can we Map other than First and Last, but another specific sub-element?

Questions
,
1

If we look at this code, I can Map First and Last, but I can’t seem to find a way to Map to the middle term, or any other term. I have tried Extract and Select in differing guises but can’t seem to find a way to do it.

b = Subsets[Range[2, 10], {3}]; 
c = First /@ b; 
d = Last /@ b;

Print[b[[1 ;; 10]],"  ",c[[1 ;; 10]],"   ",d[[1 ;; 10]]]; 

{2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {2, 3, 7}, {2, 3, 8}, 
{2, 3, 9}, {2, 3, 10}, {2, 4, 5}, {2, 4, 6}, {2, 4, 7}
{2, 2, 2, 2, 2, 2, 2, 2, 2, 2}
{4, 5, 6, 7, 8, 9, 10, 5, 6, 7}

I would like to extract the middle terms too and extend it to extract any term.

Paul.

2

First and Last are special cases of Part, so one could map a function like Part[#, k]&

3

You can also use All instead of Map.

b = Subsets[Range[2, 10], {3}];

In[1]:= b[[All, 1]]
Out[1]= {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 
5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8}

In[2]:= b[[All, 2]]
Out[2]= {3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 
6, 6, 7, 7, 7, 8, 8, 9, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 
7, 7, 7, 8, 8, 9, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 6, 6, 
6, 6, 7, 7, 7, 8, 8, 9, 7, 7, 7, 8, 8, 9, 8, 8, 9, 9}

In[3]:= b[[All, 3]]
Out[3]= {4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 7, 
8, 9, 10, 8, 9, 10, 9, 10, 10, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 7, 
8, 9, 10, 8, 9, 10, 9, 10, 10, 6, 7, 8, 9, 10, 7, 8, 9, 10, 8, 9, 10, 
9, 10, 10, 7, 8, 9, 10, 8, 9, 10, 9, 10, 10, 8, 9, 10, 9, 10, 10, 9, 
10, 10, 10}

Another (less efficient) way is to use Transpose.

In[4]:= t = Transpose[b];

In[5]:= t[[1]]
Out[5]= {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 
5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8}

In[6]:= t[[2]]
Out[6]= {3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 
6, 6, 7, 7, 7, 8, 8, 9, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 
7, 7, 7, 8, 8, 9, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 6, 6, 
6, 6, 7, 7, 7, 8, 8, 9, 7, 7, 7, 8, 8, 9, 8, 8, 9, 9}

In[7]:= t[[3]]
Out[7]= {4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 7, 
8, 9, 10, 8, 9, 10, 9, 10, 10, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 7, 
8, 9, 10, 8, 9, 10, 9, 10, 10, 6, 7, 8, 9, 10, 7, 8, 9, 10, 8, 9, 10, 
9, 10, 10, 7, 8, 9, 10, 8, 9, 10, 9, 10, 10, 8, 9, 10, 9, 10, 10, 9, 
10, 10, 10}
4

Once you get familiar with the following functions, you are the guru of list manipulation:

Specify range:

  1. Span: Span—Wolfram Documentation
  2. Take: Take: Obtain sublists, including rows, columns, submatrices and subarrays—Wolfram Documentation

Specify a condition:
1.Cases: Cases—Wolfram Documentation
2. Select: Select: Pick out elements that satisfy a criterion—Wolfram Documentation
3. Pick: Pick: Select elements of list based on mask—Wolfram Documentation

5

Thank you everyone for your quick replies, I had indeed used the method you sugged Chip on many occasion, It seems I had a momentary lapse of reason. I was trying to mix the b[[All, 2]] in with the select and mapping method which obviously didnt work, there is also another less efficient way of doing it too, RotateRight also maps across lists so I could have used First /@ b then RotateRight /@ b and repeated the process. Shenghui, I will take a look at those references for a refresher thank you.

Paul.