Split expression into list of terms

Question

I'm looking for a nice way to split an expression into a list of the terms (i.e. the addends).

The desired behavior in:

terms[a^2 + a^-2 + c]  
(* Out: {a^2, a^-2, c} *)
terms[a*b*c]
(* Out: {a*b*c} *)

I've tried a few solutions. MonomialList doesn't work if the expression is not a polynomial. I've also tried

Level[a + b + c, 1]
(* Out: {a, b, c} *)

But the problem is it breaks down for monomials.

Level[a, 1]
(* Out: {} *)
Level[a*b*c, 1]
(* Out: {a, b, c} *)

The desired output would be {a} and {a b c} respectively.

Thank you in advance!

Answer 1

ClearAll[terms]
SetAttributes[terms, HoldAll]
terms[Plus[a__]] := {a}
terms[a_?AtomQ] := {a}
terms[a_] := a

Examples:

ClearAll[a, b, c, d]

terms[a]

{a}

terms[a + b + c]

{a, b, c}

terms[a b c]

a b c

terms[a^2 + a^-2 + c]

{a^2, 1/a^2, c}

terms[a b c + 3 Sin[c + d] + Log@d]

{a b c, 3 Sin[c + d], Log[d]}

Answer 2

For the examples you mentioned, the following simple replacement works:

a^2 + a^-2 + c /. Plus -> List

(* Out: {1/a^2, a^2, c} *)

Note that the ordering is not retained, but then you probably shouldn't depend on the order of monomials anyway because MMA might rewrite your expression on its own to conform to its "canonical" format (e.g. evaluating b - a returns -a + b).

Similarly,

a*b*c /. Plus -> List     (* Out: a*b*c *)
a /. Plus -> List         (* Out: a     *)

Answer 3

No sure whether I got your point, but you can do something like (o.k. broth-force attack ;-) ):

    makeList[term_] := 
 ToExpression /@ StringSplit[ToString[term, InputForm], "+"
   ]

then

temp = a^2 + a^-2 + c

and

makeList@temp

yields:

{1/a^2, a^2, c}