How to pair corresponding elements in a list?

Questions
1

It’s tough to explain what I want to do in words, so I’ll explain with examples. What is the easiest way to create a function that does the following:

in[1]: function[{{a1, b1},{a2, b2}}]
out[1]: {{a1, a2}, {b1, b2}}

in[2]: function[{a1, b1, c1, d1}, {a2, b2, c2, d2}]
out[2]: {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}}

in[3]: function[{{a1, b1},{a2,b2},{a3,b3}}]
out[3]: {{a1, a2, a3}, {b1, b2, b3}}

Essentially I want to group the corrisponding elements of the seperate sublists, to create a new set of sublists.

Any help is greatly appreciated.

2

I think you are looking for MapThread in this case:

http://reference.wolfram.com/mathematica/ref/MapThread.html

3

MapThread is a very good choice for generalized operations, when you not only pairing but also applying a function to pairs. In your simpler case you can also use Thread and Transpose (see blow). Relations between MapThread, Thread, and Transpose are discussed here.

In[1]:= Transpose[{{a1, b1}, {a2, b2}, {a3, b3}}]
Out[1]= {{a1, a2, a3}, {b1, b2, b3}}

In[2]:= Thread[{{a1, b1}, {a2, b2}, {a3, b3}}]
Out[2]= {{a1, a2, a3}, {b1, b2, b3}}

In[3]:= Transpose[{{a1, b1, c1, d1}, {a2, b2, c2, d2}}]
Out[3]= {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}}

In[4]:= Thread[{{a1, b1, c1, d1}, {a2, b2, c2, d2}}]
Out[4]= {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}}

In[5]:= MapThread[List, {{a, b, c}, {x, y, z}}]
Out[5]= {{a, x}, {b, y}, {c, z}}
4

Transpose does exactly what you want:

In[14]:= 
Transpose[{{a1, b1}, {a2, b2}}]
Transpose[{{a1, b1, c1, d1}, {a2, b2, c2, d2}}]
Transpose[{{a1, b1}, {a2, b2}, {a3, b3}}]

Out[14]= {{a1, a2}, {b1, b2}}
Out[15]= {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}}
Out[16]= {{a1, a2, a3}, {b1, b2, b3}}