Question

When I type the following

lis = {1, 2};
pos = Position[lis, 1];
result = Extract[lis, pos]

the result is always a list.

{1}

another example

lis = {{1}, {2}};
pos = Position[lis, {1}];
result = Extract[lis, pos]

{{1}}

Mathematica always adds an extra {} in the result. What would be the best way to remove this extra {}, other than applying Flatten[result,1] each time? And is there a case where removing these extra {} can cause a problem?

Answer 1

If I understood your question correctly, you are asking why

lis = {{1}, {2}};
pos = Position[lis, {1}];
result = Extract[lis, pos]

returns

{{1}}

rather than

{1}

The answer is, I think, simple: Position[lis,{1}] gives the position at which {1}, not 1 appears in lis; when you then go and look at that position using Extract, you do indeed get {1} which is then wrapped in a list (which is exactly what happened in the first case, when you looked for 1 and obtained {1} as a result; just replace 1 by {1}, because that is now what you are asking for.

To see this more clearly, try

lis = {f[1], f[2]};
pos = Position[lis, f[1]];
result = Extract[lis, pos]

which gives

{f[1]}

The point here is that List in {1} (which is the same as List[1] if you check look at the FullForm) before was just a head, like f here. Should mathematica have remove f here? If not, then why should it have removed the innermost List earlier?

And finally, if you really want to remove the inner {} in your second example, try

lis = {{1}, {2, {1}}};
pos = Position[lis, {1}];
result = Extract[lis, pos, #[[1]] &]

giving

{1, 1}

EDIT: I am becoming puzzled with some of the answers here. If I do

lis = {{1}, {2, {1, 2, {1}}}};
pos = Position[lis, 1];
result = Extract[lis, pos]

then I get

{1, 1, 1}

in result. I only get the extra brackets when I actually obtain the positions of {1} in pos instead of the positions of 1 (and then when I look at those positions, I find {1}). Or am I missing something in your question?