lists, arrays, and sequences

A sequence is created by separating expressions by commas (see ,). The class of all sequences is Sequence.

     i1 = t = (3,4,5)
     
     o1 = 3,4,5
     
     o1 : Sequence

     i2 = # t
     
     o2 = 3

Sequences of length zero and one cannot be created with commas, so there are special constructions. for them. Use seq to create a sequence of length one, and () to create a sequence of length zero.

     i3 = u = ()
     
     o3 = 
     
     o3 : Sequence

     i4 = # u
     
     o4 = 0

     i5 = v = seq 45
     
     o5 = seq 45
     
     o5 : Sequence

     i6 = # v
     
     o6 = 1

A list is created by surrounding a sequence with braces. Use {} to create a list of length zero. The class of all lists is List.

     i7 = w = {3,4,5}
     
     o7 = {3,4,5}
     
     o7 : List

     i8 = # w
     
     o8 = 3

     i9 = # {}
     
     o9 = 0

     i10 = x = {(3,4,5)}
     
     o10 = {(3,4,5)}
     
     o10 : List

     i11 = # x
     
     o11 = 1

     i12 = y = {(3,4,5),7}
     
     o12 = {(3,4,5),7}
     
     o12 : List

     i13 = # y
     
     o13 = 2

Lists can be used as vectors.

     i14 = 2*{3,4,5} - {0,0,1}
     
     o14 = {6,8,9}
     
     o14 : List

A table is a list of lists of the same length. The inner lists are regarded as rows when the table is displayed two-dimensionally.

     i15 = z = {{a,1},{b,2},{c,3}}
     
     o15 = {{a,1},{b,2},{c,3}}
     
     o15 : List

     i16 = new MatrixExpression from z
     
     o16 = |  a   1 |
           |        |
           |  b   2 |
           |        |
           |  c   3 |
     
     o16 : MatrixExpression

An array is created by surrounding a sequence with brackets. Use [] to create a list of length zero. An array is a type of basic list, which means that the class Array of all arrays has BasicList as its parent.

     i17 = f = [3,4,5]
     
     o17 = [3,4,5]
     
     o17 : Array

     i18 = class f
     
     o18 = Array
     
     o18 : Type
     
     Array -- the class of all arrays.

     i19 = parent class f
     
     o19 = BasicList
     
     o19 : Type
     
     BasicList -- the class of all things represented internally as a
          list.  A list is a sequence of expressions indexed by integers
          0, 1, ..., N-1, where N is the length of the sequence.

Omitting an element of a sequence, list, or array, causes the non-printing symbol null to be inserted in its place.

     i20 = g = (3,4,,5)
     
     o20 = 3,4,null,5
     
     o20 : Sequence

     i21 = g#2

     i22 = (3,4,,5) == (3,4,null,5)
     
     o22 = true

One calls functions with the notation f(x,y,z); here you may think of x, y, and z as the three arguments to f, or you may regard the sequence (x,y,z) as the single argument of f. For the former, one takes a function f of the form