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Let's say I have two different lists for which I want to compute the total

list1 = {1, Null, 2, Null}
list2 = {Null, Null, Null, Null}

For list1, I want the total to be 3, i.e. ignore the Null elements and add the numeric ones. For list2, I want the total to be a Null since all elements are Null. I achieve want I want for list1 with

In[255]:= Total[DeleteCases[list1, Null]]

Out[255]= 3

However, the same command applied to list2 returns 0

In[254]:= Total[DeleteCases[list2, Null]]

Out[254]= 0

On the other hand, using only Total does not work with list1

In[256]:= Total[list1]

Out[256]= 3 + 2 Null

but works for list 2

In[257]:= Total[list2]

Out[257]= 4 Null

I'd like a command that works for both lists because the list might look like list1 or list2 depending on a parametrization.

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3 Answers 3

Reset to default
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Total@list1 /. {Plus[x_, Times[_, Null]] -> x}  (* 3 *)
Total@list2 /. {Plus[x_, Times[_, Null]] -> x}  (* 4 Null *)
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  • $\begingroup$ Thanks! nice workaround!! Though I wish Mathematica had an option to set Total of [] to Null $\endgroup$
    – mariodrumblue
    Sep 3, 2020 at 0:08
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ClearAll[totalWnulls]
totalWnulls[x_List] := If[MatchQ[{Null ..}] @ x, Total[x], Total[x] /. Null -> 0]

totalWnulls @ list1

3

totalWnulls @ list2

4 Null

Alternatively, define a function with two argument patterns:

ClearAll[totalWnulls2]
totalWnulls2[x : {Null ..}] := Total[x]
totalWnulls2[x_List] := Total[x] /. Null -> 0

totalWnulls2 @ list1

3

totalWnulls2 @ list2

4 Null
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  • $\begingroup$ Thanks. This works, though being a beginner user at Mathematica I find this solution harder to comprehend that the one posted by Alan $\endgroup$
    – mariodrumblue
    Sep 3, 2020 at 0:10
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One approach (which is not completely right as pointed out in the comments ) is

f[list_] := (Plus @@ list) /. Null -> 0

Better is:

f[list_] := 
  If[MatchQ[list, {Null ..}], Null, Plus @@ list /. Null -> 0]

Null as a return value does not display on output.

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  • $\begingroup$ sorry but I don't think this works for list2. It still returns a 0 whereas I'd like the function to return Null if all elements are Null $\endgroup$
    – mariodrumblue
    Sep 2, 2020 at 23:59
  • $\begingroup$ Good point. You are right. I updated my answer. $\endgroup$
    – PaulCommentary
    Sep 4, 2020 at 1:15

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