Lists

• You can use Count[list, x] to count the number of times x appears in list.

• You can use Apply[Plus, list] to add together all the elements of a list.

• You can determine the size of a list by using the functions Length and Dimensions. For a linear list, the command Length gives the number of elements in the list.

  In[1]:= Length[{l, i, s, t}]
  Out[1]= 4

  For a matrix, the function Length gives the number of inner lists.

  In[2]:= Length[{{n, e, s, t}, {l, i, s, t}}]
  Out[2]= 2

  The function Dimensions tells more about the inner lists. This is a 2 x 4 matrix.

  In[3]:= Dimensions[{{n, e, s, t},
                            {l, i, s, t}}]
  Out[3]= {2, 4}

  There are two inner lists, and each inner list has four elements.

• Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful and convenient constructs for doing this. Try these examples.

  Table[Nest[(Sqrt[1 + #])&, x, n],
              {n, 1, 10}] //TraditionalForm

  Table[Nest[(1/(1 + #))&, x, n], {n, 1, 10}]
              //TraditionalForm

  NestList[1/2(# + 3/#)&, 1, 10] //TableForm

  You can read more about Nest and NestList in the Help Browser.

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