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Mathematica

The Mathematica Book

A Practical Introduction to Mathematica

Lists

1.8.14 Advanced Topic: Rearranging Nested Lists

You will encounter nested lists if you use matrices or generate multidimensional arrays and tables. Rearranging nested lists can be a complicated affair, and you will often have to experiment to get the right combination of commands.

Functions for rearranging nested lists.

Here is a array.

In[1]:= t = {{a, b}, {c, d}, {e, f}}

Out[1]=

You can rearrange it to get a array.

In[2]:= Transpose[t]

Out[2]=

This "flattens out" sublists. You can think of it as effectively just removing the inner sets of braces.

In[3]:= Flatten[t]

Out[3]=

Here is a array.

In[4]:= t = Table[i^2 +j^2 +k^2, {i, 2}, {j, 2}, {k, 2}]

Out[4]=

This flattens out all the levels.

In[5]:= Flatten[t]

Out[5]=

This flattens only the first level of sublists.

In[6]:= Flatten[t, 1]

Out[6]=

This flattens out only the sublist that appears at position 2.

In[7]:= FlattenAt[{{a, b}, {c, d}}, 2]

Out[7]=

There are many other operations you can perform on nested lists. We will discuss some more of them when we look at Map, Apply, Scan and Level in Part 2.