · Accepted Answer · 2017-02-06 19:15:22Z

26

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}

answered Oct 22, 2012 at 10:30

kglr

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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
2

$\begingroup$ 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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b.gates.you.know.what · Accepted Answer · 2012-10-22 10:27:34Z

11

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, 2012 at 10:27

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$\begingroup$ Good one. And maybe sum[[0]] = List; sum $\endgroup$
– user1066
Oct 22, 2012 at 19:32
1

$\begingroup$ @TomD that is the one I like to use :) $\endgroup$
– Mike Honeychurch
Oct 22, 2012 at 22:24

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J. M.'s eventual burnout · Accepted Answer · 2012-10-22 11:25:04Z

6

Still another route:

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

answered Oct 22, 2012 at 11:25

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3 Answers 3