Advanced Topic: Symbolic Computation
Here are the six possible ways of arranging the elements a, b and c in a row.
In[1]:= Permutations[{a, b, c}]
Out[1]= 
Flatten "unravels" lists.
In[2]:= Flatten[ % ]
Out[2]= 
This gives the positions at which b appears in the list.
In[3]:= Position[ %, b ]
Out[3]= 
Here are cumulative products of the positions: 
, 
, 
, 
.
In[4]:= FoldList[Times, {1}, %]
Out[4]= 
This produces a list of successively nested cosine functions.
In[5]:= NestList[ Cos, x, 3 ]
Out[5]= 
Here are plots of the nested cosine functions. The curves meet at the point where 
.
In[6]:= Plot[ Evaluate[%], {x, 0, 1} ]
Out[6]= 
The Map operator allows you to "wrap" a function around each element in a list.
In[7]:= Map[f, {a, b, c, d}]
Out[7]= 
Here is a matrix of a special form.
In[8]:= m = IdentityMatrix[6]; a m + b Map[Reverse, m] // MatrixForm
Out[8]//MatrixForm= 
This is its determinant.
In[9]:= Factor[Det[%]]
Out[9]= 
